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\chapter{6}{Service Planning}
\label{volume:operations:chapter:service-planning}
% @ guide/06-service_planning/service-planning.src: lines 1-5: code points 1-37

\quotation{Always design a thing by considering it in its next larger context—a chair in a room, a room in a house, a house in an environment, an environment in a city plan.}{Eliel Saarinen, architect, 1873–1950}
% @ guide/06-service_planning/service-planning.src: lines 3-5: code points 1-37

Once the corridor is selected as proposed in the previous chapter, BRT system design starts by characterizing the specific services that should operate inside any planned new BRT infrastructure. The final specification will be the operational schedule, including vehicle requirements.\par
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A basic service plan should be developed before \emphasis{any} infrastructure design is done, and certainly before it is finalized. The BRT services should serve as many trips as possible (from their origin at the household to their destination) at the highest speed with a minimum of transfers. The infrastructure should then be tailored to that service plan in a way that minimizes delay for as many customers as possible.\par
% @ guide/06-service_planning/service-planning.src: lines 11-14: code points 1-109

A common mistake in BRT planning is to design BRT infrastructure without having made even basic decisions about what sort of BRT services should use the infrastructure. While political or financial constraints may make it impossible to build the optimal physical design, infrastructure design should accommodate an optimal service plan to the greatest extent possible. Once key physical design decisions have been made, however, it is generally necessary to further modify the service plan given the limitations of the final physical design, in an iterative process.\par
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The “service planning” part of this process is normally about deciding—under assumptions about infrastructure and on a route-by-route basis—which of the existing public transport services on or near the corridor will be included in the new BRT services as they exist, which to modify, which routes to add, which to leave out, and which if any to cancel.\par
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This chapter provides guidance for making these basic BRT service decisions; the introductory section presents an approach to the iterative process and the reasoning behind it; the second section details how to describe the status quo of the existing public transport system properly, which becomes the basis of clearly defining customers’ service needs. The later sections, after introducing basic service planning concepts, provide specific tools for each decision step required to transform existing public transport services into a planned BRT corridor with BRT services.\par
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The topics discussed in this chapter are:\par
% @ guide/06-service_planning/service-planning.src: lines 38-38: code points 1-41

\begin{itemize}
\item Introduction;% @ guide/06-service_planning/service-planning.src: lines 40-41: code points 1-0
\item Basic Data Collection;% @ guide/06-service_planning/service-planning.src: lines 41-42: code points 1-0
\item Basic Service Planning Concepts;% @ guide/06-service_planning/service-planning.src: lines 42-43: code points 1-0
\item Optimizing Vehicle Size and Fleet Size;% @ guide/06-service_planning/service-planning.src: lines 43-44: code points 1-0
\item Determining Which Routes to Include Inside BRT Infrastructure;% @ guide/06-service_planning/service-planning.src: lines 44-45: code points 1-0
\item Direct Services, Trunk-and-Feeder Services, or Hybrids;% @ guide/06-service_planning/service-planning.src: lines 45-46: code points 1-0
\item Deciding on Stop Elimination and Express Services;% @ guide/06-service_planning/service-planning.src: lines 46-47: code points 1-0
\item Creating New Routes and Combining Old Routes;% @ guide/06-service_planning/service-planning.src: lines 47-48: code points 1-0
\item Pulling Services onto a BRT Trunk Corridor from a Parallel Corridor.% @ guide/06-service_planning/service-planning.src: lines 48-48: code points 1-74
\end{itemize}
% @ guide/06-service_planning/service-planning.src: lines 40-48: code points 1-74

\section{1}{Introduction}
\label{volume:operations:chapter:service-planning:section:introduction}
% @ guide/06-service_planning/61-introduction.src: lines 1-63: code points 1-0

\quotation{Sometimes we stare so long at a door that is closing that we see too late the one that is open.}{Alexander Graham Bell, inventor, 1847–1922}
% @ guide/06-service_planning/61-introduction.src: lines 3-4: code points 1-44

As BRT systems are generally built on busy corridors where there are already many bus or minibus services operating, BRT service planning should start with a detailed understanding of the existing public transport services on the corridor. Sometimes these existing services are already well designed to meet the travel needs of most customers and there may be only minor changes needed to existing bus services to take advantage of the higher speeds along the BRT corridor. At other times the public transport services are poorly matched with the travel needs of customers, and a BRT project creates an opportunity to improve on any preexisting service plan. Modifying these services as part of the BRT project can result in significant benefits to customers.\par
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In order to determine whether existing services are already well designed to serve customer needs, or whether significant improvements could be made, BRT service planning should start with a careful evaluation and understanding of all the bus and minibus services currently using the corridor. The Basic Data Collection section of this chapter outlines how information should be processed and displayed in order to make this clear to both the system planners and the general public.\par
% @ guide/06-service_planning/61-introduction.src: lines 15-19: code points 1-57

In most cases, there are significant efficiencies to be gained by optimizing services as part of a BRT project. The following would be indications that the existing services are poorly designed:\par
% @ guide/06-service_planning/61-introduction.src: lines 21-23: code points 1-0

\begin{itemize}
\item Large numbers of buses running partially empty for all or part of their route;% @ guide/06-service_planning/61-introduction.src: lines 23-24: code points 1-0
\item Significant overcrowding on buses on all or part of a route;% @ guide/06-service_planning/61-introduction.src: lines 24-25: code points 1-0
\item Significant overcrowding at some stations;% @ guide/06-service_planning/61-introduction.src: lines 25-26: code points 1-0
\item Large numbers of customers transferring at locations that are not their final destination;% @ guide/06-service_planning/61-introduction.src: lines 26-27: code points 1-0
\item Large numbers of people walking or taking shared taxis from an area currently underserved by public transport;% @ guide/06-service_planning/61-introduction.src: lines 27-29: code points 1-0
\item Large numbers of buses stopping where few customers get on or off.% @ guide/06-service_planning/61-introduction.src: lines 29-29: code points 1-72
\end{itemize}
% @ guide/06-service_planning/61-introduction.src: lines 23-29: code points 1-72

The construction of specialized BRT infrastructure along a corridor will introduce three changes to existing public transport operations that will affect the optimization of services:\par
% @ guide/06-service_planning/61-introduction.src: lines 31-33: code points 1-0

\begin{itemize}
\item Speeds within the BRT infrastructure along the trunk corridor should increase significantly in comparison to speeds outside the BRT infrastructure and on parallel corridors;% @ guide/06-service_planning/61-introduction.src: lines 33-35: code points 1-0
\item The new BRT trunk corridor may require vehicles to operate most efficiently at the greatest speed;% @ guide/06-service_planning/61-introduction.src: lines 35-35: code points 1-104
\end{itemize}
% @ guide/06-service_planning/61-introduction.src: lines 33-35: code points 1-104

\begin{itemize}
\item Vehicles will need to be able to enter and exit specialized BRT infrastructure, which is often in the central median of the roadway.% @ guide/06-service_planning/61-introduction.src: lines 37-38: code points 1-37
\end{itemize}
% @ guide/06-service_planning/61-introduction.src: lines 37-38: code points 1-37

Chapter 4: Demand Analysis describes the process used to estimate the baseline public transport demand on the system, and how to model the demand of a proposed service plan under a given infrastructure. So we have at our disposal tools to evaluate future situations. However, Chapter 4: Demand Analysis gives no guidance as to how to decide which service scenarios to model. This chapter provides more guidance on how to decide what sort of services should be proposed and modeled.\par
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If a public transport system demand model has already been created (as proposed in Chapter 4: Demand Analysis), it can be extremely useful in performing the necessary route-by-route analysis and testing the benefits of various service planning alternatives. Running alternative service plan scenarios in the demand model is cumbersome, and creating too many scenarios is very confusing for the public and decision makers alike, so this chapter attempts to help craft better service plan scenarios that can later be tested in the model.\par
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The construction of alternative service plan scenarios is generally done incrementally by first making broad assumptions about the best solution. For this chapter, it will be assumed that the selected corridor has enough demand travelling at slow enough existing speeds that BRT infrastructure is justified. As such, it is reasonable to assume that when planning the services, the bus speeds on the BRT corridor would be BRT speeds, either 20 kph for a standard corridor with stations about 450 meters apart, or the speed of an existing service on the same itinerary late at night or “off-off peak.” Further detailing of the infrastructure can thus be left aside while we consider alternative service planning scenarios. Once basic service planning decisions have been made, Chapter 7: Capacity and Speed provides the tools to refine infrastructure decisions in light of these service planning decisions.\par
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\section{2}{Basic Data Collection}
\label{volume:operations:chapter:service-planning:section:basic-data-collection}
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\quotation{It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.}{Sir Arthur Conan Doyle, writer and physician, 1859–1930}
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In order to propose an optimal service plan, its costs and benefits must be known, and understanding customers’ needs is essential for achieving that. The current state of the public transport system may not exactly show all user demands, but it will certainly point in that direction more reliably than alternatives; it is composed of very objective and comprehensive information, which is cheap to collect in comparison with alternatives and overall project costs.\par
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While existing public transport operations are sometimes poorly aligned with public transport customer needs for a variety of reasons, in most cities economic forces tend to push public transport services close to consumer needs. In addition, customers are used to the services as they currently exist—and resist change. Service plans should be developed conservatively, moving away from existing services only when compelling data indicates that a change would improve services.\par
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Ideally, the data collected should be enough to understand all existing services, the demand throughout the day, and the full trip origin and destination for every public transport customer in the corridor influence area, or at least the time and location of where customers entered the existing public transport system and where they exited.\par
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Normally, this does not require having all the data about every trip, but rather having a sample of data large enough to infer the behavior of the whole. Even where all disaggregated trip data is available, as well as a computer program able to process it trip by trip (to date, no current demand modeling software has such capabilities), a systematic aggregation is still necessary so that the results can be analyzed by humans.\par
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The common way of doing this is to provide customer demand information aggregated per hour of the day in a visual format. It is always best to have data for both peak and off-peak periods. For the analysis in this chapter, much of the services and engineering will be designed around the peak hour, so an estimated peak hour demand is needed. If the frequency is very low, it may be necessary to aggregate by peak period, as in morning peak, midday off peak, afternoon peak, and so forth, and then infer the average peak hour demand from the peak period, in order to avoid data distortions. For instance, in the United States, a bus route might have only three trips between seven and eight, and only two between eight and nine, because one of the trips falls at 7:59 and one falls at 9:01, creating a false impression that demand is far more irregular than it is. In general, however, the data needs to be put in a “peak” hour format, as this is used to make key engineering decisions. Business planning decisions must also be informed by the relationship between the peak hour and the off-peak periods, as this relationship can make (or break) the financial sustainability of the project.\par
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For service planning, the following data is needed:\par
% @ guide/06-service_planning/62-basic-data-collection.src: lines 45-46: code points 1-0

\begin{itemize}
\item The itinerary of every route,% @ guide/06-service_planning/62-basic-data-collection.src: lines 46-47: code points 1-0
\item The number of departures per hour;% @ guide/06-service_planning/62-basic-data-collection.src: lines 47-48: code points 1-0
\item The average travel time between stops;% @ guide/06-service_planning/62-basic-data-collection.src: lines 48-49: code points 1-0
\item The number of customers boarding and alighting at each stop;% @ guide/06-service_planning/62-basic-data-collection.src: lines 49-50: code points 1-0
\item The number of customers transferred from each route to every other route.% @ guide/06-service_planning/62-basic-data-collection.src: lines 50-50: code points 1-79
\end{itemize}
% @ guide/06-service_planning/62-basic-data-collection.src: lines 46-50: code points 1-79

Initially, it is only relevant that this data is processed for typical days, but when the project moves forward, service plans for Saturdays and Sundays and seasonal variations (school holidays) will be required for a complete evaluation. Additional trip data, as described below, may already have been collected using the methods described in Chapter 4: Demand Analysis, and repeated here, focusing on the processing needs for the service plan design.\par
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\subsection{1}{Itineraries and Average Travel Time between Stops}
\label{volume:operations:chapter:service-planning:section:basic-data-collection:subSection:itineraries-and-average-travel-time-between-stops}
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For the process of corridor selection, all of the existing public transport routes using the planned BRT corridor should have been mapped into a GIS program (or a GIS interface of a demand modeling tool like TransCAD or Emme).\par
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If this information is not already available, or badly coded, it will be necessary to have surveyors ride each bus with a GPS and record the coordinates of each bus stop and each bus route. This is not expensive or difficult. Even if this data has already been collected by someone else, it may be out of date, so it is a good idea to check the data by randomly sampling the key routes with a GPS to make sure it is accurate. Many software applications (apps) for smartphones can collect this data.\par
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Average speeds from bus stop to bus stop should be surveyed during the peak hour and off-peak period. For a given distance, a graphic such as the one below can be generated to represent the speed over the course of a day. Data needs to be collected over multiple days to generate a reliable average speed.\par
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\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/d90e908abcc7082cea879bc9016ced2d73411314.png}
		\fignote{1}{Travel times by mode for Montgomery County, Maryland, USA, on the bus route MD 355. The red line represents observed actual bus times, the green line represents scheduled bus times, and the blue line represents the travel time of a car moving on the same route as the bus.\label{chapter:service-planning:figure:travel-times-by-mode-for-montgomery-county-maryland-usa-on-the-bus-route-md-355-the-red-line-represents-observed-actual-bus-times-the-green-line-represents-scheduled-bus-times-and-the-blue-line-represents-the-travel-time-of-a-car-moving-on-the-same-route-as-the-bus}}{Arthur Szász.}
	}
\fi

In a growing number of cities, the bus routes have already been input into an open standard format like General Transit Feed Specification (GTFS) that allows people to manipulate the data in multiple applications. Usually this data is used for customer information dissemination (its name was originally Google Transit Feed Specification), but these same data sets can be used for service planning. GTFS data may be good enough to give coordinates for mapping the existing public transport system, or it may have a lot of inaccuracies that need to be cleaned up. The route needs to be mapped in both directions, as buses may not take the same route going in different directions and bus stops have different positions.\par
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\subsection{2}{Number of Customers Boarding and Alighting at Each Stop}
\label{volume:operations:chapter:service-planning:section:basic-data-collection:subSection:number-of-customers-boarding-and-alighting-at-each-stop}
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The number of existing bus or minibus customers that are currently boarding and alighting on all of the bus routes that use the BRT corridor at each station needs to be collected and mapped. This is usually done by a survey team. Typically, along the planned BRT trunk corridor, if the stations are clearly marked and used, the boarding and alighting counts can be conducted at the stations. For the parts of bus routes that extend beyond the trunk corridor, boarding and alighting counts are generally conducted on board. If the buses or minibuses do not stop in consistent locations, the boarding and alighting numbers along a link need to be collated and assigned to a reasonable location or segment approximating most boardings and alightings, or a location where a new BRT station is being considered could also be used. Boardings and alightings are typically known within a segment, but not at an exact location.\par
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Sometimes boarding and alighting numbers can be collected from Automated Passenger Counter (APC) systems if the locale has this technology. APC data can sometimes give very detailed and accurate numbers of boarding and alighting customers per bus route, but frequently they are coded by time of day, and the station location is not fully clear, so a correlation between APC and existing stops needs to be determined.\par
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With this data, a map such as the shown in figure 6.2 should be generated:\par
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\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/d4f2508ad1c72c3c70826120dfb6f7449822e625.jpeg}
		\fignote{2}{This figure shows in black the proposed BRT corridor in Yichang, China, and in green and red the estimated peak-hour boardings and alightings at all the stations on routes that are using the BRT trunk corridor. The number of existing boarding and alighting customers at each existing station will give a good preliminary indication of which stations are more important than others.\label{chapter:service-planning:figure:this-figure-shows-in-black-the-proposed-brt-corridor-in-yichang-china-and-in-green-and-red-the-estimated-peak-hour-boardings-and-alightings-at-all-the-stations-on-routes-that-are-using-the-brt-trunk-corridor-the-number-of-existing-boarding-and-alighting-customers-at-each-existing-station-will-give-a-good-preliminary-indication-of-which-stations-are-more-important-than-others}}{ITDP.}
	}
\fi

This data can already be used to identify some stations that could possibly be eliminated in the new BRT service, or stations that might become express stops. In the United States, there has been a tendency over the years to accommodate citizens’ demands for adding additional stations to the point where there are stations every 200 meters or less. If a stop has very few customers boarding or alighting, extra delay is being imposed on all the customers on board the bus to accommodate only a handful of people. \emphasis{The} \emphasis{BRT Standard} imposes a deduction of 2 points for station stops closer together than 200 meters. In some of the high-demand BRT systems in Asia and Latin America, stations are sometimes 200 meters long. In addition, this data is used to identify locations where off-board fare collection may be the most important.\par
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Further, it is used to identify important transfer nodes. Where large boarding and alighting volumes are observed in locations with perpendicular public transport routes and no other clear destinations, it is likely that many of the customers are transferring. Identifying these transfer points is important to service planning, and additional surveys will need to be conducted at these transfer points as discussed in the next subsection.\par
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\subsection{3}{Number of Customers Transferring between Routes}
\label{volume:operations:chapter:service-planning:section:basic-data-collection:subSection:number-of-customers-transferring-between-routes}
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The boarding and alighting data can be used to either construct and\slash{}or calibrate a public transport trip origin-destination (OD) matrix. This public transport OD matrix reveals where public transport customers want to go, regardless of where the current bus or minibus routes go. It can be developed in a number of ways depending on the sort of data available.\par
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For a single corridor, when there is no other data, modelers typically use the same boarding and alighting counts done above to first create a “stop-to-stop” OD matrix for routes serving the selected BRT trunk corridor. This is generally done by a Fratar distribution model. This mathematical method makes assumptions about where people are getting on and off public transport vehicles based on uniform probability. This data will generally reliably re-create where customers are starting and stopping their journeys along a single public transport route, but it misses where customers may be transferring to other routes.\par
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In order to transform the stop-to-stop OD matrix into an OD matrix for full trips along the pilot BRT corridor, transfer surveys that identify not only the number of people transferring but also their final destinations need to be conducted where large volumes of customers board and alight or at locations that intersect other public transport routes. All major likely transfer points should be surveyed. Many systems, however, have large numbers of transfers distributed across the entire corridor and not necessarily concentrated at particular stops, so it is harder to create a full public transport OD matrix from this methodology alone.\par
% @ guide/06-service_planning/62-basic-data-collection.src: lines 144-150: code points 1-6

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/40b8628cc0d7046f1e78c2ab4680ad41457f8ec2.jpeg}
		\fignote{3}{Location of transfer surveys done for Yichang BRT modeling. Image\label{chapter:service-planning:figure:location-of-transfer-surveys-done-for-yichang-brt-modeling-image}}{ITDP.}
	}
\fi

The transfer survey should interview a statistically significant sample of the boarding and alighting customers at each stop and ask them their trip origin, destination, and the public transport route they used to make the trip. Once this data is collected, the stop-to-stop OD matrix should be modified based on the transfer survey data, to link the appropriate proportion of stop-to-stop trips based on the transfer survey results.\par
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In the developed world, there is usually more data available than can be easily processed. For instance, in the United States, a growing number of cities are creating public transport OD matrices from new ticketing system information. A growing number of public transport ticketing systems can track by ticket ID number where a customer enters the system (where he or she swipes at a payment site). By noting where he or she enters the system next, usually in the evening from his or her destination or at some transfer point, one can create a matrix of trip origins and destinations for virtually all public transport customers. All of this is used to generate a detailed customer “origin and destination matrix.”\par
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After this is done, there is sufficient data in the demand model to test alternative service plan scenarios. If put into a public transport demand model like TransCAD or Emme, more refined alternative service planning options can be developed and tested.\par
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\subsection{4}{Data Processing}
\label{volume:operations:chapter:service-planning:section:basic-data-collection:subSection:data-processing}
% @ guide/06-service_planning/62-basic-data-collection.src: lines 172-238: code points 1-0

For each existing bus or minibus route along the selected trunk corridor, as stated above, data of existing operations needs to be collected for the full length of daily operations. Then, the following information can be generated for assisting the service plan:\par
% @ guide/06-service_planning/62-basic-data-collection.src: lines 174-177: code points 1-0

\begin{itemize}
\item Total route distance;% @ guide/06-service_planning/62-basic-data-collection.src: lines 177-178: code points 1-0
\item Route travel time: total, disaggregated by section and hour of day per section;% @ guide/06-service_planning/62-basic-data-collection.src: lines 178-179: code points 1-0
\item Stop-by-stop boarding and alighting customers;% @ guide/06-service_planning/62-basic-data-collection.src: lines 179-180: code points 1-0
\item Vehicle loads at each link (between each station);% @ guide/06-service_planning/62-basic-data-collection.src: lines 180-181: code points 1-0
\item Overall public transport vehicle and occupancy per section;% @ guide/06-service_planning/62-basic-data-collection.src: lines 181-182: code points 1-0
\item Overall public transport vehicle frequencies.% @ guide/06-service_planning/62-basic-data-collection.src: lines 182-182: code points 1-51
\end{itemize}
% @ guide/06-service_planning/62-basic-data-collection.src: lines 177-182: code points 1-51

From this data, the critical link and load of the corridor can be identified, also known as the maximum load on the critical link (MaxLoad). At this location, it is important to have full-day public transport vehicle and occupancy counts with consistent data.\par
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From the full-day counts at the critical link, the degree to which the demand has peaked on the corridor can be calculated. This is needed in order to calculate the required fleet under different scenarios and to convert peak hour ridership numbers to daily numbers. The total route distance and link-by-link peak hour speed are needed to calculate the route-by-route full-circuit total cycle time (TC).\par
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Though not completely necessary at this stage, it will also be useful to know:\par
% @ guide/06-service_planning/62-basic-data-collection.src: lines 193-194: code points 1-0

\begin{itemize}
\item The existing fleet size;% @ guide/06-service_planning/62-basic-data-collection.src: lines 194-195: code points 1-0
\item The total customers per line per day and per peak hour (to calculate the renovation rate [$Ren$]);% @ guide/06-service_planning/62-basic-data-collection.src: lines 195-196: code points 1-0
\item The total vehicle distance operated on the route.% @ guide/06-service_planning/62-basic-data-collection.src: lines 196-196: code points 1-55
\end{itemize}
% @ guide/06-service_planning/62-basic-data-collection.src: lines 194-196: code points 1-55

It will also be necessary to calculate:\par
% @ guide/06-service_planning/62-basic-data-collection.src: lines 198-199: code points 1-0

\begin{itemize}
\item The total amount of the route that overlaps the corridor;% @ guide/06-service_planning/62-basic-data-collection.src: lines 199-200: code points 1-0
\item The total cycle time that occurs on the planned corridor and off the planned corridor.% @ guide/06-service_planning/62-basic-data-collection.src: lines 200-200: code points 1-92
\end{itemize}
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This information gives us the preliminary tools to begin a service planning analysis.\par
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As an example, Figure 6.4 shows a corridor identified as a future BRT corridor in Montgomery County, Maryland, USA, to which the involved routes are shown in Figure 6.5. The Table 6.1 presents the total amount of the route that overlaps the corridor, and the part of total cycle time that occurs on and off the planned corridor.\par
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Figure 6.6 shows travel time differences with the BRT speeds (the pink line) and with the current speeds (red line) and the benefit per trip in minutes (the difference between the lines) for the route to be incorporated into the BRT corridor in each period of the day. Off-peak benefits will be smaller. The potential benefits of implementing each alternative are calculated in table in figure 6.6 for the proposed preliminary service plan by multiplying the number of customers for each trip throughout the day by the estimated travel time saved.\par
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		\img{\hsize}{operations/assets/00221c62490ad7f0bf9c2ddb98c8d7bbfa5e44ef.png}
		\fignote{4}{Planned BRT corridor in Montgomery County, Maryland, USA.\label{chapter:service-planning:figure:planned-brt-corridor-in-montgomery-county-maryland-usa}}{ITDP and Logit}
	}
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		\img{\hsize}{operations/assets/43eac4df78836176933243d4f906049973673aa1.png}
		\fignote{5}{Map of proposed BRT services for a planned corridor in Montgomery County, Maryland, USA.\label{chapter:service-planning:figure:map-of-proposed-brt-services-for-a-planned-corridor-in-montgomery-county-maryland-usa}}{ITDP and Logit}
	}
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		\img{\hsize}{operations/assets/44326342497af735cab286388a35b604a03bc10e.png}
		\fignote{6}{Travel times by mode for Montgomery County, Maryland, USA, on MD 355 along with an estimated BRT travel time.\label{chapter:service-planning:figure:travel-times-by-mode-for-montgomery-county-maryland-usa-on-md-355-along-with-an-estimated-brt-travel-time}}{Logit}
	}
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					\tabletitle{1}{Existing bus routes using the Route 355 proposed BRT corridor, proposed changes for two scenarios and time savings for Montgomery County, Maryland, USA.}
\label{chapter:service-planning:table:existing-bus-routes-using-the-route-355-proposed-brt-corridor-proposed-changes-for-two-scenarios-and-time-savings-for-montgomery-county-maryland-usa}

					\img{\hsize}{operations/assets/d68bd11e2ceda3662ecd2d9832ecd55f14dd3114.jpeg}
				}
			\fi

In Table 6.1, which was generated for Montgomery County using the GTFS and APC data corresponding to the routes in Figure 6.5, route extension is the percentage of the bus route that overlaps with the proposed BRT corridor, and passenger time is the percentage of the customer’s time that is the spent on that section of the bus route that overlaps with the proposed BRT corridor. While these two indicators essentially measure the same thing, the comparison between the two allows for identification of congestion and thus where BRT would significantly improve travel times. If the customer time in the corridor (last column marked “passenger time”) is higher than the percentage of full bus route length that overlaps with the BRT corridor (second to last column named “route extension”), this indicates that the corridor is where most of the congestion is, which suggests BRT should help significantly improve travel times.\par
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\section{3}{Basic Service Planning Concepts}
\label{volume:operations:chapter:service-planning:section:basic-service-planning-concepts}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 3-1024: code points 1-80

\quotation{When I was young, I had to learn the fundamentals of basketball. You can have all the physical ability in the world, but you still have to know the fundamentals.}{Michael Jordan, former professional basketball player, 1963–}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 5-6: code points 1-62

\subsection{1}{BRT Stations and Saturation}
\label{volume:operations:chapter:service-planning:section:basic-service-planning-concepts:subSection:brt-stations-and-saturation}
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With rail systems, the constraint on capacity tends to be the frequency that the signaling system can handle. Rail system designers thus frequently try to add longer and longer trains, but on city streets eventually this runs up against block lengths. In BRT systems, by contrast, the constraint on capacity is the BRT station. Vehicles can platoon, in which many can follow very closely, one behind the next, with very high frequencies. A traffic signal can handle far more vehicles passing through it over the course of an hour than a bus stop can process. As a result, for BRT, the station saturation problem is the critical issue that needs to be solved to maintain system speeds—not intersections or headways, which can be defined as the time between two vehicles offering a service, conveying exactly the same information as frequency.\par
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Thus understanding the saturation level of a station is a basic starting point in achieving high capacities and high speeds (covered in the next chapter), and if there is a risk of station saturation it also becomes a primary concern of service planning (covered in this chapter). Saturation level of a station refers to the percentage of time that a vehicle stopping bay is occupied. The term \emphasis{saturation} is also used to characterize a roadway, and in particular, the degree to which traffic has reached the design capacity of the road.\par
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When engineers talk about the capacity of a road or a BRT system, they will give a capacity for an acceptable level of service, rather than for the maximum number of vehicles or customers that could pass through a road or a system. After a certain point, the lane or BRT system becomes congested. With congestion, the total flow of vehicles may not change (usually it increases at first and later decreases), but the vehicles are going slower and slower.\par
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Saturation, of course, changes as the demand (arrival of vehicles) is not perfectly regular; so when we talk about saturation we are assuming a permanent flow subject to the irregularity normally observed in a roadway or in a busway. The peak hour is an appropriate measure of saturation for dimensioning a system.\par
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Exactly because of this irregularity, a level of saturation of (x=) 0.85 is commonly considered acceptable for mixed traffic. Below a saturation level of 0.85, increases in traffic will have only a minimal impact on average speeds, and the level of service is acceptable. Once saturation levels exceed 0.85, there is a dramatic drop in speeds.\par
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However, with BRT stations, there is no clear breaking point. The queues and delays at bus stations occur at small amounts even at low saturation levels, and these delays simply increase with saturation. In the case of a bus station, saturation is defined as the percentage of time that the station is occupied by vehicles boarding and alighting customers.\par
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		\img{\hsize}{operations/assets/26cd726b8364be73e9da631abcec244bb47f6930.jpeg}
		\fignote{7}{Relationship between travel time and saturation levelsi.\label{chapter:service-planning:figure:relationship-between-travel-time-and-saturation-levelsi}}{Steer Davies Gleave.}
	}
\fi

In general, stations should be planned at less than 40 percent saturation, or else the risk of congestion increases significantly. The impact of stopping bay saturation on speed is shown in Figure 6.7.\par
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Rather than a clear point at which the system collapses, station saturation tends to lead to a gradual deterioration of service quality. For this reason, the optimum level of station saturation is not clear. Some studies argue that the optimum should be around 0.30, but saturation levels as high as 0.60 can be tolerated in specific locations if this condition is not general throughout a BRT corridor. However, for saturation levels above 0.60, the system can be deemed unstable, and risk of severe congestion and system breakdown is considerable.\par
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A low saturation level, or a high level of service, means that there is a low likelihood of vehicles waiting in a queue at a BRT stop. A high saturation level means that there will likely be long queues at stopping bays. For saturation levels over one (x > 1), the station will certainly have queues increasing to the point where the system does not move until long after the peak is over.\par
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\subsection{2}{Sub-Stops and Docking Bays}
\label{volume:operations:chapter:service-planning:section:basic-service-planning-concepts:subSection:sub-stops-and-docking-bays}
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A docking bay is the designated area in a BRT station where a vehicle will stop and align itself to the boarding platform. Docking bays are typically aligned quite close together, so close in fact that one vehicle does not have the space to pull around and pass another vehicle stopped in front of it at another docking bay.\par
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Sub-stops, by contrast, are the stopping areas where one or more docking bays may be located. A station may be composed of more than one sub-stop. The critical thing about a sub-stop is that it be far enough away from the next sub-stop that any vehicle pulled up to a docking bay in the sub-stop in front of it has enough space to pull around and pass the other vehicle. This requires that one BRT vehicle be able to pass another BRT vehicle at the sub-stop, which necessitates a passing lane. Because sub-stops and passing lanes are extremely critical to avoiding station saturation and hence reaching higher speeds and capacities, and making express and limited stop services viable, they are both given points in \emphasis{The} \emphasis{BRT Standard}.\par
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In the first BRT systems, each station had only one docking bay and one sub-stop. A key innovation of Bogotá’s TransMilenio system was that more capacity and speed could be obtained, if, at each station, instead of having just one sub-stop with one docking bay, each station might have two or more sub-stops, and each sub-stop might have one or two docking bays. In Figure 6.8 the TransMilenio stop has two sub-stops, one with one docking bay and one with two docking bays.\par
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\ifxetex
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		\img{\hsize}{operations/assets/fcd782c4e5f7459970e9c68996fcf79d5f5808ef.jpeg}
		\fignote{8}{The use of multiple sub-stops and docking bays with passing lanes in Bogotá helps minimize vehicle congestion.\label{chapter:service-planning:figure:the-use-of-multiple-sub-stops-and-docking-bays-with-passing-lanes-in-bogot-helps-minimize-vehicle-congestion}}{Oscar Diaz and Por el País que Queremos (PPQ).}
	}
\fi

By adding more sub-stops and docking bays (the sub-stops are far more important than the number of docking bays), the saturation level of each sub-stop can be kept to a maximum value of 0.40 until very high levels of demand are reached. TransMilenio strives to keep the maximum variation in the saturation value at no more than 0.10 between sub-stops at the same station, so the values should not vary from a range of 0.35 to 0.45.\par
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\subsection{3}{Direct Services}
\label{volume:operations:chapter:service-planning:section:basic-service-planning-concepts:subSection:direct-services}
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Direct services, sometimes called “trunk extensions” or “complementary” routes, are new BRT services that operate both in mixed traffic and inside dedicated BRT infrastructure on trunk routes. Usually, they follow former bus or minibus routes that have been converted into BRT services.\par
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When designing BRT services, the easiest thing to do is to simply convert existing public transport routes into identical new BRT routes, and allow whatever portion of the existing route that does not overlap with planned BRT infrastructure to simply operate in mixed traffic. One of the main advantages of BRT over rail-based modes is that buses, unlike rails, can easily leave the trunk infrastructure and operate on any normal road.\par
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If a city has already done a good job designing its bus services, and the routes are well correlated to trip origins and destinations, it may be a good idea to leave several or most of them more or less where they are. Riders are already familiar with these routes, and a conservative approach to BRT service planning will minimize the likelihood of major mistakes or public confusion when the new system opens. Because such routes need to operate both in mixed traffic and along specialized BRT trunk infrastructure, the buses and the fare collection system need to be able to operate in both environments. Generally, this will require the procurement of a fleet compatible with the new BRT infrastructure and mixed traffic operation. Developing BRT vehicle technical specifications that allow for both BRT trunk and mixed traffic operation (see Figure 6.9) significantly improves the flexibility of the system. If the system has central median platforms on the BRT trunk corridor, vehicles will need to have doors on both sides. Direct service systems increasingly use low-floor buses to ease boarding and alighting off the trunk corridor. Direct service operations with flexible vehicles also make it easier to expand BRT trunk infrastructure onto other linked corridors without major disruptions in service or new fleet procurement. Direct services within a closed system can employ off-board fare collection at BRT stations, but need to have an on-board or proof-of-payment fare collection system when using regular bus stops outside the BRT corridor. With proof-of-payment systems, inspectors will be needed, and there is risk of fare evasion.\par
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		\img{\hsize}{operations/assets/5e67871072a312ca02cc85e52529ac3d4b40edf6.jpeg}
		\fignote{9}{Two-sided doorway configuration for a direct-service system where the bus operates both in the BRT corridor and outside the corridor in mixed traffic.\label{chapter:service-planning:figure:two-sided-doorway-configuration-for-a-direct-service-system-where-the-bus-operates-both-in-the-brt-corridor-and-outside-the-corridor-in-mixed-traffic}}{ITDP.}
	}
\fi

Until 2010, the only direct-service BRT reaching Silver or Gold Standard was the Brisbane Busway (Australia). Many of the Bronze-rated BRT systems with direct services lacked basic administrative controls over access to the trunk BRT infrastructure, with lower quality vehicle infrastructure improvements, and these systems frequently encountered station saturation problems. Problems of station saturation are not caused by direct services, but rather by a misalignment between the service plan and the infrastructure design that could happen regardless of service type. Since 2010, several systems have opened (Guangzhou, China; Cali, Colombia; Johannesburg, South Africa) that feature Gold- or Silver-Standard BRT infrastructure and direct services. These systems all offer services that operate both on Gold- or Silver-Standard BRT trunk infrastructure and continue beyond the trunk into mixed traffic.\par
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		\img{\hsize}{operations/assets/ca2421dcb8b7c92788168427d49c5dd47ba0c50a.jpeg}
		\fignote{10}{Complementary service in Cali.\label{chapter:service-planning:figure:complementary-service-in-cali}}{Karl Fjellstrom.}
	}
\fi

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		\fignote{11}{Complementary service in Johannesburg.\label{chapter:service-planning:figure:complementary-service-in-johannesburg}}{Yoga Adiwinarto.}
	}
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		\fignote{12}{Complementary services in Guangzhou.\label{chapter:service-planning:figure:complementary-services-in-guangzhou}}{Far East BRT.}
	}
\fi

Guangzhou’s BRT proved that direct services in a closed system with Gold Standard BRT infrastructure and properly sized stations can reach very high capacity and speed with high customer service levels. Guangzhou’s peak-hour, single-direction passenger flows, at over 27,000 passengers per hour per direction (PPHPD), are double all but the best trunk-and-feeder BRT systems in the world.\par
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Figure 6.13 provides a map of the services for the Guangzhou BRT system. The BRT routes illustrated in Figure 6.13 are allowed to operate along the BRT trunk corridor. The physically segregated busways and prepaid boarding stations were built along the trunk corridor illustrated in this figure, which also shows the bike-sharing stations implemented along the BRT corridor. Although the trunk corridor is only 23 kilometers long, BRT service coverage extends to 273 kilometers of roadways in the city.\par
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		\img{\hsize}{operations/assets/06f1a4418cb1a8b0ec03f0781eb67b63e65a9ea5.jpeg}
		\fignote{13}{Vehicles operating on the BRT system in Guangzhou move directly from an exclusive busway to feeder routes, and thus greatly reduce the need for transfers. This image also shows bike-sharing stations implemented along the BRT corridor, and the city’s metro stations. Image\label{chapter:service-planning:figure:vehicles-operating-on-the-brt-system-in-guangzhou-move-directly-from-an-exclusive-busway-to-feeder-routes-and-thus-greatly-reduce-the-need-for-transfers-this-image-also-shows-bike-sharing-stations-implemented-along-the-brt-corridor-and-the-citys-metro-stations-image}}{ITDP.}
	}
\fi

\subsection{4}{Trunk-and-Feeder Services}
\label{volume:operations:chapter:service-planning:section:basic-service-planning-concepts:subSection:trunk-and-feeder-services}
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Until recently, the most famous BRT systems operated “trunk-and-feeder” or “trunk-only” services. In some cases, a new BRT service will run only up and down the BRT trunk infrastructure. This would be called a “trunk-only” service. Trunk-only services can either allow the previous routes to continue to operate in mixed-traffic lanes parallel to the BRT corridor, and then continue as the route extends past, or they can be rerouted off the corridor, or they can be eliminated and force their former customers to transfer to the new BRT. The approach of allowing former bus routes to continue in mixed traffic is what occurred in Jakarta, Indonesia, and in many Chinese systems. It has the advantage that it does not force customers to transfer against their will. These systems have the disadvantage that the ridership of the BRT system tends to be lower, undermining returns to scale in the BRT system operation. Also, as it leaves many bus routes in the mixed traffic lanes, this approach also tends to degrade the level of service in the mixed traffic lanes, resulting in lowered mixed traffic speeds due to increased congestion.\par
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Initially, trunk-and-feeder service design was the result of BRT system developers copying the service characteristics of rail systems without considering direct service alternatives that were possible with BRT. Often, designers of “trunk-only” services think that informal operators will automatically provide feeder services to the trunk routes. In some cases, where enforcement and regulation of informal operators is reasonably effective, this can bring some customers to the trunk system, though it normally forces customers to pay twice, and does little to improve the quality of the trip still being performed by the informal part of the service. More typically, however, informal operators will refuse to stop at trunk stations in an effort to retain their customers for the longer haul trip, draining the BRT system of ridership and revenue, and congesting parallel mixed-traffic lanes.\par
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TransJakarta remained for many years a “trunk” system without a “feeder.” As a result, despite being one of the longest BRT systems in the world at over 172 kilometers, in early 2012 it carried only 350,000 customers per day and about 4,000 customers per hour per direction at peak times. Roughly two-thirds of all public transport customers using the TransJakarta corridors continued to use their former bus routes and operate in very congested mixed traffic conditions. While some operational improvements have been made, and a few new direct services have been added, the system has yet to fully optimize its services and operates at a loss.\par
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Mexico City also operates a trunk-only system. Rather than allowing former bus routes to operate in parallel, it cancelled them, reducing mixed traffic congestion and pushing up ridership on Metrobús. The new routing did not cause that many new forced transfers, because most of the former bus routes were already organized to operate on corridors in a manner that was not fully consistent with demand pattern. As the Mexico City system expanded, inter-corridor routes were added, and the system began to serve more customers, while reducing unnecessary transfers and station saturation.\par
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The better systems, such as Bogotá’s TransMilenio, Curitiba’s system, Rio’s Transoeste, Lima’s Metropolitano, and others provide fully integrated feeder bus services that connect to the trunk services in formal transfer terminals, offering a better quality and more comprehensive door-to-door service than the trunk-only services. In this case, a former bus route that overlaps the trunk BRT corridor for only part of its route is split into two services: a trunk service operating only inside the BRT system, and a feeder route that operates in mixed traffic.\par
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In the best systems, the BRT system operator operates both trunk services and feeder services under professional quality of service contracts with private vehicle operating companies. Such feeder services are not operated by informal operators, but by modern companies, and they form an integral part of the BRT system, with consistent branding, fare systems, information technology, and other BRT amenities. In some cases, especially in higher-income countries, a public transport authority is likely to operate both a BRT trunk service with special vehicles and branding, and a feeder service using normal buses in mixed-traffic lanes that are unlikely to be identified as part of the BRT system.\par
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		\img{\hsize}{operations/assets/66ca8d439de46186e72a1ea45349ebd035b9888e.jpeg}
		\fignote{14}{A Kopaja bus provides direct services in the TransJakarta BRT infrastructure. These buses run in mixed traffic and then enter the BRT corridor for part of their journey, but they are not officially part of the BRT system and have their own fare structure.\label{chapter:service-planning:figure:a-kopaja-bus-provides-direct-services-in-the-transjakarta-brt-infrastructure-these-buses-run-in-mixed-traffic-and-then-enter-the-brt-corridor-for-part-of-their-journey-but-they-are-not-officially-part-of-the-brt-system-and-have-their-own-fare-structure}}{Aimee Gauthier.}
	}
\fi

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		\img{\hsize}{operations/assets/02145f2019311a1f86cdc4899a4c386f346fdfd9.jpeg}
		\fignote{15}{A Mio BRT vehicle in Cali operates off-corridor to provide direct services to some destinations.\label{chapter:service-planning:figure:a-mio-brt-vehicle-in-cali-operates-off-corridor-to-provide-direct-services-to-some-destinations}}{Luc Nadal.}
	}
\fi

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		\img{\hsize}{operations/assets/79dd20f9770a31911a99f35e989638ba0398326b.jpeg}
		\fignote{16}{New TransJakarta direct service.\label{chapter:service-planning:figure:new-transjakarta-direct-service}}{Karl Fjellstrom.}
	}
\fi

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	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/d315a32e7795ba818a834ce6a93a00d8b385fcc8.jpeg}
		\fignote{17}{Many Chinese BRT systems operate trunk-only services, where the majority of the ridership remains on parallel traditional bus services operating in mixed-traffic conditions. Beijing’s BRT features many more customers and vehicles in the mixed-traffic lane adjacent to the BRT than are included in the BRT roadways.\label{chapter:service-planning:figure:many-chinese-brt-systems-operate-trunk-only-services-where-the-majority-of-the-ridership-remains-on-parallel-traditional-bus-services-operating-in-mixed-traffic-conditions-beijings-brt-features-many-more-customers-and-vehicles-in-the-mixed-traffic-lane-adjacent-to-the-brt-than-are-included-in-the-brt-roadways}}{Karl Fjellstrom, Far East BRT.}
	}
\fi

\subsection{5}{Services That Skip Stops: Limited, Express, Early Return, and Deadheading}
\label{volume:operations:chapter:service-planning:section:basic-service-planning-concepts:subSection:services-that-skip-stops-limited-express-early-return-and-deadheading}
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The most basic type of public transport service along a corridor is typically known as “local service.” This term refers to a service where stops are made at each station along a route. Thus, while local services provide the most complete route coverage along a corridor, such services also result in the longest travel times and the slowest speeds.\par
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Each stop a vehicle makes adds some delay. One of the easiest ways to increase vehicle speeds is to add services that skip stations. Services that skip a few stations at regular intervals are usually called “limited stop services.” Services that skip many stations are generally called “express services.” One of the main advantages of BRT is that it is relatively simple and inexpensive to allow one vehicle to pass another by simply having passing lanes at station stops.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 235-239: code points 1-61

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/56dfb6060eaf8b4d5697fe4a6ccc234d3aa26021.jpeg}
		\fignote{18}{Passing lanes at stations, like these in Bogotá, allow for the provision of express and limited stop services.\label{chapter:service-planning:figure:passing-lanes-at-stations-like-these-in-bogot-allow-for-the-provision-of-express-and-limited-stop-services}}{Karl Fjellstrom.}
	}
\fi

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/16cfbe82df21f7aeda9fb0f8eb97b732a2a5877a.jpeg}
		\fignote{19}{Passing lanes prevent queue formation at stations in São Paulo, deliver significant travel time savings to customers.\label{chapter:service-planning:figure:passing-lanes-prevent-queue-formation-at-stations-in-so-paulo-deliver-significant-travel-time-savings-to-customers}}{Karl Fjellstrom, ITDP China.}
	}
\fi

Single-track metro and light rail transit (LRT) systems and simple, single-lane BRT systems like TransJakarta and RIT Curitiba (except for the new Linea Verde), which do not have passing lanes, have few options but to operate only local services. There are no provisions within the infrastructure of these systems for vehicles to pass one another. Allowing passing in the infrastructure design can provide more service options and is a main reason why \emphasis{The} \emphasis{BRT Standard} weighs heavily the inclusion of passing lanes in the design.\par
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Many of the examples in this chapter assume that it is possible to build physical infrastructure that can accommodate the passing of one service by another, generally through the inclusion of passing lanes inside the BRT infrastructure. The best solution is to simply provide enough space for passing lanes at station stops. The space is not needed along the entire corridor, only at stations that can be set back from the intersection to avoid compromising intersection capacity. When right-of-way for passing lanes is simply unattainable, figuring out how to accommodate passing to allow longer distance limited and express vehicles to pass local BRT services and still use the dedicated BRT infrastructure is a challenge. A variety of alternatives have been discussed, though with fairly limited application to date. Most of these techniques only work up to a certain maximum frequency.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 254-262: code points 1-61

If the barrier between the busway and the mixed-traffic lanes is not rigid and can be easily permeated, it is possible for express and limited buses to simply pass each other in the mixed-traffic lanes. This is often done in bus system improvements like Select Bus Service in New York, but so far there are no examples of this in full BRT systems. Its effectiveness depends on the degree of mixed traffic congestion at the critical points where the buses need to pass one another.\par
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Another technique is to time services so that limited stop or express services only catch up with the local services at the terminal point of a route, or at select stations where passing lanes are available. Such services, called “catch up” services, are more commonly seen in rail systems. Thus, an express service may begin ten minutes behind a local service, and this starting-time difference ensures that the express service does not overtake the local service. Such an approach may be applicable to BRT for relatively short corridors with relatively long headways (e.g., ten minutes), but to date there is limited experience, and its application has been limited to express-service demands only.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 270-276: code points 1-69

Some cities have considered adding a pull-by bay in front of stations, where a local BRT vehicle can pull aside and let an express bus pass. This solution has the benefit of only requiring right-of-way where it is least needed for other purposes, such as BRT stations or turning lanes. Some preliminary analysis indicated that pull-by bays at some stations might be feasible in systems with headways greater than about five minutes, but there remains limited real-world experience with their application.\par
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If the BRT infrastructure does not include passing lanes at station stops, it may be advisable to leave express services in mixed traffic lanes. Curitiba’s RIT system, for instance, excluded longer-distance express buses from BRT services due to the lack of passing lanes. This was a second-best solution, the benefits of which degraded as traffic congestion increased in the mixed-traffic lanes. One of the main innovations of Bogotá’s TransMilenio was to introduce express, limited, and local services, all inside the BRT infrastructure.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 284-289: code points 1-23

Sometimes the overabundance of stops is mitigated by stop-on-demand. Stop-on-demand does not work well during peak hours, however, as there is usually demand for all of the stops. It is also virtually incompatible with BRT services. Since stop-on-demand offers limited benefits during the critical peak period, and does not integrate well with BRT, it is generally not used in BRT services and hence is not further considered here.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 291-295: code points 1-5

In many developing-nation cities, public transport services operate on a hail-and-ride basis. Even in cities in the United States, minibus services effectively stop wherever hailed by a customer, whether at a bus shelter or not. This has the advantage of minimizing walking times. Hail-and-ride vehicles may also offer a variety of service options and very high frequency. Hail-and-ride services are not compatible with operations inside a BRT system, though it is possible to allow hail-and-ride services to continue to operate in mixed-traffic lanes and to continue to provide services to locations where stops have been removed. Hail-and-ride is also not further considered herein.\par
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“Early return” services are another form of service that eliminates stops, in this case from the extreme ends of the route. Typically, the highest-demand segment of a route is in the city center, so early return services only operate the service on the highest demand part of the BRT corridor, allowing other services to operate on the full length of the corridor. With a limited fleet of vehicles, these early return services will significantly reduce operating costs for the system operator, while reducing the fleet size, but the demand profile needs to allow this type of service.\par
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“Deadheading” is when buses are run without stopping for customers in the nonpeak direction. Because demand frequently varies in the two directions of a BRT service, the optimal frequency is likely to differ for the two directions. Full optimization of services therefore requires the programming of services separately for the two directions. TransMilenio, in fact, coded the different directions with different route numbers, and these routes had different stopping patterns optimized to the specific peak and contra-peak demand patterns. It is often more efficient to run some of the buses in the contra-peak flow direction to skip more stops or to not stop at all, allowing the bus to return more quickly to the peak flow direction. This is known as deadheading.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 312-319: code points 3-29

\subsection{6}{Speed, Travel Time, and Distance Relationships}
\label{volume:operations:chapter:service-planning:section:basic-service-planning-concepts:subSection:speed-travel-time-and-distance-relationships}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 321-344: code points 1-47

Frequently, a BRT route’s length and travel time will be known, but not the average speed, or the average speed and time but not the distance. These are the basic relationships:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 323-324: code points 1-71

$ \text{average speed} = {\text{travel distance} \over \text{travel time}} \Leftrightarrow \text{travel time} =  {\text{travel distance} \over \text{average speed}} \Leftrightarrow  \text{travel distance} = {\text{travel time} * \text{average speed}} $\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 326-326: code points 1-254

\beginbox{1}{Reminder for time units conversion}
\label{chapter:service-planning:box:reminder-for-time-units-conversion}
1 hour = 60 minutes = 3,600 seconds;\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 331-331: code points 1-36

1 day = 24 hours = 1,440 minutes = 86,400 seconds\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 333-334: code points 1-0

\endbox
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 329-334: code points 1-7

Most commonly, one calculates the length of a proposed or existing route (usually the transit authority knows the route length, or it can be taken from GTFS, or calculated using GPS on board the bus), and usually a speed survey is conducted so that several peak hour trips can be timed and the average taken, so one can calculate existing bus speeds by using the above formula.\par
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If a trip takes one hour, and the distance is 20 kilometers, the speed is 20 kph. As the best BRT systems in urban conditions tend to move about 20 kph for a single track BRT and up to 30 kph for a BRT with passing lanes and sub-stops, if existing bus speeds are well below 20 kph, we know there is a reasonable likelihood of improving the speed on the route.\par
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\subsection{7}{Peak Hour, Peak Hour Ridership, Peak Hour Travel Time, Peak Hour Speed}
\label{volume:operations:chapter:service-planning:section:basic-service-planning-concepts:subSection:peak-hour-peak-hour-ridership-peak-hour-travel-time-peak-hour-speed}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 346-512: code points 1-6

Most service planning decisions require a calculation of the peak hour, or the hour of the day when there are the most public transport customers using the system on a particular route. It is also often important to estimate the speed on the route.\par
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How the peak hour is determined depends on what data is most readily available. In the United States, where it is fairly common to have transit agency data with boarding, alighting, and time at each bus stop (or at least each link), a chart like Table 6.2 can be created. It will show the total 6:00 a.m. departure for Route “A,” the 6:15 a.m. departure, and so on. The total boardings per vehicle are then calculated for each departing vehicle on Route A, and the total travel time for each Route A departure.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 352-356: code points 1-103

\tabletitle{2}{Route A: Boarding, Alighting, and Loads}
\label{chapter:service-planning:table:route-a-boarding-alighting-and-loads}
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	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\cr
	\color{gray75}\bfseries & \color{gray75}\bfseries 6:00 a.m. Departure& \color{gray75}\bfseries & \color{gray75}\bfseries & \color{gray75}\bfseries & \color{gray75}\bfseries 6:15 a.m. Departure& \color{gray75}\bfseries & \color{gray75}\bfseries & \color{gray75}\bfseries & \color{gray75}\bfseries 6:30 a.m. Departure& \color{gray75}\bfseries & \color{gray75}\bfseries & \color{gray75}\bfseries & \color{gray75}\bfseries 6:45 a.m. Departure& \color{gray75}\bfseries & \color{gray75}\bfseries & \color{gray75}\bfseries  \cr
	\noalign{\vskip 1mm} \hline \noalign{\vskip 2mm} 
	\color{gray50}&
	\color{gray50}Boarding&
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	\color{gray50}Load&
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	\noalign{\vskip 2mm 
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% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 358-375: code points 1-9

The salient information per route (total boardings and total trip time) for all peak period departures can then be created as shown in next table\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 377-378: code points 1-73

\tabletitle{3}{Example of Average Peak Hour Riders and Times}
\label{chapter:service-planning:table:example-of-average-peak-hour-riders-and-times}
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% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 380-425: code points 1-9

In Table 6.3, the peak hour for Route “A” is from 6:15 a.m. to 7:14 a.m. It is during this hour that total boardings of all Route A trips reach their maximum.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 427-428: code points 1-57

Alternatively, if this data is not available, the peak hour can be calculated from frequency and occupancy counts for each bus route. In this case, a surveyor would stand at the critical link (highest demand section of the route) and count the number of Route “A” buses and estimate their occupancy. The hour with the maximum frequency and highest occupancy is roughly the peak hour.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 430-433: code points 1-74

In the example above, the peak hour headway is fifteen minutes and peak-hour frequency is four minutes. The average peak hour demand per bus is twenty-five, or a hundred per hour, and the average travel time is 1:55. When inputting this data into a model (for calculating costs, benefits, stations, bus sizes, fleets, travel times, or simulating the network), one generally converts the above messy data into a constant flow that represents average peak hour conditions.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 435-439: code points 1-59

\tabletitle{4}{Example of Average Peak Hour Riders and Times}
\label{chapter:service-planning:table:example-of-average-peak-hour-riders-and-times}
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% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 441-508: code points 1-9

It is these averages that will tend to be used in a traffic model. The existing speed of the bus route should be used to code the link speed for the existing public transport route.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 510-512: code points 1-6

\subsection{8}{Public Transport Loads: Load, Critical Link, Maximum Hourly Load on the Critical Link (MaxLoad), Passengers per Hour per Direction (PPHPD), and Load Factor}
\label{volume:operations:chapter:service-planning:section:basic-service-planning-concepts:subSection:public-transport-loads-load-critical-link-maximum-hourly-load-on-the-critical-link-maxload-passengers-per-hour-per-direction-pphpd-and-load-factor}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 514-615: code points 1-73

The “load” of a given segment (or link) of a system is the total number of customers that travel through that segment within a given time period, usually an hour; if no other qualification is made it refers to “passengers per hour across the given segment”; this, like other measures presented, changes throughout the day (and from one day to the next), but for the service planning exercises presented in this chapter, if nothing else is said, the load of a segment refers to the peak hour load.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 516-520: code points 1-76

\tabletitle{5}{Table 6.5 Load Example at a Corridor}
\label{chapter:service-planning:table:table-65-load-example-at-a-corridor}
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	\color{gray75}\bfseries & \color{gray75}\bfseries Route A Northbound peakhour& \color{gray75}\bfseries & \color{gray75}\bfseries & \color{gray75}\bfseries Route B Northbound peakhour& \color{gray75}\bfseries & \color{gray75}\bfseries & \color{gray75}\bfseries Combined Northbound peakhour& \color{gray75}\bfseries & \color{gray75}\bfseries  \cr
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% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 528-544: code points 1-9

Once the peak hour load has been calculated (as in Section 6.3.6), the consolidated boardings, alightings, and loads at each stop on the planned BRT corridor can be calculated by simply adding up the hourly boardings and alightings of all the routes that will use the new BRT corridor, as illustrated above. In Table 6.5, the maximum load is thirty-four and it occurs after the bus departs the 70th Street Station until it reaches the 80th Street Station. The link between 70th Street and 80th Street is carrying the heaviest load of customers, and as such is called the “Critical Link.” The load on this link (thirty-four in Table 6.5) is known as the “maximum load on the critical link.”\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 546-552: code points 1-92

Note that this is usually only for one direction of travel. To avoid confusion due to the fact that a segment normally has two directions, it is common for the unit PPHPD to be used for the expression of loads. It is an abbreviation for “passengers per hour per direction” and it means “passengers per hour in one direction.” PPHPD (or even \emphasis{pphpd}) is used here with this intended meaning.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 554-557: code points 1-88

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/e209cba6c98fa49b43838c4f0549ba90a96c2c4a.png}
		\fignote{20}{Output of a boarding and alighting survey for bus route 248R in Guangzhou, China, during the peak hour. The "Critical Link" is between Stop 13 and Stop 16. Graph\label{chapter:service-planning:figure:output-of-a-boarding-and-alighting-survey-for-bus-route-248r-in-guangzhou-china-during-the-peak-hour-the-critical-link-is-between-stop-13-and-stop-16-graph}}{ITDP.}
	}
\fi

Figure 6.20 illustrates the same idea graphically. The link between Stop 13 and Stop 16 carries the heaviest load, so it is the critical link, and the maximum load on this critical link is about 1,800 passengers per hour per direction (or PPHPD). The maximum load on the critical link is of primary interest to BRT system planners, as it is used for making many crucial design and service planning decisions. The duration of one hour is considered the appropriate measure of peak duration (shorter measurements have considerable oscillation). In the formulas that follow, this peak load is called the “maximum hourly load on the critical link” (MaxLoad). Identifying this location and this load is paramount in any service planning exercise as it is the load at this point that will determine the fleet needed and the appropriate vehicle size. The expressions \emphasis{corridor maximum load} and eventually \emphasis{system maximum load} also refer to this measurement.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 562-571: code points 1-20

The “load factor” is the percentage of a vehicle’s total capacity that is actually occupied. For example, if a vehicle has a maximum capacity of 160 customers and 128 customers in a segment of a trip, then the load factor is 80 percent (128 divided by 160) on that given segment. The total load factor of the system would account for the average load for all services throughout the system (this average could be weighted by segment extension or time vehicles need to cross it), and it is used to show the efficiency with which the system’s vehicles are used. When the term \emphasis{load factor} is used without further qualification, it refers to the \emphasis{design load factor}—that is, the planned average load factor to happen on the busiest segment of the service, or the critical link, when the system is implemented as discussed in the following paragraphs.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 573-581: code points 1-11

The actual load factors of any BRT system are determined by the frequency of the vehicles, the capacity of the vehicles, and the demand. In a service plan, the load factor is easily altered by changing the frequency of the services, changing the vehicle size, or changing the routes of competing services. Designing services using a lower load factor than the real capacity of the vehicle is recommended.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 583-586: code points 1-88

While systems with high load factors tend to be more profitable, generally it is not advisable to plan to operate at a load factor of 100 percent. If designing for 100 percent load, 50 percent or more of the vehicles will be overcrowded, because the distribution of customers will never be uniform from vehicle to vehicle, but will likely be some variation within 10 to 20 percent of the design load factor. Even if the vehicles were at capacity and not overcrowded, the conditions in the vehicle will be uncomfortable to customers, as well as create negative consequences for operations. At 100 percent capacity, small system delays or inefficiencies, especially with boarding and alighting, can lead to severe overcrowding conditions.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 588-595: code points 1-11

The desired load factor may vary between peak and nonpeak periods. In Bogotá’s TransMilenio system, typical load factors are 80 percent for peak periods and 70 percent for nonpeak periods. However, as ridership levels increase in Bogotá, overcrowding becomes an increasing concern.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 597-599: code points 1-80

The load factor is unlikely to be uniform for the entirety of a route. Designing services that maintain high load factors for as much of the route as possible will tend to improve system performance and efficiency, including its financial performance.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 601-603: code points 1-36

A system’s capacity is considered to be met when the load factor reaches 100 percent at the maximum load on the critical link. Systems can also sometimes operate at a load factor exceeding 100 percent, but not by much, and such a system would be considered to be operating at “above capacity.” BRT system capacity is generally measured by the peak PPHPD. This measurement would be taken at the point of the maximum load on the critical link\highlight{.}\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 605-609: code points 1-47

TransMilenio has a capacity of about 36,000 PPHPD based on its service plan, but its peak PPHPD has been counted as over 40,000. Such a level implies that customers are more closely packed than the maximum recommended levels. This situation is sometimes known as the “crush capacity.” While such extreme capacities can be expected in some unusual circumstances (e.g., immediately after special events such as sporting events or concerts), it is not desirable to regularly overcrowd vehicles.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 611-615: code points 1-73

\subsection{9}{Service Frequency and Headways}
\label{volume:operations:chapter:service-planning:section:basic-service-planning-concepts:subSection:service-frequency-and-headways}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 617-724: code points 1-59

The service frequency refers to the number of times a specific service is offered during a given time interval. Normally, frequency is expressed per hour, but service frequencies can also be expressed for any time interval, such as: “ten trips per day” or “twenty trips per three-hour peak period,” or even “a quarter of a trip per minute.” As with everything else in BRT service planning, frequency of service (existing or planned) changes throughout the day, but the sizing of the system should be based on the frequency during the peak hour. So, if no further mention is made, frequency means “the number of services provided in one hour, during the peak.”\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 619-625: code points 1-39

The time between two vehicles offering a service, which conveys exactly the same information as frequency, is known as the “headway.” Headways can be expressed as, for example: “one trip every two hours” or as “one trip every ninety minutes” or “one trip every thirty seconds.” The characteristic of headway measuring is that time is referenced to \emphasis{one bus trip}\highlight{.}\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 627-630: code points 1-57

Based on the concept definitions, the below equations are always true (mathematical identities).\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 632-632: code points 1-96

Eq. 6.1:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 634-634: code points 1-8

$ \text{Freq} = {1 \over \text{hdwy}}  \Leftrightarrow  \text{hdwy} = {1 \over \text{Freq}}  $\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 636-636: code points 1-96

Where:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 638-639: code points 1-0

\begin{itemize}
\item $\text{Freq}$: Service frequency; that is number of times a specific service is offered during a given time interval;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 639-641: code points 1-0
\item $\text{hdwy}$: Service headway, that is time between two vehicles offering a service.% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 641-641: code points 1-93
\end{itemize}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 639-641: code points 1-93

The service headway is the inverse of the frequency, but beware of units used for each one; for example: four buses per hour implies a headway of ¼ of hour, i.e., a headway of fifteen minutes. So the service headway in minutes is calculated as sixty divided by the frequency in hours and the frequency (in hours) is calculated as sixty divided by the headway in minutes.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 643-646: code points 1-57

The “minimum frequency” is the frequency that is needed to provide enough capacity to satisfy the existing demand without the average peak hour bus having a load factor above a policy-determined norm, usually 85 percent.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 648-650: code points 1-11

When planning services, if the vehicle size has already been determined, and an acceptable maximum load factor has been determined (normally 85 percent), then the minimum frequency can be determined based on the following formula:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 652-654: code points 1-25

Eq. 6.2:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 656-656: code points 1-8

$ \text{Freq} = {\text{MaxLoad} \over {V_\text{Size} * \text{LoadFactor}}} $\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 658-658: code points 1-78

Where:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 660-661: code points 1-0

\begin{itemize}
\item $\text{Freq}$: Service frequency; the number of times a specific service is offered during a given time interval;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 661-663: code points 1-0
\item $\text{MaxLoad}$: Maximum hourly load on the critical link;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 663-664: code points 1-0
\item $V_\text{Size}$: Vehicle capacity;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 664-665: code points 1-0
\item $\text{LoadFactor}$: Percentage of a vehicle’s total capacity that is actually occupied.% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 665-665: code points 1-96
\end{itemize}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 661-665: code points 1-96

For example, if the bus specification has already been determined to have a capacity of 150 customers per vehicle, and the maximum hourly load on the critical link is 3,000, and the maximum acceptable load factor is 85 percent, or if:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 667-669: code points 1-28

$ \text{MaxLoad} = 2550 $;\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 671-671: code points 1-28

$ \text V_\text{Size} = 150; $\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 673-673: code points 1-32

$ \text{LoadFactor} = 85 \% $\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 675-675: code points 1-31

Then:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 677-677: code points 1-5

$ F = {2550 \over {150 \times 0.85} } =  20 $\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 679-679: code points 1-47

And if $F = 20$, then the headway is $ {60 \text{(minutes)} \over {20}} = 3\text{(minutes)} $\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 681-681: code points 1-97

In general, it is desirable to provide frequent services in order to reduce customer waiting times. At headways of ten minutes or longer, customers will no longer have confidence that they can just show up at the station at any time and a bus will come in a reasonable period of time. With headways longer than 10 minutes, customers tend to view the system as a timetable service, which leads to loss of ridership. In Mexibus corridor III, illegal services operating parallel to the corridor serve most of the demand in off-peak hours.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 683-688: code points 1-18

In low demand systems where authorities want to promote increased public transport ridership, they sometimes set frequency based on a policy decision rather than on the minimum frequency. As very low demand routes are quite common in the developed world, it is often the case that frequency is set as a matter of policy rather than as a function of capacity. Services operating at frequencies higher than can be justified by the demand, however, are likely to contribute to operating deficits.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 690-694: code points 1-88

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/48518bc301a2e3085724a511c64034f43db2688f.jpeg}
		\fignote{21}{The perception of a relatively empty busway next to heavily congested mixed-traffic lanes, as seen in this image of Guangzhou can create political pressures. Images\label{chapter:service-planning:figure:the-perception-of-a-relatively-empty-busway-next-to-heavily-congested-mixed-traffic-lanes-as-seen-in-this-image-of-guangzhou-can-create-political-pressures-images}}{ITDP.}
	}
\fi

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/680ba99a2769a02ea4f3f96bfab455e81856dbb6.jpeg}
		\fignote{22}{Despite carrying far more passengers per lane than a car lane, this buswayi, in Jakarta, can also be perceived as empty.\label{chapter:service-planning:figure:despite-carrying-far-more-passengers-per-lane-than-a-car-lane-this-buswayi-in-jakarta-can-also-be-perceived-as-empty}}{ITDP.}
	}
\fi

On a BRT system, a corridor with relatively high frequency should have been chosen, so the chances are that frequencies will rarely drop below six in any case. But what appears as high frequency in mixed traffic appears as low frequency on a busway. A five-minute frequency in mixed traffic is very high; on a busway, it is comparatively low. A busway with a headway of five minutes will appear empty most of the time to motorists sitting in traffic congestion. The lower the frequency, the greater the likelihood that motorists will complain that the road is being underutilized. Such complaints can ultimately undermine political support for future busways. In Quito, pressure from motorist organizations led the national police to open up exclusive busway corridors to mixed traffic for a period of time in 2006. This was also the case in León, Mexico in 2008. This conversion occurred despite the fact that each busway lane was moving three to four times the volume of customers as a mixed traffic lane. Nevertheless, the perception of an empty busway next to heavily congested mixed-traffic lanes can create political difficulties. A similar political battle has been fought over the BRT corridor in Indore, India.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 702-713: code points 1-80

On the other hand, if headways are very low, and frequency is very high, congestion at the station and service irregularity become a risk. Figure 6.23 illustrates the relationship between service frequency and congestion.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 715-717: code points 1-15

\ifxetex
	% disabled for now
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	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/efe3c587c0364917a4a22a5935fa3b66063deae7.jpeg}
		\fignote{23}{Service frequency and the potential impact on vehicle velocity at a station with no passing lanes. Graph\label{chapter:service-planning:figure:service-frequency-and-the-potential-impact-on-vehicle-velocity-at-a-station-with-no-passing-lanes-graph}}{Steer Davies Gleave.}
	}
\fi

Service irregularity (bus bunching) is an even greater risk with higher frequency. For these reasons, it is usually advisable to split a service into two distinct services (for example, one limited and one express) if the frequency rises above 30 vehicles per hour.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 722-724: code points 1-59

\subsection{10}{Dwell Time}
\label{volume:operations:chapter:service-planning:section:basic-service-planning-concepts:subSection:dwell-time}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 726-761: code points 1-48

One of the main aims of BRT system design and service planning is to reduce the delay caused by vehicles slowing down to stop at stations, allowing the customers to board and alight, and then to accelerate to a free-flow speed. The entirety of this delay is known as “total dwell time,” or Td, in this chapter’s equations.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 728-731: code points 1-10

The dwell time consists of two separate types of delay: “fixed dwell time” ($T_0$) and “variable dwell time.” In BRT system planning, it is critical to keep these two causes of delay distinct, because different decisions will affect different types of dwell time. Fixed dwell time, also called “dead time,” is the time consumed by a vehicle slowing down on approaching a station, opening its doors (and after a variable dwell time for boarding and alighting), closing its doors, and then regaining free-flow speed. This delay is called fixed dwell time because it does not vary with the number of customers boarding and alighting at each stop, and it does not vary much between stops in a system. The only way to reduce fixed dwell time is to remove stopping at particular stations in the service design, by offering express or limited stop services or eliminating the stop from the system.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 733-741: code points 1-54

In some countries, it is more typical to model fixed dwell time as only the time at the station when a bus is opening and closing its doors, and the time consumed accelerating and decelerating on the approach to the stop is modeled as a reduction in the link speed between station stops. It is important to keep in mind that this guide, when it talks of fixed dwell time, refers to both.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 743-746: code points 1-75

Variable dwell time consists of customer boarding time ($T_b$) and alighting time ($T_a$). Because it varies with the number of customers boarding and alighting at a given station, it is called “variable dwell time,” ($ T_b + T_a$ or $max(T_a, T_b)$ depending on the vehicle\slash{}system configuration).\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 748-750: code points 1-91

Many key elements of BRT that are recognized by \emphasis{The} \emphasis{BRT} \emphasis{Standard} are measures that will tend to reduce variable dwell time, such as:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 752-754: code points 1-0

\begin{itemize}
\item Number of vehicle doorways;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 754-755: code points 1-0
\item Width of vehicle doorways;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 755-756: code points 1-0
\item Level boarding;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 756-757: code points 1-0
\item Fare collection outside the vehicle.% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 757-757: code points 1-42
\end{itemize}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 754-757: code points 1-42

BRT systems are able to operate metro-like service in large part due to the ability to reduce dwell time per customer from an average of five or six seconds per passenger for a typical bus service to only 0.3 seconds per customer on a Gold Standard BRT.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 759-761: code points 1-48

\subsection{11}{Renovation Factor}
\label{volume:operations:chapter:service-planning:section:basic-service-planning-concepts:subSection:renovation-factor}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 763-786: code points 1-73

The renovation factor ($\text{Ren}$) is total demand of a bus route divided by the load on the critical link of that route (note that operators customarily use the vehicle capacity instead of load on the critical link). It is the multiplier used to convert the number of customers that one would observe travelling on a route at the critical link (for example, in a vehicle occupancy survey) into the total number of customers on the route. Higher renovation factors are seen when there are many short trips along the line; corridors with very high renovation factor rates are more profitable because the same number of total paying customers is handled with fewer vehicles. For example, the Insurgentes corridor in Mexico City has a recorded renovation factor of five, which means that there are five times more people getting on and off the vehicle as there are people on the vehicle at the most loaded time.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 765-773: code points 1-82

Corridors with very high renovation factors meet higher demand more easily than corridors with low renovation factors, simply because more people are getting on and off vehicles along the corridor after shorter rides, so more people can be served.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 775-777: code points 1-44

Eq. 6.3:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 779-779: code points 1-8

$\text{Ren}_\text{route} = {D_\text{route} \over \text{MaxLoad}_\text{route}}$\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 781-781: code points 1-80

Where:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 783-784: code points 1-0

\begin{itemize}
\item $\text{Ren}_\text{route}$: Renovation factor of a route;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 784-785: code points 1-0
\item $D_\text{route}$: Route demand (in passengers);% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 785-786: code points 1-0
\item $\text{MaxLoad}_\text{route}$: Route demand on the critical link.% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 786-786: code points 1-73
\end{itemize}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 784-786: code points 1-73

\subsection{12}{Irregularity Index (Irr)}
\label{volume:operations:chapter:service-planning:section:basic-service-planning-concepts:subSection:irregularity-index-irr}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 788-828: code points 5-37

The irregularity index is a number that expresses the reliability of actual headways against scheduled headways. An irregularity index of one means that the vehicles are arriving at completely random times, and an irregularity index of zero means that vehicles are arriving precisely when they are scheduled. It is measured as:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 790-793: code points 1-18

Eq. 6.4:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 795-795: code points 1-8

$ \text{Irr} = {\text{Variance of the headway} \over {\text{Scheduled headway}} ^2 } $\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 797-797: code points 1-88

Where:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 799-800: code points 1-0

\begin{itemize}
\item $\text{Irr}$: Irregularity index, the measure of the variance between the actual headways and the scheduled headways;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 800-802: code points 1-0
\item $\text{Variance of the headway}$: Amount that the headways are spread out;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 802-803: code points 1-0
\item $\text{Scheduled}_text{headway}$: Average waiting time between vehicles.% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 803-803: code points 1-81
\end{itemize}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 800-803: code points 1-81

Variance of the headway is statistically defined as the expected value of the squared deviation from the mean headway. When calculating it from a sample it would be equal to the sum of the square of the differences between each observed headway and the average headway divided by the number of observations minus one, given by:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 805-808: code points 1-20

Eq. 6.5:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 810-810: code points 1-8

$V_\text{hdwy} = {\sum_{i=1}^{N_\text{obs}} (\text{hdwy}_i - \text{hdwy}_\text{average}) ^ 2 \over {N_\text{obs} - 1}} $\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 812-812: code points 1-122

Where:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 814-814: code points 1-6

\begin{itemize}
\item $V_\text{hdwy}$: Variance of the headway, expected value of the squared deviation from the mean headway;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 816-817: code points 1-0
\item $N_\text{obs}$: Number of observed headways;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 817-818: code points 1-0
\item $\text{hdwy}_i$: Observed headway for “i”;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 818-819: code points 1-0
\item $\text{hdwy}_\text{average}$: Average headway, average waiting time between vehicles = scheduled headway.% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 819-819: code points 1-113
\end{itemize}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 816-819: code points 1-113

The average headway will generally be equal to the scheduled headway, unless fewer trips than scheduled regularly occur. Consider the extreme case where we should have one bus every twenty minutes every hour during ten hours, which would be thirty buses throughout the day (or three buses per hour for ten hours), and imagine that the first bus was on time and the other twenty-nine arrive one after another in the last half hour of the tenth hour. The headway of the first bus would be 571 minutes and the other 29 would be 1 minute, so on average the headway would still be 20 minutes per bus (600 minutes divided by 30 buses). Without an operational control system, empirical observation indicates that under many conditions, the irregularity index is around 0.3.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 821-828: code points 1-37

\subsection{13}{Cycle Time-Related Concepts: Cycle Time (TC) and Maximum Demand Load per Cycle Time (MaxLoadperCycle)}
\label{volume:operations:chapter:service-planning:section:basic-service-planning-concepts:subSection:cycle-time-related-concepts-cycle-time-tc-and-maximum-demand-load-per-cycle-time-maxloadpercycle}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 830-897: code points 1-121

Assuming that a vehicle will keep repeating a service (in both directions, or as a circular route), cycle time is the amount of time that it takes for a bus to travel the entire length of its route, in both directions, and be ready to begin a second circuit, including any time waiting and reversing direction at the end points. It is extremely important to know the cycle time per route for service planning. If a cycle time is short, the same bus can rapidly come back to the beginning of the route and take a second load of customers. If the cycle time is long, additional buses will be needed. Knowing the cycle time is therefore necessary for determining the required fleet.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 832-838: code points 1-58

When proposing an initial service plan, one should already have the existing route travel times in mixed traffic. In order to estimate the cycle time for the proposed routes, one must replace the travel time inside the BRT structure assuming a typical speed (say 20 kph if the corridor is in a dense downtown area, or 29 kph if it is on a limited-access high-speed arterial with few intersections). In the next chapter, methods of calculating more refined projected speeds will be presented, but for this chapter, these baseline speeds will be assumed for inside the BRT trunk operations.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 840-845: code points 1-74

It should be noted that drivers must have some rest time at the end of the route; in short routes this can be done once per cycle. Even if it would be possible to reduce the time to turn the vehicle by changing drivers, the practice is to have the driver always using the same vehicle, which eases operations management and fleet maintenance as well as improving the quality of driving.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 847-850: code points 1-66

Once the cycle time is estimated for each planned service, it is possible to estimate the Maximum Demand Load per Cycle Time\highlight{ }(MaxLoadperCycle). This is the number of customers that are likely to accumulate over the course of the cycle time expecting to cross the critical link of the route. In other words, how many customers will accumulate for a specific route at the critical link over a time period equal to the cycle time? This figure, which can be calculated from the surveys of existing routes, is critical in several calculations in service planning. This figure is basically the same thing as the number of customer places that need to be serviced with vehicles, and is sometimes identified as “passenger places served.”\highlight{ }It can be thought of as the size of the vehicle that would be needed if only one vehicle were used to service the peak hour demand.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 852-860: code points 1-54

For planning purposes, it is critical to know the peak load demand on a typical day over the course of a single cycle time (also during the peak period). If demand is reasonably constant throughout the day, and one can assume that hourly MaxLoad is constant, then MaxLoadperCycle would be estimated by:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 862-864: code points 1-100

Eq. 6.6a:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 866-866: code points 1-9

$ \text{MaxLoadperCycle} = \text{MaxLoad} *\text{TC} $\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 868-868: code points 1-56

Where:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 870-871: code points 1-0

\begin{itemize}
\item $ \text{MaxLoadperCycle}$: Maximum demand load per cycle time;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 871-872: code points 1-0
\item $ \text{MaxLoad}$: Maximum hourly load on the critical link;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 872-873: code points 1-0
\item $ \text{TC}$: Cycle time in hours.% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 873-873: code points 1-42
\end{itemize}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 871-873: code points 1-42

However, demand is rarely constant before and after the peak hour, nor even during the peak hour. If demand is at its peak, then the maximum demand load per cycle time will appear higher for an increment of time shorter than an hour than if it is averaged over an hour. For a cycle time longer than an hour, the maximum demand load for the cycle time will appear to be lower than for the peak hour because it is being averaged over a longer period of time during which the demand has already fallen. The more demand is peaked, the greater the distortion.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 875-880: code points 1-38

Therefore, to be more accurate, one has to apply a correction factor:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 882-883: code points 1-0

\begin{itemize}
\item Increases demand if the cycle time is shorter than one hour;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 883-884: code points 1-0
\item Decreases demand if the cycle time is longer than one hour.% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 884-884: code points 1-65
\end{itemize}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 883-884: code points 1-65

One way to apply such a correction is using the formula below:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 886-886: code points 1-62

Eq. 6.6b with “peak hour to cycle correction factor” (PHtoCC):\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 888-888: code points 1-62

$ \text{MaxLoadperCycle} = \text{MaxLoad} * TC * [ 1 - \text{PHtoCC} * (\text{TC} -1) ] $\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 890-890: code points 1-91

Where:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 892-893: code points 2-0

\begin{itemize}
\item {$\text{PHtoCC}$: Nonnegative correction factor, the calibration of which is based on survey data, is discussed in Box 6.2. The usual value is near 0.1;\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 893-894: code points 7-0

\begin{itemize}
\item If $\text{TC}$ is larger than one hour: correction $ 1 - \text{PHtoCC} * (\text{TC} -1) $ will result smaller than one;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 894-895: code points 1-0
\item If $\text{TC}$ is smaller than one hour: correction $ 1 - \text{PHtoCC} * (\text{TC} -1) $ will result larger than one;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 895-896: code points 1-0
\item If $\text{TC}$ is equal one hour: correction $   1 - \text{PHtoCC} * (\text{TC} -1) $ will result in one;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 896-897: code points 1-0
\item If $\text{PHtoCC}$ is equal zero, there will be no correction, and the formula is equal to the previous formula.% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 897-897: code points 1-120
\end{itemize}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 894-897: code points 1-120

}
\end{itemize}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 893-897: code points 1-121

\subsection{14}{Waiting Time (Twait) and Waiting Time Cost (Costwait)}
\label{volume:operations:chapter:service-planning:section:basic-service-planning-concepts:subSection:waiting-time-twait-and-waiting-time-cost-costwait}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 899-981: code points 1-75

Throughout this chapter it will be necessary to compare the relative costs and benefits of different service planning scenarios. One of the most important costs to consider in service planning is the cost of time spent waiting by customers.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 901-903: code points 1-35

Assuming customers arrive randomly at a bus stop, the average waiting time for a customer is only half of the observed headway of the route. Hence, the wait time per customer is the headway multiplied by 0.5, plus a little extra if there is irregularity in the actual headways from scheduled service (Irr). The equation below expresses this, replacing headway with frequency (its inverse value).\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 905-908: code points 1-88

Eq. 6.7:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 910-910: code points 1-8

$ T_\text{wait}= 0.5 * (1 + \text{Irr}_\text{route}) * \text{hdwy} = {0.5 * (1 + \text{Irr}_\text{route}) \over \text{Freq}}$\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 912-912: code points 1-127

Where:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 914-915: code points 1-0

\begin{itemize}
\item $T_\text{wait}$: Time spent waiting per customer;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 915-916: code points 1-0
\item $\text{Irr}$: Irregularity index; measure of the variance between the actual headways and the scheduled headways (usually near 0.3, see Section 6.3.9);% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 916-918: code points 1-0
\item $\text{hdwy}$: Route Headway;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 918-919: code points 1-0
\item $\text{Freq}$: Route Frequency.% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 919-919: code points 1-39
\end{itemize}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 915-919: code points 1-39

The cost of waiting ($\text{Cost}_\text{wait}$) is defined as the amount an average customer would spend to avoid waiting for a vehicle, it is measured in currency per unit of time—for example: “5 Rp. per minute” and “6 US\$ per hour”—and is calculated as a fraction of customer income. Costwait varies depending on a city’s income and proclivity, but typically, people value their time at about one-third of the average wage rate, and are willing to pay twice as much to avoid waiting for a vehicle (i.e., 66 percent of the average user wage).\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 921-926: code points 1-6

Customers do not like to wait for a vehicle. If the demand of a given route proposed on a service plan is known (initially it can be approximated by using the demand on a similar existing route), the total waiting cost caused by a route is the sum of the cost of waiting time imposed on all its customers (assuming for now that this is captive demand), then multiplied by their value of waiting time:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 928-931: code points 1-85

Eq. 6.8a:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 934-934: code points 1-9

$\text{WaitCost}_\text{route} = \text{D}_\text{route} * \text{Cost}_\text{wait}*\text{T}_\text{wait}$\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 936-936: code points 1-103

Where:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 938-938: code points 1-6

\begin{itemize}
\item $\text{WaitCost}_\text{Route}$: Total waiting time cost for the users of the route (in US\$);% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 940-941: code points 1-0
\item $\text{D}_\text{route}$: Route demand (in passengers);% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 941-942: code points 1-0
\item $ \text{Cost}_\text{wait}$: Average user waiting cost (\$\slash{}time);% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 942-943: code points 1-0
\item $\text{T}_\text{wait}$: Average user waiting time (time\slash{}passenger).% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 943-943: code points 1-75
\end{itemize}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 940-943: code points 1-75

This is the total cost of waiting faced by all the customers on a particular route during the peak hour. The average value of waiting as defined is the same all day.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 945-946: code points 1-66

The $\text{D}_\text{route}$ formula for estimating the cost of waiting on the route would be more usefully expressed as a function of the maximum load on the critical link and of the route frequency because normally one has a sense of where the most crowded link on a public transport route is, and one can count the number of buses per hour, and estimate their occupancy from vehicle frequency and occupancy counts. One might know the total ridership on one route, but not all of them, so one can estimate the total demand on the corridor for all the routes by using an average renovation rate on the corridor. To do this, the formula can be rewritten as follows:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 948-954: code points 1-28

Eq. 6.3 can be rewritten:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 956-956: code points 1-25

$\text{Ren}_\text{route} = {{D}_\text{route} \over \text{MaxLoad}_\text{route}}  \Leftrightarrow  \text{D}_\text{route} = \text{MaxLoad}_\text{route} * \text{Ren}_\text{route}$\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 958-958: code points 1-178

This is simply true by definition. Remember that the renovation rate of the route is by definition the total demand on the route divided by the maximum load on the critical link, or that the demand on the route is a function of the maximum load on the critical link multiplied by the renovation rate.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 960-962: code points 1-99

We can then replace Droute and Twait from Equation 6.2 and Equation 6.6 in Equation 6.7, so that we have:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 964-965: code points 1-5

Eq. 6.8b:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 967-967: code points 1-9

$ \text{WaitCost}_\text{route} = \text{D}_\text{route} * \text{Cost}_\text{wait} * \text{T}_\text{wait}$\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 969-969: code points 1-106

$ \text{WaitCost}_\text{route}= {\text{MaxLoad}_\text{route} *\text{Ren}_\text{route} * \text{Cost}_\text{wait} * 0.5  * (1 + \text{Irr}_\text{route}) \over \text{Freq}_\text{route} }$\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 971-971: code points 1-186

Where:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 973-974: code points 1-0

\begin{itemize}
\item $ \text{WaitCost}_\text{route}$ = Total waiting time cost generated to the route users (now in \$\slash{}hour because instead of giving Droute absolute value in passengers, it is being given in passengers\slash{}hour);% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 974-976: code points 1-0
\item $ \text{Ren}_\text{route}$: Renovation factor of a route;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 976-977: code points 1-0
\item $ \text{MaxLoadroute}$: Route demand on the critical link (now in passengers\slash{}hour or “pax” per hour);% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 977-978: code points 1-0
\item $ \text{Cost}_\text{wait}$: Average user waiting cost (\$\slash{}time);% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 978-979: code points 1-0
\item $ \text{Irr}\text{route}$: Irregularity index of the route; measure of the variance between the actual headways and the scheduled headways (usually near 0.3, see Section 6.3.9);% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 979-981: code points 1-0
\item $\text{Freq}_\text{route}$: Frequency of the route (vehicles\slash{}time).% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 981-981: code points 1-75
\end{itemize}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 974-981: code points 1-75

\subsection{15}{Vehicle Operating Cost}
\label{volume:operations:chapter:service-planning:section:basic-service-planning-concepts:subSection:vehicle-operating-cost}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 983-1024: code points 1-80

Often, in service planning, the costs of waiting for customers, which is a function of the frequency and regularity of service, will need to be balanced against the cost of operating more vehicles. As the costs of waiting have been calculated for the peak hour above, to make a valid comparison the vehicle operating costs should also be derived per hour. The formulas below can be used to estimate cost per bus (Costbus) and the fixed cost per bus (BusFixedCost or Costbus-fixed). Vehicle operating cost per hour is simply the total cost of operating a vehicle divided by the number of hours a vehicle is in service.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 985-990: code points 1-108

The fixed operating cost of a vehicle is the part of the vehicle operating cost that does not depend of the number of customers carried nor the size of the vehicle. It can be thought of as the cost operators would incur if they put a second vehicle in operation, but that vehicle never opened its doors and always ran empty. It is mostly the cost of the driver, but also the minimum cost in terms of fuel and maintenance that any vehicle would incur regardless of its size. This figure is important to calculating the optimal fleet size. This part of the cost exists whether one is expressing the costs per route, per vehicle, per vehicle hour, or per vehicle kilometer.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 992-998: code points 1-43

To calculate the total fixed operational cost for a route, simply multiply the fixed operating cost per vehicle times the total fleet needed to service that route, or:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 1000-1001: code points 1-67

Eq. 6.9:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 1003-1003: code points 1-8

$\text{RouteFixedCost} = \text{BusFixedCost} * \text{Fleet}_\text{route} $\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 1005-1005: code points 1-76

Where:\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 1007-1008: code points 1-0

\begin{itemize}
\item $ \text{RouteFixedCost}$: Total fixed operational cost for the route;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 1008-1009: code points 1-0
\item $ \text{BusFixedCost}$: Fixed operating costs per vehicle;% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 1009-1010: code points 1-0
\item $ \text{Fleet}_\text{route}$: Number of buses needed to operate the route.% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 1010-1010: code points 1-82
\end{itemize}
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 1008-1010: code points 1-82

Total operating cost per vehicle goes down when a stop is removed, as the speed of the vehicles increases. As such, total vehicle operating costs are used in Section 6.7 on limited stop services. When optimizing the size of the vehicle, as in Section 6.4, as well as when comparing direct against trunk-and-feeder services in Section 6.6, it is only the fixed costs of vehicle operation that need to be known because it will be necessary to determine the benefits of using larger vehicles, and what is eliminated by using larger vehicles is the cost of the vehicle that does not go up proportionally with the size of the vehicle. It can be calculated by simply calculating the hourly operating cost of the smallest vehicle in the fleet. Typically, this ranges from US\$10 to US\$100 per bus hour. It will vary from country to country, but not much from city to city, so it only needs to be calculated once in a given city or country. The BusFixedCosts value consists of a list of average costs per vehicle. Fixed maintenance and fuel costs, which are likely to vary somewhat by vehicle size, should be calculated for the smallest vehicle being considered, and any additional costs for these will be included in variable costs. In most of this chapter one should use a common $ \text{Cost}_\text{bus-fixed} $ value of US\$30 per vehicle hour.\par
% @ guide/06-service_planning/63-basic-service-planning-concepts.src: lines 1012-1024: code points 1-80

\section{4}{Optimizing Vehicle Size and Fleet Size}
\label{volume:operations:chapter:service-planning:section:optimizing-vehicle-size-and-fleet-size}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1-1158: code points 1-7

The approach to service planning laid out in this guide generally assumes that the system operators can and will adjust the number of vehicles they operate per route, and the size of the vehicles used on each route, to best serve the demand on each route.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 3-3: code points 1-255

This section covers some basic formulas needed to calculate the vehicle fleet and optimal vehicle size. These are two critical considerations when making service planning decisions, so they are covered first. The two decisions have to be made at the same time, since the larger the vehicle, the smaller the fleet. The process of optimizing vehicle size and fleet size is an iterative one.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 5-5: code points 1-388

Selecting an appropriate vehicle size requires balancing the operational cost savings of larger vehicles with the social costs of customers having to wait longer for the next vehicle. There are returns to scale with larger vehicles; the cost per customer served tends to fall with size. Drivers usually represent a disproportionate share of vehicle operating costs, and as the number of drivers is generally fixed and does not change with vehicle size, the cost of the driver relative to the total customers tends to fall the larger the vehicle.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 7-12: code points 1-28

On the other hand, larger vehicles also directly translate into lower frequency, and lower frequency means longer waiting times. Therefore, the costs of these two effects need to be measured in specific conditions when selecting an optimal vehicle size.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 14-16: code points 1-50

Given the goal of having the lowest possible costs using the design load factor, if the vehicle size has been decided (there are only a limited number of options), and the route has been decided and its demand estimated, then the fleet size can be easily calculated. The fleet size is calculated based on the number of vehicles needed to serve the maximum customer load on the highest demand section of the corridor during the peak time, as is explained in detail below.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 18-22: code points 1-63

\subsection{1}{Vehicle Sizing, Basic Concepts}
\label{volume:operations:chapter:service-planning:section:optimizing-vehicle-size-and-fleet-size:subSection:vehicle-sizing-basic-concepts}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 24-113: code points 1-54

Vehicle types for BRT systems are not infinite, and for vehicles to operate inside a BRT corridor, there is rarely such low demand that a vehicle smaller than nine meters is ever likely to make sense. While new models are being launched in this market, manufacturers do not make an infinite number of vehicle sizes that are compatible with BRT infrastructure, so in general the range of vehicle options is limited to those listed in Table 6.6.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 26-31: code points 1-0

\tabletitle{6}{Range of BRT Vehicle Options}
\label{chapter:service-planning:table:range-of-brt-vehicle-options}
\halign to 30\tablemodule{%
	\vtop{\sffamily\footnotesize\noindent\hsize=11\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=9\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=8\tablemodule#}\cr
	\color{gray75}\bfseries Type& \color{gray75}\bfseries Vehicle Length (meters)& \color{gray75}\bfseries Capacity (customers) \cr
	\noalign{\vskip 1mm} \hline \noalign{\vskip 2mm} 
	\color{gray50}Minibus&
	\color{gray50}9&
	\color{gray50}60\cr
	\noalign{\vskip 2mm 
}	\color{gray50}Bus&
	\color{gray50}12&
	\color{gray50}90\cr
	\noalign{\vskip 2mm 
}	\color{gray50}Articulated&
	\color{gray50}18&
	\color{gray50}150\cr
	\noalign{\vskip 2mm 
}	\color{gray50}Bi-Articulated&
	\color{gray50}25&
	\color{gray50}220\cr
	\noalign{\vskip 2mm 
}}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 31-52: code points 1-9

In practice, the number of systems that use 9 meter or bi-articulated buses is quite limited. Most BRT systems use either 12-meter buses or 18-meter articulated buses. Bi-articulated buses are very expensive, generally double the cost of an articulated bus, and their primary use is in corridors with very high demand with very limited road space. They were first introduced in Curitiba by Volvo, and since then some are also in use in Mexico City on the Insurgentes Corridor, in TransMilenio in Bogotá, and in Istanbul. A few new BRT systems are planning to use 9-meter buses, but so far none are operational.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 54-59: code points 1-89

Note that the relationship between the vehicle length and the vehicle capacity is roughly the length (in meters) minus three (meters for the driver\slash{}engine\slash{}stairs, etc.) times 10 (or 10 customers per meter of operable bus length), or:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 61-63: code points 1-28

Eq. 6.10:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 65-65: code points 1-9

$ \text{V}_\text{Size} = (V_\text{Length} – 3) * 10 $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 67-67: code points 1-55

Where:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 69-69: code points 1-6

\begin{itemize}
\item $ \text{V}_\text{Size}$: Vehicle capacity in passengers (also written “pax”);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 71-72: code points 1-0
\item $ \text{V}_\text{Length}$: Vehicle length in meters.% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 72-72: code points 1-60
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 71-72: code points 1-60

At the early stages of planning BRT services, one generally looks at the highest demand routes currently using the planned BRT corridor, and measures the maximum load on the critical link, i.e., the highest demand segment during the peak period.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 74-76: code points 1-38

The vehicle capacity (VSize) should be roughly equal to the maximum hourly load per route on the critical link (MaxLoad) divided by the frequency (Freq), or:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 78-79: code points 1-51

Eq. 6.11a:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 81-81: code points 1-10

$ \text{V}_\text{Size} = { \text{MaxLoad} \over \text{Freq} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 83-83: code points 1-84

Where:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 85-85: code points 1-6

\begin{itemize}
\item $ \text{V}_\text{Size}$: Vehicle capacity;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 87-88: code points 1-0
\item $ \text{MaxLoad}$: Maximum hourly load on the critical link;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 88-89: code points 1-0
\item $ \text{Freq}$: Frequency;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 89-90: code points 1-0
\item $ \text{LoadFactor}$: Design load factor (usually 0.85).% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 90-90: code points 1-64
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 87-90: code points 1-64

This becomes clear by seeing the impact that vehicle size has on frequency:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 92-92: code points 1-75

Eq. 6.11b:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 94-94: code points 1-10

$ \text{Freq} = { \text{MaxLoad} \over \text{V}_\text{Size} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 96-96: code points 1-84

Or a third format as follows:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 98-98: code points 1-29

Eq. 6.11c:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 100-100: code points 1-10

$ \text{Freq} *  \text{V}_\text{Size} * \text{LoadFactor} = \text{MaxLoad} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 102-102: code points 1-78

As examples of capacity:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 104-104: code points 1-24

\begin{itemize}
\item {To serve 4,500 passengers (per hour per direction) on the critical link, a corridor may have:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 106-107: code points 7-0

\begin{itemize}
\item 50 buses (per hour) capable of carrying 90 passengers each; or% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 107-108: code points 1-0
\item 30 buses (per hour) capable of carrying 150 passengers each; or% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 108-109: code points 1-0
\item 18 buses (per hour) capable of carrying 250 passengers each.% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 109-109: code points 1-66
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 107-109: code points 1-66

}
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 106-109: code points 1-67

\begin{itemize}
\item {To serve 900 passengers (per hour), a corridor may have:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 111-112: code points 7-0

\begin{itemize}
\item 10 buses (per hour) serving 90 passengers each;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 112-113: code points 1-0
\item 6 buses (per hour) serving 150 passengers each.% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 113-113: code points 1-53
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 112-113: code points 1-53

}
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 111-113: code points 1-54

\subsection{2}{Vehicle Sizing, Initial Iteration}
\label{volume:operations:chapter:service-planning:section:optimizing-vehicle-size-and-fleet-size:subSection:vehicle-sizing-initial-iteration}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 115-180: code points 1-40

For reasons that will be explained in greater detail below, it is generally optimal to have a frequency set at about twenty-two vehicles per hour per route, as this tends to minimize the irregularity with which vehicle services operate while also minimizing waiting time. Once the frequency is above thirty or so, irregularity becomes a serious problem. At that point, it is generally advisable to introduce additional routes (i.e., limited stop routes, or routes serving other off-corridor destinations) rather than simply continuing to increase frequency or procuring larger and larger vehicles.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 117-122: code points 1-85

Since the BRT-compatible vehicle options are fairly limited, and generally the MaxLoad is known on existing bus routes from frequency and occupancy counts, it is sufficient as a starting point to use that maximum hourly load to determine vehicle size needed for each route. If the existing public transport routes’ maximum load is known, some estimate of what demand will be like in ten years needs to be made, as the vehicle is likely to last ten years. A reasonably secure methodology is to double existing ridership on the route, and divide by twenty-two vehicles per hour (an optimal frequency).\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 124-129: code points 1-80

Vehicle size can be determined by taking a given maximum load and dividing it by an ideal frequency of twenty-two vehicles per hour (Eq. 6.11a applied to the route):\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 131-132: code points 1-65

Eq. 6.11d:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 134-134: code points 1-10

$ \text{VSize}_\text{route} = { \text{MaxLoad}_\text{route}\over \text{Freq}_\text{route}* \text{LoadFactor}_\text{route}} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 136-136: code points 1-126

Where:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 139-139: code points 1-6

\begin{itemize}
\item $ \text{VSize}_\text{route} $: Vehicle serving the route capacity;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 141-142: code points 1-0
\item $ \text{MaxLoad}_\text{route} $: Route demand on the critical link;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 142-143: code points 1-0
\item $ \text{Freq} \text{route} $: Frequency of the route (ideal frequency suggested of 22 vehicles per hour);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 143-144: code points 1-0
\item $ \text{LoadFactor} $: Design load factor (usually 0.85).% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 144-144: code points 1-65
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 141-144: code points 1-65

Using that formula as a preliminary first pass, Table 6.7 shows that, with a maximum load greater than 3,500 existing customers per route, and a maximum 10-year estimated future load of 7,000, a frequency of 22 vehicles per hour, and a load factor of 0.85, the route should be separated into separate routes. If the maximum load on the critical link of a BRT route is currently between 1,500 and 3,000, bi-articulated buses can be used, but splitting the route should also be considered, as bi-articulated buses are expensive to purchase and maintain. For current loads between 1,000 and 1,500, articulated buses should be considered. Most BRT systems have more than one route per BRT corridor.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 146-152: code points 1-87

\tabletitle{7}{Bus Size by Varying MaxLoad per Route Using the Ideal Frequency of Twenty-Two Vehicles per Hour: First Iteration for Bus Sizing}
\label{chapter:service-planning:table:bus-size-by-varying-maxload-per-route-using-the-ideal-frequency-of-twenty-two-vehicles-per-hour-first-iteration-for-bus-sizing}
\halign to 30\tablemodule{%
	\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=12\tablemodule#}\cr
	\color{gray75}\bfseries Existing Max Load& \color{gray75}\bfseries Future Max Load& \color{gray75}\bfseries Optimal Size& \color{gray75}\bfseries Proposal \cr
	\noalign{\vskip 1mm} \hline \noalign{\vskip 2mm} 
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	\color{gray50}Split the route\cr
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	\color{gray50}Split the route\cr
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	\color{gray50}Split the route\cr
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	\color{gray50}267&
	\color{gray50}Split the route\cr
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	\color{gray50}214&
	\color{gray50}Bi-articulated or split route\cr
	\noalign{\vskip 2mm 
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	\color{gray50}3500&
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	\color{gray50}Bi-articulated or split route\cr
	\noalign{\vskip 2mm 
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	\color{gray50}3000&
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	\color{gray50}Bi-articulated or split route\cr
	\noalign{\vskip 2mm 
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	\color{gray50}Articulated\cr
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	\noalign{\vskip 2mm 
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	\color{gray50}12 meter bus\cr
	\noalign{\vskip 2mm 
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	\color{gray50}1000&
	\color{gray50}53&
	\color{gray50}9 meter bus\cr
	\noalign{\vskip 2mm 
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	\color{gray50}27&
	\color{gray50}9 meter bus\cr
	\noalign{\vskip 2mm 
}}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 154-170: code points 1-9

This very initial estimate takes into consideration the need to minimize irregularity, but it does not consider the more critical element in bus size optimization, namely the relative costs of waiting (which will be higher for larger buses operating at lower frequencies) and the fixed cost of vehicle operation (which will be lower per customer for larger vehicles). Final vehicle size optimization will need to weigh these relative costs before finalizing the size.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 172-176: code points 1-62

This should only be a first iteration of vehicle size optimization. These preliminary vehicle-capacity figures can be used to calculate the necessary fleet, before returning to a more detailed methodology of calculating the optimal vehicle size.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 178-180: code points 1-40

\subsection{3}{Detailed Vehicle Size Optimization}
\label{volume:operations:chapter:service-planning:section:optimizing-vehicle-size-and-fleet-size:subSection:detailed-vehicle-size-optimization}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 182-336: code points 1-61

Further along in the planning process, when the design team already has a general idea of the sorts of services that will operate and their likely maximum loads at the critical link should have been developed, the following approach gives a more refined methodology for calculating the optimal vehicle size. This approach initially assumes there is no limitation to the size of vehicles available, that limitation will be considered in the application examples.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 184-188: code points 1-47

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/0ab6a8a5805dabc3c7d8ad0797e0f99b98870250.jpeg}
		\fignote{24}{The social cost of waiting (blue line) increases and operational costs (red line) decrease as bus size increases. The trick is to balance the two to find the optimum where the sum of costs is minimized. Image\label{chapter:service-planning:figure:the-social-cost-of-waiting-blue-line-increases-and-operational-costs-red-line-decrease-as-bus-size-increases-the-trick-is-to-balance-the-two-to-find-the-optimum-where-the-sum-of-costs-is-minimized-image}}{Elebeta.}
	}
\fi

Put another way, vehicle capacity should be set where the cost of waiting faced by the users of that route (WaitCost) added to the fixed operating costs (FixedCost) of the route are minimized.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 194-195: code points 1-91

The total wait cost for a route ($\text{WaitCost}_\text{route}$) can be written as a function of bus capacity (VSize), by replacing Equation 6.11a:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 197-198: code points 1-28

$ \text{V}_\text{Size} = { \text{MaxLoad} \over \text{Freq} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 200-200: code points 1-84

with Eq. 6.2\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 202-202: code points 1-12

$ \text{Freq} = {\text{MaxLoad} \over {V_\text{Size} * \text{LoadFactor}}} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 204-204: code points 1-78

Resulting in Eq. 6.12:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 206-206: code points 1-22

$ \text{WaitCost}_\text{route} = { {\text{MaxLoad}_\text{route} *\text{Ren}_\text{route} *\text{Cost}_\text{wait} *  0.5 * ( 1+ Irr_\text{route} ) } \over ( { \text{MaxLoad}_\text{route} \over {\text{LoadFactor}*\text{VSize}} } ) } $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 208-208: code points 1-235

$ \text{WaitCost}_\text{route} =  \text{Ren}_\text{route} * \text{Cost}_\text{wait} * 0.5 * (1+ Irr_\text{route}) *\text{LoadFactor} * \text{VSize} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 210-210: code points 1-151

Where:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 212-212: code points 1-6

\begin{itemize}
\item $\text{WaitCostRoute}$: Total waiting time cost generated to the route users (in \$);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 214-215: code points 1-0
\item $\text{MaxLoadroute}$: Route demand on the critical link;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 215-216: code points 1-0
\item $\text{Renroute}$: Renovation factor of the route;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 216-217: code points 1-0
\item $ \text{Costwait}$ Average user waiting cost (\$\slash{}time);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 217-218: code points 1-0
\item $ \text{Irr}\text{route}$: Irregularity index of the route; measure of the variance between the actual headways and the scheduled headways (usually near 0.3, see Section 6.3.9);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 218-220: code points 1-0
\item $\text{Freq}_\text{route}$: Frequency of the route;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 220-221: code points 1-0
\item $ \text{V}_\text{Size}$: Vehicle capacity;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 221-222: code points 1-0
\item $ \text{MaxLoad}$: Maximum hourly load on the critical link;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 222-223: code points 1-0
\item $ \text{LoadFactor}$: Design load factor (usually 0.85).% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 223-223: code points 1-64
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 214-223: code points 1-64

This shows that the cost to the customer rises as frequency falls. Hence, from the customer’s perspective, the larger the vehicle, the more time he or she has to spend waiting for it. On a high-demand corridor, there is usually high frequency, and the wait will be short, but there will be many more customers suffering the wait.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 225-228: code points 1-9

Assuming the other values are known (and they are estimated once a service plan is proposed), this can be expressed as:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 230-231: code points 1-20

Eq. 6.13\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 233-233: code points 1-8

$ \text{WaitCost}_\text{route} = A * VSize $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 235-235: code points 1-46

Where:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 237-238: code points 1-0

\begin{itemize}
\item $\text{WaitCostRoute}$: Total waiting time cost to the route users (in \$);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 238-239: code points 1-0
\item $\text{V}_\text{Size}$: Vehicle capacity;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 239-240: code points 1-0
\item $A$: Known constant value% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 240-240: code points 1-33
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 238-240: code points 1-33

$ A =\text{Ren}_\text{route} * \text{Cost}_\text{wait} * 0.5 * (1+ Irr_\text{route}) *\text{LoadFactor} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 242-242: code points 3-109

At the same time, fixed operating costs do not vary with vehicle size: the cost of the driver; the cost of the bus company’s overhead, the minimum cost of fueling any vehicle, and maintaining any vehicle no matter its size.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 244-246: code points 1-19

So the total fixed costs of a route operation are only a function of the route fleet (as proposed in Equation 6.9:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 248-249: code points 1-13

$\text{RouteFixedCost} = \text{BusFixedCost} * \text{Fleet}_\text{route} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 251-251: code points 1-76

The route fleet (the number of vehicles needed to serve a route) is, in turn, dependent on the vehicle capacity (VSize) according to the following:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 253-254: code points 1-44

Eq. 6.14:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 256-256: code points 1-9

$ \text{Fleet}_\text{route} = {\text{MaxLoadperCycle}_\text{route} \over {\text{VSize} * \text{LoadFactor}}} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 258-258: code points 1-112

Where:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 260-260: code points 1-6

\begin{itemize}
\item $ \text{Fleet}_\text{route}$: Number of vehicles needed to serve the route;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 262-263: code points 1-0
\item $ \text{VSize}_\text{route}$: Vehicle serving the route capacity;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 263-264: code points 1-0
\item $ \text{MaxLoadperCycle}\text{route}$: Maximum demand across the critical segment of the route that will accumulate for the duration of one cycle during the busiest moment of the typical day (see Subsection 6.3.13);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 264-266: code points 1-0
\item $ \text{Freq}_\text{route}$: Frequency of the route (ideal frequency suggested of 22 vehicles per hour);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 266-267: code points 1-0
\item $ \text{LoadFactor}$: Design load factor (usually 0.85).% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 267-267: code points 1-64
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 262-267: code points 1-64

In one extreme, if the route operated with a vehicle as large as the demand willing to cross the critical segment of the route that would be waiting for the duration of one cycle, only one vehicle would be needed.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 269-270: code points 1-107

As the vehicle operating on the route is smaller, the necessary fleet to carry all these customers will be larger, and so the fixed costs will be higher.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 272-273: code points 1-54

If we apply Equation 6.14 in Equation 6.11a we have:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 275-275: code points 1-52

$ \text{FixedCost}_\text{route} = {\text{BusFixedCost} * \text{MaxLoadperCycle}_\text{route} \over { \text{VSize}*\text{LoadFactor}}} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 277-277: code points 1-137

Assuming the other values are known (and they are estimated once a service plan is proposed), this can be expressed as:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 279-280: code points 1-20

Eq. 6.15:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 282-282: code points 1-9

$ \text{FixedCost}_\text{route} = {B \over \text{VSize} } $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 284-284: code points 1-61

Where:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 286-287: code points 1-0

\begin{itemize}
\item $ \text{FixedCost}_\text{route}i $: Total fixed operating cost for the route (in \$\slash{}hour);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 287-288: code points 1-0
\item $ \text{VSize}_\text{route} $: Vehicle serving the route capacity;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 288-289: code points 1-0
\item $ B $: Known constant value:% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 289-289: code points 1-36
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 287-289: code points 1-36

$ B = {\text{BusFixedCost}*\text{MaxLoadperCycle}_\text{route} \over \text{LoadFactor}} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 291-291: code points 1-91

The graph in Figure 6.24 simply shows that the total social cost of waiting (the blue line) rises in direct linear proportion to the vehicle capacity, while the total fixed operational cost falls with vehicle capacity. The minimum total cost will be where Cw total (1 hour) = Cf total (1 hour).\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 294-296: code points 1-85

The vehicle size that minimizes the cost of waiting imposed on the users (WaitCost) added to the fixed operating costs (FixedCost) to a given planned route is a vehicle size where FixedCost and WaitCost are equal.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 298-300: code points 1-6

$ {{d(\text{WaitCost}_\text{route} + \text{FixedCost}_\text{route})} \over {d(\text{VSize})}} = { {d( A * \text{VSize} + {B \over \text{VSize}} )} \over {d(VSize)} } =  A - {{B} \over {\text{VSize}^2}} =0 $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 302-302: code points 1-208

$  A - { {B} \over {\text{VSize}^2} } = 0  \Leftrightarrow  A =  {B \over { {\text VSize}^2}}  \Leftrightarrow  \text{VSize}^2 = {B \over A} \Leftrightarrow \text{VSize} = \sqrt{B \over A} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 304-304: code points 1-192

The vehicle capacity (VSize) that provides minimal added cost will result in:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 306-306: code points 1-77

$ \text{WaitCost}_\text{route} = A*\text{VSize} = A * \sqrt{B \over A} = \sqrt{{A^2 *B} \over{A}}  = \sqrt{A * B} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 308-308: code points 1-117

$ \text{FixedCost}_\text{route} = {B \over \text{VSize}} = {B \over \sqrt{B \over A}} = {B \over \sqrt{B \over A}} ({\sqrt{B \over A} \over \sqrt{B \over A}})= \sqrt{B^2 \over {B \over A}} =  \sqrt{A * B} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 310-310: code points 1-208

The optimal size is one where the waiting costs imposed on the last set of users from reducing the frequency is precisely equal to the benefits to the vehicle operator in terms of reduced operating costs of using a slightly larger vehicle. Any movement away from this point, and the total cost of customers waiting, plus operating costs, will be higher.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 312-315: code points 1-46

Therefore, optimal vehicle capacity ($ \text{VSize}_\text{optimum}$) is:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 317-317: code points 1-74

$ \text{VSize}_\text{optimum} = \sqrt{B \over A} = \sqrt{ {\text{BusFixedCost}*\text{MaxLoadperCycle}_\text{route} \over \text{LoadFactor}} \over {\text{Ren}_\text{route}*\text{Costi}_\text{wait}} * 0.5 * ( 1 + Irr_\text{route} * \text{LoadFactor}}  $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 319-319: code points 1-253

Eq. 6.16a:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 321-321: code points 1-10

$ \text{VSize}_\text{optimum}*\text{LoadFactor} = \sqrt{\text{BusFixedCost}*\text{MaxLoadperCycle}_\text{route} \over {\text{Ren}_\text{route}*\text{Costwait} * 0.5 (1+Irr_\text{route}} } $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 323-323: code points 1-191

Where:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 326-326: code points 1-6

\begin{itemize}
\item $ \text{VSize}_\text{optimum} $: Optimal size of vehicle to serve the route capacity;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 328-329: code points 1-0
\item $ \text{BusFixedCost}$: Total fixed operating cost for the route (in \$\slash{}hour);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 329-330: code points 1-0
\item $ \text{MaxLoadperCycle}_\text{route}$: Maximum demand across the critical segment of the route that will accumulate for the duration of one cycle during the busiest moment of the typical day (see Subsection 6.3.13);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 330-332: code points 1-0
\item $  \text{LoadFactor} $: Design load factor (usually 0.85);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 332-333: code points 1-0
\item $\text{Renroute}$: Renovation factor of the route;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 333-334: code points 1-0
\item $ \text{Costwait}$ Average user waiting cost (\$\slash{}time);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 334-335: code points 1-0
\item $ \text{Irr}\text{route}$: Irregularity index of the route; measure of the variance between the actual headways and the scheduled headways (usually near 0.3, see Section 6.3.9);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 335-336: code points 1-61
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 328-336: code points 1-61

\subsection{4}{Vehicle Size Optimization Formula Applied}
\label{volume:operations:chapter:service-planning:section:optimizing-vehicle-size-and-fleet-size:subSection:vehicle-size-optimization-formula-applied}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 338-440: code points 1-9

The following variables in Table 6.8 will be relatively constant, so the data can be collected either at the corridor level (Ren, Irr) or citywide (Costwait, BusFixedCost) and only needs to be done once. Below is some reasonable sample data, and because these tend to be consistent citywide, they can be turned into constants, except for the renovation rate, which needs to be calculated per corridor and is not consistent citywide.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 340-344: code points 1-20

\tabletitle{8}{Sample Data Used for Examples}
\label{chapter:service-planning:table:sample-data-used-for-examples}
\halign to 30\tablemodule{%
	\vtop{\sffamily\footnotesize\noindent\hsize=12\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\cr
	\color{gray75}\bfseries Variable& \color{gray75}\bfseries Symbol& \color{gray75}\bfseries Value& \color{gray75}\bfseries Unit \cr
	\noalign{\vskip 1mm} \hline \noalign{\vskip 2mm} 
	\color{gray50}Fixed operating cost per bus&
	\color{gray50}BusFixedCost&
	\color{gray50}30&
	\color{gray50}\$\slash{}bus\slash{}hour\cr
	\noalign{\vskip 2mm 
}	\color{gray50}Waiting cost per passenger&
	\color{gray50}Cost\_Wait&
	\color{gray50}12&
	\color{gray50}\$12\slash{}passenger\slash{}hour\cr
	\noalign{\vskip 2mm 
}	\color{gray50}Renovation factor on the corridor&
	\color{gray50}Ren\_route&
	\color{gray50}1.5&
	\color{gray50}\cr
	\noalign{\vskip 2mm 
}	\color{gray50}Irregularity Index on the corridor&
	\color{gray50}Irr\_route&
	\color{gray50}0.3&
	\color{gray50}\cr
	\noalign{\vskip 2mm 
}}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 346-352: code points 1-9

For this purpose, we can write Equation 6.16 as follows:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 354-354: code points 1-56

Eq. 6.16b:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 356-356: code points 1-10

$ \text{VSize}_\text{optimum} * \text{LoadFactor}= \sqrt{\text{BusFixedCost} *\text{MaxLoadperCycle}_\text{route} \over \text{Ren}_\text{corridor} *\text{Costwait} * 0.5* (1+Irr_\text{city})} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 358-358: code points 1-195

$ \text{VSize}_\text{optimum} * \text{LoadFactor}= \sqrt{ KA *\text{MaxLoadperCycle} } $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 360-360: code points 1-90

Where:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 362-363: code points 1-0

\begin{itemize}
\item $KA={\text{BusFixedCost} \over \text{Ren}_\text{corridor} *\text{Costwait} * 0.5* (1+Irr_\text{route})} $% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 363-363: code points 1-113
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 363-363: code points 1-113

Using the data from the table and applying it to Equation 6.16, then:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 365-365: code points 1-69

$ KA={30 \over 1.5*12*1+0.3*0.5 } = 2.56 $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 367-367: code points 1-44

In other words, so long as the basic information about fixed costs, the renovation rate, the irregularity rate, the cost of waiting, and so forth are all calculated for the corridor, the difference in the vehicle size for each route will be a function of the difference in the maximum load over the course of a cycle time under each scenario, or put another way, the number of customer places (Pl) that the vehicles need to serve.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 369-373: code points 1-9

In applying this to Equation 6.16, then:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 375-375: code points 1-40

$ \text{VSize}_\text{optimum} = \text{LoadFactor}=\text{MaxLoadperCycle}_\text{route} * 2.56 $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 377-377: code points 1-96

In this way, the optimum vehicle capacity is simply a function of the demand over the course of the route’s cycle time that needs to be served under each scenario, times a constant, this of course must be divided by design load factor. Some examples of an application of this formula are shown in Table 6.9, where each row represents a different scenario.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 379-382: code points 1-52

For expediency in the examples below in Table 6.9, approximate values for MaxLoadperCycle are assumed rather than determining the actual value across multiple cycle times. A peak hour correction factor (PHtoCC) of 0.1 is also assumed, which is relatively typical. Other values are given in Table 6.9.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 384-386: code points 1-89

Using Equation 6.11 and the values in Table 6.9, optimal vehicle size ($Cb_\text{optimum}$) can be solved for, as shown in the last column of Table 6.9.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 388-389: code points 1-41

Eq. 6.17\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 391-391: code points 1-8

$ \text{MaxLoadperCycle} = \text{MaxLoad} * TC * [ 1 - \text{PHtoCC} * (\text{TC} -1) ] $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 393-393: code points 1-91

Where:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 395-396: code points 1-0

\begin{itemize}
\item $ \text{MaxLoadperCycle}$: Maximum demand load per cycle time;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 396-397: code points 1-0
\item $ \text{MaxLoad}$: Maximum hourly load on the critical link;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 397-398: code points 1-0
\item $ \text{TC}$: Cycle time in hours.% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 398-399: code points 1-0
\item $ \text{PHtoCC}$: Nonnegative correction factor, the calibration of which is based on survey data, is discussed in Box 6.2.% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 399-399: code points 1-131
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 396-399: code points 1-131

\tabletitle{9}{Examples of Optimum Vehicle Size Derived from the Sample Data}
\label{chapter:service-planning:table:examples-of-optimum-vehicle-size-derived-from-the-sample-data}
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	\color{gray75}\bfseries MaxLoad& \color{gray75}\bfseries TC& \color{gray75}\bfseries PHtoCC& \color{gray75}\bfseries MaxLoadperCycle& \color{gray75}\bfseries Size*LoadFactor \cr
	\noalign{\vskip 1mm} \hline \noalign{\vskip 2mm} 
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	\noalign{\vskip 2mm 
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	\noalign{\vskip 2mm 
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	\color{gray50}7\cr
	\noalign{\vskip 2mm 
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	\color{gray50}1&
	\color{gray50}0.1&
	\color{gray50}180&
	\color{gray50}21\cr
	\noalign{\vskip 2mm 
}	\color{gray50}2,000&
	\color{gray50}1&
	\color{gray50}0.1&
	\color{gray50}1,800&
	\color{gray50}68\cr
	\noalign{\vskip 2mm 
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	\color{gray50}1&
	\color{gray50}0.1&
	\color{gray50}7,200&
	\color{gray50}136\cr
	\noalign{\vskip 2mm 
}	\color{gray50}20&
	\color{gray50}4&
	\color{gray50}0.1&
	\color{gray50}48&
	\color{gray50}11\cr
	\noalign{\vskip 2mm 
}	\color{gray50}200&
	\color{gray50}4&
	\color{gray50}0.1&
	\color{gray50}480&
	\color{gray50}35\cr
	\noalign{\vskip 2mm 
}	\color{gray50}2,000&
	\color{gray50}4&
	\color{gray50}0.1&
	\color{gray50}4,800&
	\color{gray50}111\cr
	\noalign{\vskip 2mm 
}	\color{gray50}8,000&
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	\noalign{\vskip 2mm 
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% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 401-415: code points 1-9

On this very wide range of maximum hourly loads and cycle times, optimum size assuming load factor equal to 1.0, varies from a car to a bi-articulated vehicle. If the optimal vehicle size ($\text{VSize}_\text{optimum}$) is four, in most cases the demand is too low to justify the procurement costs of special new BRT vehicles, and such small vehicles do not come in BRT-compatible forms, so are likely to congest the BRT corridor. Hence, this route would simply be excluded from the proposed BRT services, or turned into a feeder route for the BRT corridor. As BRT vehicle options are not actually infinite, once the optimal vehicle capacity is identified using the formula, VSizeoptimum will need to be set by rounding up to the nearest vehicle suitable for the BRT services and design load factor.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 417-424: code points 1-88

\tabletitle{10}{Examples for Determining Optimum Vehicle Size}
\label{chapter:service-planning:table:examples-for-determining-optimum-vehicle-size}
\halign to 30\tablemodule{%
	\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\hbox to 0.5\tablemodule{}&
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	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=6\tablemodule#}\cr
	\color{gray75}\bfseries MaxLoad& \color{gray75}\bfseries TC& \color{gray75}\bfseries PHtoCC& \color{gray75}\bfseries MaxLoadperCycle& \color{gray75}\bfseries Size*LoadFactor \cr
	\noalign{\vskip 1mm} \hline \noalign{\vskip 2mm} 
	\color{gray50}pass\slash{}h&
	\color{gray50}hours&
	\color{gray50}&
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	\noalign{\vskip 2mm 
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	\noalign{\vskip 2mm 
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	\color{gray50}4&
	\color{gray50}0.1&
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	\noalign{\vskip 2mm 
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	\noalign{\vskip 2mm 
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% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 426-440: code points 1-9

\subsection{5}{Vehicle Fleet Optimization}
\label{volume:operations:chapter:service-planning:section:optimizing-vehicle-size-and-fleet-size:subSection:vehicle-fleet-optimization}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 442-1158: code points 1-7

One of the key purposes of developing a service plan is to know how many vehicles will need to be purchased. The factors involved in determining the operational size of the vehicle fleet include:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 444-446: code points 1-0

\begin{itemize}
\item Maximum hourly load on the critical link of a corridor (MaxLoad);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 446-447: code points 1-0
\item Total cycle time (TC);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 447-448: code points 1-0
\item Capacity of the vehicle (VSize);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 448-449: code points 1-0
\item The degree to which demand is peaked (usually measured by a peak hour to cycle time correction factor, or PHtoCC as explained below);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 449-451: code points 1-0
\item The need for a reserve fleet.% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 451-451: code points 1-35
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 446-451: code points 1-35

A reserve fleet needs to be added to the total fleet size, as vehicles will need to be serviced either preventatively or because they have broken down. As a rule, a reserve fleet is about 10 percent of the actual fleet needed to provide the service, although it can be lower than that.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 453-455: code points 1-79

\subsubsection{1}{Vehicle Fleet Calculation with Uniform Demand}
\label{volume:operations:chapter:service-planning:section:optimizing-vehicle-size-and-fleet-size:subSection:vehicle-fleet-optimization:subSubSection:vehicle-fleet-calculation-with-uniform-demand}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 457-545: code points 1-8

As a first estimate of the fleet needed to provide a new BRT service, the maximum load on the critical link of the existing bus routes currently using the BRT corridor during the peak hour should be calculated. The existing bus route lengths and cycle times also need to be calculated. This can usually be done at low cost with a GPS. From this information it is possible to estimate the current needed fleet.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 459-462: code points 1-95

Eq. 6.18\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 464-464: code points 1-8

$ \text{Fleet}_\text{route} = {\text{MaxLoad}_\text{route} \over \text{VSize} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 467-467: code points 1-102

Where:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 469-469: code points 1-6

\begin{itemize}
\item $ \text{Fleet}_\text{route}$: Number of buses needed to serve the route;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 471-472: code points 1-0
\item $ \text{VSize}_\text{route}$: Vehicle serving the route capacity;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 472-473: code points 1-0
\item $ \text{MaxLoad}_\text{route}$:Maximum demand across the critical segment of the route that will accumulate for the duration of one hour, here is assumed constant;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 473-475: code points 1-0
\item $ \text{Freq}_\text{route}$:Frequency of the route;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 475-476: code points 1-0
\item $  \text{LoadFactor} $: Design load factor (usually 0.85);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 476-476: code points 1-66
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 471-476: code points 1-66

To provide an example, assume the following:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 478-478: code points 1-44

\begin{itemize}
\item $ \text{MaxLoad}_\text{route} = 224 $;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 480-480: code points 1-46
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 480-480: code points 1-46

\begin{itemize}
\item $ TC= 2 \text{hours} $% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 482-482: code points 1-30
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 482-482: code points 1-30

\begin{itemize}
\item $ \text{VSize} = 72 $;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 484-484: code points 1-30
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 484-484: code points 1-30

\begin{itemize}
\item $\text{Load Factor} = 0.85 $;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 486-486: code points 1-37
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 486-486: code points 1-37

$ Fleet = {224 * 2 \over 72 * 0.85}   = 7.32 $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 488-488: code points 1-48

If the formula produces a fraction, round up to the next integer, since vehicles have to be procured in units of one. So, in this scenario, the result is eight vehicles.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 490-491: code points 1-68

Once other service planning decisions have been made, and the route structure has been optimized and the vehicle size has been optimized, and future demand for this specific service scenario has been modelled, the fleet required for the new services should then again be calculated using this formula.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 493-495: code points 1-91

To explain this formula, begin with cycle time. If the total round-trip cycle time for the vehicle is two hours, at the end of one hour, the first vehicle will still have an hour to go before it can reach the beginning of the route and pick up a second load of customers. Since demand is uniform in this example, there will be the same number of customers on the critical link needing service in the second hour as during the first hour. As such, having a cycle time of two hours means that vehicles that travelled during the first hour will not be back to pick up customers on the critical link in the second hour. They will only just be starting their return trip. Thus, a second set of vehicles will be needed to serve the same demand on the critical link during the second hour while the first set of vehicles is returning. This is why one should multiply the MaxLoad by the cycle time. In this scenario, it is as if the number of customers is doubled.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 497-506: code points 1-21

If the cycle time were one, however, the same vehicle could return to the starting position after one hour to take the second hour of customers. Therefore, the same fleet can serve the demand on the critical link each hour (and in this scenario, the demand is the same each hour). Thus, cutting the cycle time to one cuts the needed fleet in half:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 508-511: code points 1-37

\begin{itemize}
\item $ \text{MaxLoad}_\text{route} = 224 $;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 513-513: code points 1-46
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 513-513: code points 1-46

\begin{itemize}
\item $ TC= 1 \text{hour} $% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 515-515: code points 1-29
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 515-515: code points 1-29

\begin{itemize}
\item $ \text{VSize} = 72 $;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 517-517: code points 1-30
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 517-517: code points 1-30

\begin{itemize}
\item $\text{Load Factor} = 0.85 $;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 519-519: code points 1-37
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 519-519: code points 1-37

$ Fleet = {224 * 1 \over 72 * 0.85}   = 3.66  $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 521-521: code points 1-49

As the fleet has to be rounded up to the nearest integer, it would be four vehicles.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 523-523: code points 1-84

For this reason deadheading, or running some buses in the contra-peak direction without customers, can reduce the total cycle time, and hence the fleet needed.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 525-526: code points 1-60

The size of the vehicle (VSize) is also important. Bigger vehicles can move the same number of customers with a smaller fleet. In the example above with a cycle time of two hours, if an articulated vehicle is used that can hold 180 customers, only three vehicles are needed:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 528-530: code points 1-68

\begin{itemize}
\item $ \text{MaxLoad}_\text{route} = 224 $;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 532-532: code points 1-46
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 532-532: code points 1-46

\begin{itemize}
\item $ TC= 2 \text{hours} $% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 534-534: code points 1-30
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 534-534: code points 1-30

\begin{itemize}
\item $ \text{VSize} = 180 $;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 536-536: code points 1-31
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 536-536: code points 1-31

\begin{itemize}
\item $\text{Load Factor} = 0.85 $;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 538-538: code points 1-37
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 538-538: code points 1-37

$ Fleet = {224 * 2 \over 180 * 0.85}   = 2.923 $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 540-540: code points 1-50

By increasing the vehicle size, the required fleet size decreases. This means fewer vehicles are required, but the result is that the frequency is lower, and customers will wait longer. Similarly, by decreasing the vehicle size, a larger fleet is needed, but frequency increases, and customers will not have to wait as long.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 542-545: code points 1-8

\subsubsection{2}{Fleet Calculation with Peaked Demand}
\label{volume:operations:chapter:service-planning:section:optimizing-vehicle-size-and-fleet-size:subSection:vehicle-fleet-optimization:subSubSection:fleet-calculation-with-peaked-demand}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 547-1158: code points 1-7

The above formula is good for rough calculations of fleet needs, but it is not sufficient to calculate the actual needed fleet in most real-world conditions where demand varies throughout the peak hours. Vehicles are expensive to purchase and operate, so more refined analysis is necessary.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 549-551: code points 1-86

To explain intuitively why the fleet needs for peaked demand are different than for uniform demand, the following example is useful. Assume a two-hour cycle time (TC) and sixty customers per vehicle (VSize), but this time, rather than assuming that MaxLoad is the same throughout three or four hours, from 6:00 a.m. to 9:00 a.m. assume that MaxLoad occurs only during the peak demand hour, let us say this is 6:45 a.m. to 7:45 a.m. just to get the idea.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 553-557: code points 1-39

With a two-hour cycle time, the first bus will return to pick up a second load of customers only after two hours. Thus, the total number of vehicles needed to serve the demand during the first peak hour is this plus the total needed to serve the demand during the second on-peak hour. A smaller fleet of vehicles is needed to serve that link during the second hour, because there are fewer customers.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 559-562: code points 1-87

The fleet needed is therefore not simply a function of the maximum load at the critical link and the vehicle size, but it is also a function of the cycle time and the degree to which demand is peaked.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 564-565: code points 1-99

Now, rather than simply calculating the fleet based on one single hourly demand, one must determine the maximum load on the critical link over the course of the cycle time, or MaxLoadperCycle. After the cycle time has passed, no more buses are needed as the first bus has returned to the beginning of the route.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 567-570: code points 1-6

The maximum load over the course of a cycle time is the total number of customers that will accumulate during one full route cycle time willing to cross the critical link on a given vehicle route. This can also be thought of as the number of passenger places that need to be served, or Pl.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 572-574: code points 1-83

Only so many vehicles are needed as would satisfy the customers that will accumulate before the first vehicle can complete its cycle and pick up a second round of customers. The original formula, Equation 6.5, can therefore be replaced with the following:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 576-578: code points 1-50

Eq. 6.19:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 580-580: code points 1-9

$ \text{Fleet}_\text{route} = {\text{MaxLoadperCycle}_\text{route} \over \text{VSize}*\text{LoadFactor}} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 582-582: code points 1-108

Where:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 584-585: code points 1-0

\begin{itemize}
\item $ \text{Fleet}_\text{route}$: Number of buses needed to serve the route;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 585-586: code points 1-0
\item $ \text{VSize}_\text{route}$: Vehicle serving the route capacity;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 586-587: code points 1-0
\item $ \text{MaxLoadperCycle}_\text{route}$: Maximum demand across the critical segment of the route that will accumulate for the duration of one cycle during the busiest moment of the typical day (see Subsection 6.3.13);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 587-589: code points 1-0
\item $ \text{Freq}_\text{route}$:Frequency of the route(ideal frequency suggested of 22 vehicles per hour);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 589-590: code points 1-0
\item $  \text{LoadFactor} $: Design load factor (usually 0.85);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 590-590: code points 1-66
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 585-590: code points 1-66

This then requires the development of a methodology for calculating the maximum load over the course of a specific cycle time.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 592-593: code points 1-25

At this point in the service planning effort, the service planner will have collected ridership data in fixed increments of time, such as fifteen-minute intervals, and determined the critical link. With that data, in order to calculate the fleet requirements, two questions must be answered:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 595-598: code points 1-0

\begin{enumerate}
\item Given an expected cycle time (TC) period for a BRT route, what “TC period” of the day experiences the highest demand?% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 598-600: code points 1-0
\item How does one calculate fleet numbers based on the peak TC period?% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 600-600: code points 1-73
\end{enumerate}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 598-600: code points 1-73

In order to answer the first question, the example in Table 6.11 is a sample of fifteen-minute increment ridership data. In this example, the cycle time (TC) is one hour, so one should look for the peak hour.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 602-604: code points 1-0

\tabletitle{11}{Peak Period Critical Link Demand Profile for a Bus Route over Fifteen-Minute Increments and One-Hour TC Increments}
\label{chapter:service-planning:table:peak-period-critical-link-demand-profile-for-a-bus-route-over-fifteen-minute-increments-and-one-hour-tc-increments}
\halign to 30\tablemodule{%
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	\color{gray75}\bfseries 15-Minute Time Increment& \color{gray75}\bfseries 15-Minute Observed Demand& \color{gray75}\bfseries One-Hour Time Increment& \color{gray75}\bfseries TC = One- Hour Accumulated Demand \cr
	\noalign{\vskip 1mm} \hline \noalign{\vskip 2mm} 
	\color{gray50}6:00–6:15&
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	\color{gray50}N\slash{}A&
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	\noalign{\vskip 2mm 
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	\color{gray50}31&
	\color{gray50}N\slash{}A&
	\color{gray50}N\slash{}A\cr
	\noalign{\vskip 2mm 
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	\color{gray50}51&
	\color{gray50}6:00–7:00&
	\color{gray50}118\cr
	\noalign{\vskip 2mm 
}	\color{gray50}7:00–7:15&
	\color{gray50}63&
	\color{gray50}6:15–7:15&
	\color{gray50}166\cr
	\noalign{\vskip 2mm 
}	\color{gray50}7:15–7:30&
	\color{gray50}69&
	\color{gray50}6:30–7:30&
	\color{gray50}214\cr
	\noalign{\vskip 2mm 
}	\color{gray50}7:30–7:45&
	\color{gray50}67&
	\color{gray50}6:45–7:45&
	\color{gray50}250\cr
	\noalign{\vskip 2mm 
}	\color{gray50}\emphasis{7:45–8:00}&
	\color{gray50}\emphasis{66}&
	\color{gray50}\emphasis{7:00–8:00}&
	\color{gray50}\emphasis{265}\cr
	\noalign{\vskip 2mm 
}	\color{gray50}8:00–8:15&
	\color{gray50}53&
	\color{gray50}7:15–8:15&
	\color{gray50}255\cr
	\noalign{\vskip 2mm 
}	\color{gray50}8:15–8:30&
	\color{gray50}45&
	\color{gray50}7:30–8:30&
	\color{gray50}231\cr
	\noalign{\vskip 2mm 
}	\color{gray50}8:30–8:45&
	\color{gray50}34&
	\color{gray50}7:45–8:45&
	\color{gray50}198\cr
	\noalign{\vskip 2mm 
}	\color{gray50}8:45–9:00&
	\color{gray50}32&
	\color{gray50}8:00–9:00&
	\color{gray50}164\cr
	\noalign{\vskip 2mm 
}	\color{gray50}9:00–9:15&
	\color{gray50}21&
	\color{gray50}8:15–9:15&
	\color{gray50}132\cr
	\noalign{\vskip 2mm 
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% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 604-675: code points 1-9

In Table 6.11, ridership data was collected and entered in fifteen-minute increments (“Fifteen-Minute Observed Demand”).\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 677-678: code points 1-18

Here the column on the right shows the accumulated demand over each distinct one-hour (i.e., TC) period. For example, from 6:00 to 7:00, all of the demand observed passing the critical link from 6:00 to 6:15, 6:15 to 6:30, 6:30 to 6:45, and 6:45 to 7:00 has accumulated, for a total of 118. Since a full hour has not yet passed until 7:00, N\slash{}A is entered into the first three cells.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 680-683: code points 1-69

Now Question 1—what is the highest demand period for a given cycle time?—can be answered by looking at the table and choosing the hour with the greatest accumulated demand. In this case, it is 7:00–8:00 when accumulated demand reaches its maximum at 265 (the row highlighted in yellow). This is called the maximum load per cycle time (MaxLoadperCycle). If the cycle time is one hour, the final result is MaxLoadperCycle = 265.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 685-689: code points 1-6

If the cycle time TC were two hours, the table would look different:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 691-692: code points 1-0

\tabletitle{12}{Peak Period Critical Link Demand Profile over Fifteen-Minute Increments and Two-Hour TC Increments}
\label{chapter:service-planning:table:peak-period-critical-link-demand-profile-over-fifteen-minute-increments-and-two-hour-tc-increments}
\halign to 30\tablemodule{%
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	\color{gray75}\bfseries 15-Minute Time Increment& \color{gray75}\bfseries 15-Minute Observed Demand& \color{gray75}\bfseries Two-Hour Time Increment& \color{gray75}\bfseries TC = Two- Hour Accumulated Demand \cr
	\noalign{\vskip 1mm} \hline \noalign{\vskip 2mm} 
	\color{gray50}6:00–6:15&
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	\color{gray50}21&
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	\noalign{\vskip 2mm 
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	\color{gray50}31&
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	\noalign{\vskip 2mm 
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	\noalign{\vskip 2mm 
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	\noalign{\vskip 2mm 
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	\noalign{\vskip 2mm 
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	\color{gray50}\emphasis{448}\cr
	\noalign{\vskip 2mm 
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	\noalign{\vskip 2mm 
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% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 692-763: code points 1-9

With a two-hour cycle time, the MaxLoadperCycle becomes 6:45–8:45 with a maximum demand of 448. Here, MaxLoadperCycle = 448.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 765-766: code points 1-22

If, on the other hand, the cycle time were fifteen minutes, the peak would be 7:15–7:30 and the MaxLoadperCycle = 69.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 768-769: code points 1-5

Now to address Question 2—how to calculate fleet numbers based on the peak TC period. There are two ways to obtain the fleet numbers. The simplest way is to determine the peak load over the course of the cycle time ($ L_\text{peak}[TC]$), as shown above, and simply divide by vehicle capacity. That is:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 771-773: code points 1-100

Eq. 6.20:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 775-775: code points 1-9

$ \text{Fleet}_\text{route} = {\text{MaxLoadperCycle}_\text{route} \over \text{VSize}*\text{LoadFactor}} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 777-777: code points 1-108

Where:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 779-780: code points 1-0

\begin{itemize}
\item $ \text{Fleet}_\text{route}$: Number of buses needed to serve the route;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 780-781: code points 1-0
\item $ \text{VSize}_\text{route}$: Vehicle serving the route capacity;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 781-782: code points 1-0
\item $ \text{MaxLoadperCycle}_\text{route}$: Maximum demand across the critical segment of the route that will accumulate for the duration of one cycle during the busiest moment of the typical day (see Subsection 6.3.13);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 782-784: code points 1-0
\item $ \text{Freq}_\text{route}$:Frequency of the route(ideal frequency suggested of 22 vehicles per hour);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 784-785: code points 1-0
\item $  \text{LoadFactor} $: Design load factor (usually 0.85);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 785-785: code points 1-66
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 780-785: code points 1-66

So, for a TC of one hour, using the observed $\text{MaxLoadperCycle}$ of 265, it is calculated that:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 787-787: code points 1-102

$ \text{Fleet}(TC=1 \text{hour}) = { 265 \over 72 * 0.85} = 4.33 $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 789-789: code points 1-68

Thus, the fleet needed for that peak cycle time is five.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 791-791: code points 1-56

So, for a TC of two hours, using the actual $\text{MaxLoadperCycle}$ of two hours based on the data:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 793-793: code points 1-102

$ \text{Fleet}(TC=2 \text{hours}) = { 448 \over 72 * 0.85} = 7.32 $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 795-795: code points 1-69

This equates to a fleet of eight vehicles. A cycle time that is twice as long as another does not necessarily result in doubling the fleet. In this case, the cycle time increased from one to two hours, but the needed fleet went from five to eight, instead of to ten.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 797-799: code points 1-49

\beginbox{2}{How to determine correction factor from hour to cycle time (PHtoCC) based on load observations}
\label{chapter:service-planning:box:how-to-determine-correction-factor-from-hour-to-cycle-time-phtocc-based-on-load-observations}
When one is analyzing many existing or potential routes with different cycle times, it is cumbersome to calculate the necessary fleet in the more intuitive manner listed above. For this reason, this section offers another way to calculate the fleet with the use of a common peak to cycle factor derived from corridor specific data. The maximum-hour load only can be determined and then a Peak Hour to Cycle Correction Factor (PHtoCC) can be applied to that to expand the demand across the full array of possible cycle times. The calculation of the PHtoCC should be done per corridor and should be made separately for weekdays, Saturdays, and Sundays.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 804-816: code points 1-23

To calculate the peak hour to cycle correction factor, we present an example of a typical demand profile for the critical link on a BRT corridor during the morning peak derived from on Table 6.13.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 818-821: code points 1-67

\tabletitle{13}{Peak Period Critical Link Demand Profile}
\label{chapter:service-planning:table:peak-period-critical-link-demand-profile}
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	\noalign{\vskip 2mm 
}	\color{gray50}10:30 a.m.&
	\color{gray50}25&
	\color{gray50}746\cr
	\noalign{\vskip 2mm 
}}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 823-845: code points 1-9

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/1d4a16c9a50d41e2cbe36e6aa61179524837be5f.jpg}
		\fignote{25}{The graph shows 15-minute loads (blue) versus overall accumulated loads (red). Peak 15-minute period occurs where blue curve hits its max, or 7:00–7:15 a.m.\label{chapter:service-planning:figure:the-graph-shows-15-minute-loads-blue-versus-overall-accumulated-loads-red-peak-15-minute-period-occurs-where-blue-curve-hits-its-max-or-700715-am}}{Arthur Szász.}
	}
\fi

The blue line in Figure 6.25 is the number of customers every 15 minutes at the critical link, or the location where there is the maximum load (MaxLoad) of customers. The column labeled “15-minute loads” shows the number of people passing the critical link in 15-minute increments at different times. The red line is the accumulated load for the full peak period. The number of customers at 6:00 is fifteen. If the cycle time (TC) is two hours, the accumulation of customers at 8:00 (t + TC) is 436 minus the fifteen customers that were already on board at 6:00, or 421.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 852-862: code points 1-61

Note that the number of customers passing the critical link varies in each 15-minute interval. The maximum load for a 15-minute interval would be 69 at 7:15. This is equivalent to saying that the maximum load, or the number of customers that would be riding on vehicles past the critical link, if the cycle time were only 15 minutes, would be 69.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 866-873: code points 1-34

All of the possible time periods that are equivalent to the cycle time (TC) need to be tested to see which time period results in the maximum accumulated customers. To do this, create a table that simulates the number of customers that would accumulate per vehicle under different cycle times, such as in Table 6.14, where the first column to the right of the time cycle represents the observed loads at the critical link for every 15-minute interval. The second column places the 6:15 load next to the 6:00 load, and the 6:30 load next to the 6:15 load, and so on, because this is what the load would be for a 30-minute interval. It is not simply double the 6:00 a.m. demand, because the demand at 6:15 is different from the demand at 6:00 a.m. The third column places the 6:45 demand adjacent to the 6:30 demand, and so on.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 875-890: code points 1-46

\tabletitle{14}{Peak Period Loads by Cycle Time}
\label{chapter:service-planning:table:peak-period-loads-by-cycle-time}
\halign to 30\tablemodule{%
	\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\hbox to 0.5\tablemodule{}&
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	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\cr
	\color{gray75}\bfseries Time& \color{gray75}\bfseries 5 minute loads& \color{gray75}\bfseries Accumulated Passengers& \color{gray75}\bfseries Time& \color{gray75}\bfseries 15 minute loads& \color{gray75}\bfseries 15 min& \color{gray75}\bfseries 15 min& \color{gray75}\bfseries 15 min& \color{gray75}\bfseries 15 min& \color{gray75}\bfseries 15 min& \color{gray75}\bfseries 15 min& \color{gray75}\bfseries 15 min& \color{gray75}\bfseries 15 min& \color{gray75}\bfseries 15 min \cr
	\noalign{\vskip 1mm} \hline \noalign{\vskip 2mm} 
	\color{gray50}6:00&
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	\color{gray50}45\cr
	\noalign{\vskip 2mm 
}	\color{gray50}6:05&
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}	\color{gray50}8:00&
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% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 894-922: code points 1-9

In Table 6.15, the 15-minute column is the same as the column above. The 30-minute column simply adds together the first two 15-minute columns from above, to give accumulated customers for a 30-minute interval. The 45-minute column totals the accumulated customers of the first three columns, and so on. In this simple way, a chart can be generated for the loads that would accumulate for each cycle time.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 924-931: code points 1-20

Table 6.15\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 934-935: code points 1-0

\tabletitle{15}{Accumulated Passengers for Different Cycle Times}
\label{chapter:service-planning:table:accumulated-passengers-for-different-cycle-times}
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	\color{gray75}\bfseries Time& \color{gray75}\bfseries 15 min& \color{gray75}\bfseries 30 min& \color{gray75}\bfseries 45 min& \color{gray75}\bfseries 60 min& \color{gray75}\bfseries 75 min& \color{gray75}\bfseries 90 min& \color{gray75}\bfseries 105 min& \color{gray75}\bfseries 120 min& \color{gray75}\bfseries 135 min& \color{gray75}\bfseries 150 min& \color{gray75}\bfseries 165 min& \color{gray75}\bfseries 180 min \cr
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% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 935-955: code points 1-9

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/42c9ee57717fb03378f122c8bd344985ac6a6727.png}
		\fignote{26}{Accumulated demands for varying cycle times, using the same data as in Tables 6.13 – 6.15.\label{chapter:service-planning:figure:accumulated-demands-for-varying-cycle-times-using-the-same-data-as-in-tables-613--615}}{Arthur Szász.}
	}
\fi

The maximum point on each curve shows the maximum accumulated customers, which is needed to derive the necessary fleet. Table 6.15 shows that the longer the cycle time, the more demand will accumulate before the same vehicle can get back to the beginning of the route to pick up more customers.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 962-967: code points 1-77

For the first example (the top brown-red line), different accumulated demands are graphed for different two-hour periods. Between 6:00 a.m. and 8:00 a.m. accumulated customers are 383 (the first data point at 6:00 a.m. on the top brown-red line). This is because at 8:00 a.m. there are already fifteen customers, and after two hours, 398 customers have accumulated, so enough vehicles to carry 383 (398-15) customers are needed. The accumulated customers from 6:00 to 8:00 are not the same, however, as the accumulated customers from 6:15 to 8:15, or from 6:30 to 8:30, etc. The top brown red line graphs the accumulated customers for each two-hour time increment are listed in Table 6.15 in the column labeled “120 minutes.” The peak period for this cycle time is about 6:45 to 8:45, when 448 passengers accumulate over two hours. Thus, for a two-hour cycle time, we can say that 448 is the MaxLoadperCycle = 448.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 969-986: code points 1-29

In each scenario, the load that needs to be accommodated with a fleet is the maximum load for each cycle time, or MaxLoadperCycle. In Table 6.15, the maximums are shown at the bottom of each cycle time. Because of the shape of the peak in demand, the maximum loads will vary depending on the cycle time. If the accumulated customers (load) per cycle time are divided by the cycle time, this gives the hourly load (MaxLoad [one hour]) for a specific cycle time.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 988-996: code points 1-54

\tabletitle{16}{Calculation of How the Maximum Load Varies with Cycle Time}
\label{chapter:service-planning:table:calculation-of-how-the-maximum-load-varies-with-cycle-time}
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	\color{gray75}\bfseries Hours& \color{gray75}\bfseries 0.25& \color{gray75}\bfseries 0.5& \color{gray75}\bfseries 0.75& \color{gray75}\bfseries 1& \color{gray75}\bfseries 1.25& \color{gray75}\bfseries 1.5& \color{gray75}\bfseries 1.75& \color{gray75}\bfseries 2& \color{gray75}\bfseries 2.25& \color{gray75}\bfseries 2.5& \color{gray75}\bfseries 2.75& \color{gray75}\bfseries 3 \cr
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	\color{gray50}Cycle time (min)&
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% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 998-1076: code points 1-9

If the maximum load for each cycle time is then further divided by the maximum load for a one-hour cycle time (265), then this gives an indicator (ML) that shows how much the maximum load for a specific cycle time varies from the maximum load for one hour. The peak hour to cycle correction factor (PHtoCC) is the slope of this line, indicating the degree to which the maximum load varies by the cycle time in general. In this way, a PHtoCC can be derived that can then be applied in the future to calculate the fleet needs for many routes of different cycle times.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1078-1089: code points 1-25

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/00899ba9d63a58cfdf4bcf7931defffb27c24420.png}
		\fignote{27}{Accumulated maximum load (ML) for various cycle times as a proportion of the accumulated max load for a one-hour cycle time. The slope, as shown by the formula and the straight black line, represents the PHtoCC. Image\label{chapter:service-planning:figure:accumulated-maximum-load-ml-for-various-cycle-times-as-a-proportion-of-the-accumulated-max-load-for-a-one-hour-cycle-time-the-slope-as-shown-by-the-formula-and-the-straight-black-line-represents-the-phtocc-image}}{Arthur Szász.}
	}
\fi

In Figure 6.27, rounding a bit, the PHtoCC = 0.11. MS-Excel will generate this number if instructed to provide the formula for a trend line when generating a graph.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1098-1101: code points 1-61

Once the PHtoCC is known, the following formula may be used to determine MaxLoadperCycle for varying cycle times with peaked demand from the known MaxLoad, which is determined per hour. This formula is a simplification of a derivative, i.e., it describes a set of relationships that are linear in most real-world applications but that do not hold at the extremities, resulting in the previously presented.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1103-1110: code points 1-63

Eq. 6.21a $ \text{MaxLoadperCycle} = \text{MaxLoad} * TC * [ 1 - \text{PHtoCC} * (\text{TC} -1) ] $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1112-1113: code points 1-91

Where:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1115-1116: code points 2-0

\begin{itemize}
\item {$\text{PHtoCC}$: Nonnegative correction factor, the calibration of which is based on survey data, is discussed in Box 6.2. The usual value is near 0.1;\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1116-1117: code points 7-0

\begin{itemize}
\item If $\text{TC}$ is larger than one hour: correction $ 1 - \text{PHtoCC} * (\text{TC} -1) $ will result smaller than one;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1117-1118: code points 1-0
\item If $\text{TC}$ is smaller than one hour: correction $ 1 - \text{PHtoCC} * (\text{TC} -1) $ will result larger than one;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1118-1119: code points 1-0
\item If $\text{TC}$ is equal one hour: correction $  1 - \text{PHtoCC} * (\text{TC} -1) $ will result in one;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1119-1120: code points 1-0
\item If $\text{PHtoCC}$ is equal zero, there will be no correction.% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1120-1120: code points 1-70
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1117-1120: code points 1-70

}
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1116-1120: code points 1-71

And therefore the fleet needed for any route with any cycle time can be calculated as follows, by expanding Equation 6.14 with Equation 6.6b.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1122-1122: code points 1-141

Eq. 6.21b\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1124-1124: code points 1-9

$ \text{Fleet}_\text{route} = {\text{MaxLoadperCycle}_\text{route} \over {\text{VSize} * \text{LoadFactor}}} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1126-1126: code points 1-112

$ \text{Fleet}_\text{route} = {\\text{MaxLoad} * TC * [ 1 - \text{PHtoCC} * (\text{TC} -1) ] \over {\text{VSize} * \text{LoadFactor}}} $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1128-1128: code points 1-138

Where:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1130-1131: code points 1-0

\begin{itemize}
\item $ \text{Fleet}_\text{route}$: Number of buses needed to serve the route;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1131-1132: code points 1-0
\item $ \text{MaxLoad}$: Maximum hourly load;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1132-1133: code points 1-0
\item $ \text{VSize}_\text{route}$: Vehicle serving the route capacity;% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1133-1134: code points 1-0
\item $ \text{Freq}_\text{route}$:Frequency of the route(ideal frequency suggested of 22 vehicles per hour);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1134-1135: code points 1-0
\item $  \text{LoadFactor} $: Design load factor (usually 0.85);% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1135-1135: code points 1-66
\end{itemize}
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1131-1135: code points 1-66

This approximation expands the peak one-hour load based on the degree to which the one-hour load is peaked within the full cycle time.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1137-1137: code points 1-134

So, for a TC of two hours using the example from above, the maximum load is:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1139-1139: code points 1-76

$ MaxLoadperCycle=265*2*1-0.11*2-1=471.7$\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1141-1141: code points 1-43

Hence, for a TC of two hours, the fleet needed is:\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1143-1143: code points 1-50

$ 265*2*1-0.11*2-160 = 7.50 $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1145-1145: code points 1-31

$ Fleet2hours=265*2*1-0.11*2-172*0.85=7.71 $\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1147-1147: code points 1-46

The resulting 7.71 is a close approximation to the 7.32 used in the other formula, and again, one should round up to eight vehicles. (The discrepancy is because both formulas are simplifications to avoid the use of derivatives, to make the math easier in a way that is sufficient for most real-world uses.)\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1149-1150: code points 1-173

In most real-world cases, the peak hour to cycle correction factor (PHtoCC) is around 0.1. For a rough approximation, in a relatively normal peaked corridor, one can make a back-of-the-envelope adjustment by just using a generic peak factor such as 0.1, but it is better to calculate the actual peak factor. While this impact of the peak factor on the needed fleet is significant when calculating the fleet for any vehicle route, it makes a very big difference when a multitude of direct-service routes are severed into a trunk route and multiple feeder routes.\par
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 1152-1156: code points 1-253

\endbox
% @ guide/06-service_planning/64-optimizing-vehicle-size-and-fleet-size.src: lines 801-1158: code points 1-7

\section{5}{Determining Which Routes to Include Inside BRT Infrastructure}
\label{volume:operations:chapter:service-planning:section:determining-which-routes-to-include-inside-brt-infrastructure}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 3-1702: code points 1-0

\quotation{An almost indispensable skill for any creative person is the ability to pose the right questions. Creative people identify promising, exciting, and, most important, accessible routes to progress—and eventually formulate the questions correctly.}{Lisa Randall, theoretical physicist, 1962–}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 5-6: code points 1-44

At this point one should have some basic idea of how to calculate the best vehicle size and how to calculate the necessary fleet for a variety of alternative services one might want to run inside the BRT infrastructure. One now has enough information to start doing the basic service planning for a proposed BRT corridor.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 8-11: code points 1-13

The first question that needs to be answered is what of the existing bus services currently using the corridor should one include, at least in some form, as part of the new BRT services. If properly designed, new BRT infrastructure should increase the speed of all the vehicles that use the BRT infrastructure. Ideally, then, \emphasis{all} the customers currently using the BRT corridor should be served by the BRT system’s new operations. The simplest way to ensure this is being done is to simply include as new BRT services all of the services currently using the corridor. Most of these will be direct services that use the BRT corridor for only a part of their route.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 13-19: code points 1-44

However, there are a variety of circumstances where the benefits to the customers of specific bus services are outweighed by the disadvantages that allow this bus route to use the BRT system would impose on the remainder of the BRT customers. There are three reasons to exclude some of the existing services:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 21-24: code points 1-0

\begin{enumerate}
\item Avoidance of station saturation;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 24-25: code points 1-0
\item Lack of administrative authority over an operator with incompatible operations;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 25-26: code points 1-0
\item Minimal overlap with the corridor.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 26-26: code points 1-42
\end{enumerate}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 24-26: code points 1-42

If a preexisting bus route is excluded from the BRT infrastructure, there are a few things that can happen to it. First, it can be allowed to continue to operate in the mixed traffic lanes along the BRT corridor. Most of the examples in this first section assume that if the route is not allowed to use the BRT infrastructure, it will operate in the mixed traffic lanes. The route could also simply be cancelled, and its demand transferred onto some similar service.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 28-32: code points 1-53

However, there are other alternatives. It could be allowed to operate inside the BRT corridor but not stop at BRT stations. This option is worth considering in situations when there are no important stations on a particular route along a BRT trunk corridor. Finally, the route could be converted into a feeder route. This option will be considered in the next section on trunk-and-feeder routes.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 34-37: code points 1-85

\subsection{1}{Administrative Authority}
\label{volume:operations:chapter:service-planning:section:determining-which-routes-to-include-inside-brt-infrastructure:subSection:administrative-authority}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 39-143: code points 1-8

The best BRT systems minimize boarding and alighting delay by requiring special vehicles that have a clean interface with the station, as described below. Further, the image and quality of service of the BRT system matters.\par
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On any given corridor, there may be a wide variety of bus and minibus operations owned by different companies or government agencies and regulated and administered by different government entities. For instance, a major arterial might have school buses, charter buses, intercity buses, regional buses, private express buses, and local buses.\par
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The best BRT systems limit access to special BRT infrastructure to prescribed operators that operate with the specific permission of a BRT authority and provide bus services following detailed technical specifications required by the BRT authority. These are sometimes called “closed systems.” In general, the highest-quality examples of BRT, such as Bogotá, Lima, Guangzhou, Brisbane, and Curitiba, take advantage of the possibility of restricting access to the new BRT infrastructure to leverage improvements in bus services. In Bogotá and Lima, companies compete for the right to provide public transport services in the BRT system through a process of competitive tendering. These systems only permit vehicles with highly defined specifications operating under a specific contract to a single public authority to operate on the corridor. Because BRT systems try to maintain a higher quality of service than regular bus services, BRT operating contracts are generally far tougher than regular bus operating contracts, and the number of vehicles able to use the BRT infrastructure is normally limited to levels that will avoid saturation of the busway.\par
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By contrast, systems that have implemented a simple busway system open to some bus operations not under the full administrative control of a BRT authority are known as “open systems.” Very few BRT systems have completely open access: Regional or intercity buses, charter buses, and school buses are rarely allowed access to BRT infrastructure. As a rule of thumb, if the BRT authority cannot regulate the vehicle specification and the operation of the bus operator, it is not a good idea to allow that service to operate inside special BRT infrastructure.\par
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Many cities with simple busways that do not qualify as BRT using \emphasis{The} \emphasis{BRT Standard}, or qualify in some cases as “basic” BRT, utilize an open-system structure, where any bus regardless of type is allowed to use the bus lane. One of the major problems with open busways is that the lack of regulation tends to lead to lower service quality. For instance, in the Delhi busway, which is open to a wide variety of bus operations reporting to different regulatory bodies, some of them with extremely weak maintenance oversight, frequent bus breakdowns tend to plague the services inside the busway. Another problem typical of open busways is that they are more likely to become congested, as the number of buses is harder to control at levels that will avoid saturation.\par
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\ifxetex
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		\img{\hsize}{operations/assets/134b909acd16f973477f0e2fde723e6a9f919270.jpeg}
		\fignote{28}{Open busway congestion in Delhi.\label{chapter:service-planning:figure:open-busway-congestion-in-delhi}}{ITDP.}
	}
\fi

In general, a closed structure is more conducive to efficient traffic operations. Since the number of operators and the number of vehicles are controlled, a closed system can be designed around the optimum conditions for customer movement.\par
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Furthermore, limiting access to new BRT infrastructure is often effectively used by governments to leverage industry modernization and higher quality of service, as discussed in Volume IV: Business Plan, especially Chapter 13: Business Structure. By placing certain minimum requirements on potential bus operators as a condition to bid for a BRT operating contract, the BRT administrative authority can use this leverage in a variety of ways, from encouraging ownership structures that include adversely impacted former operators, to requiring companies to comply with best modern business practices, and so forth.\par
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\ifxetex
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		\img{\hsize}{operations/assets/17ca46605b8d65b8e192af21ddeeeb4eb6c61539.jpeg}
		\fignote{29}{Bogotá originally operated an open busway system. Individually owned, unreformed informal “collectivo” bus services with merely a route license, but no formal operating contract plied the corridor. The bus operators were largely unaccountable. Vehicles were polluting, poorly maintained, and of a variety of types that did not interface cleanly with BRT infrastructure. Frequencies were too high to avoid congestion.\label{chapter:service-planning:figure:bogot-originally-operated-an-open-busway-system-individually-owned-unreformed-informal-collectivo-bus-services-with-merely-a-route-license-but-no-formal-operating-contract-plied-the-corridor-the-bus-operators-were-largely-unaccountable-vehicles-were-polluting-poorly-maintained-and-of-a-variety-of-types-that-did-not-interface-cleanly-with-brt-infrastructure-frequencies-were-too-high-to-avoid-congestion}}{TransMilenio SA.}
	}
\fi

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		\img{\hsize}{operations/assets/4b700ee267ec5a5391f6bd6f488fb63a0e17296c.jpeg}
		\fignote{30}{By contrast, the development of the closed TransMilenio system along the same corridor, where schedules are fixed and where operators meeting certain minimum corporate standards have to comply with tight technical specifications and maintain quality-of-service standards, has dramatically improved travel times and customer comfort\label{chapter:service-planning:figure:by-contrast-the-development-of-the-closed-transmilenio-system-along-the-same-corridor-where-schedules-are-fixed-and-where-operators-meeting-certain-minimum-corporate-standards-have-to-comply-with-tight-technical-specifications-and-maintain-quality-of-service-standards-has-dramatically-improved-travel-times-and-customer-comfort}}{Lloyd Wright}
	}
\fi

The vehicle types allowed will also greatly affect several performance indicators, including boarding and alighting times and station congestion levels. A single small bus with a very small door can badly congest an exclusive BRT lane, and for this reason, such buses are incompatible with high-speed, high-capacity BRT systems. Specifying maximum vehicle age and maintenance practices can also affect performance. Breakdowns contribute to corridor congestion. Thus, weak regulatory control over the vehicle fleet is incompatible with consistent high-speed, high-capacity, and high-quality service. Tight regulation of emissions, operating speeds, and noise is also important to protecting the environmental quality of the corridor.\par
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Prior to developing its TransMilenio system, Bogotá actually operated a median busway on its Avenida Caracas corridor. The Avenida Caracas busway operated as an open system, permitting all existing operators to utilize the infrastructure. The result was excessive busway congestion and average commercial speeds of approximately 10 kph (Figures 6.29 and 6.30). The busway was partially effective in improving conditions for mixed traffic, but did little to improve travel conditions for public transport customers. It should be noted, though, that having a closed system is a necessary but insufficient condition for ensuring good system performance.\par
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Emergency vehicles, such as ambulances, are generally permitted access on most BRT systems (Figures 6.31 and 6.32), whether they are open or closed systems. This public service provides an additional motivation for approving a BRT project, especially since many rail options are not compatible with emergency vehicles. In many cities, mixed traffic congestion significantly inhibits emergency access and delivery. By facilitating rapid emergency services for the injured and critically ill, the BRT system is in effect helping save lives.\par
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\ifxetex
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		\img{\hsize}{operations/assets/fc2de9b65597246ee9d32f7e03736935e229b0a8.jpeg}
		\fignote{31}{In cities such as Quito, the exclusive busways also permit emergency vehicles.\label{chapter:service-planning:figure:in-cities-such-as-quito-the-exclusive-busways-also-permit-emergency-vehicles}}{Lloyd Wright.}
	}
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		\img{\hsize}{operations/assets/c90d91d7fccd48428cda462af4a234a464940bdb.jpeg}
		\fignote{32}{Allowing emergency vehicles to avoid traffic delays should provide quicker responses to those in need.\label{chapter:service-planning:figure:allowing-emergency-vehicles-to-avoid-traffic-delays-should-provide-quicker-responses-to-those-in-need}}{Lloyd Wright.}
	}
\fi

Some cities also permit “official” vehicles to utilize the busway. This usage may include presidential and ministerial motorcades, as well as travel for low-ranking public officials (Figure 6.33). The justification for such usage can be questionable. Certainly, for the highest-ranked officials, such as a president or prime minister, the exclusive busway does allow for potentially safer movements. The usage by lower-ranking officials is harder to justify and can ultimately have a highly detrimental impact on system speeds and capacity. In Quito, sometimes the appropriation of busway space even extends to public utility vehicles, such as garbage trucks (Figure 6.34). The presence of such vehicles can do much to hinder proper BRT operation.\par
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\ifxetex
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	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/992b67139936e25532813512e978e4f402e80776.jpeg}
		\fignote{33}{When usage of the exclusive busway by lower-ranking government officials becomes commonplace, there can be negative impacts on the efficiency of the system.\label{chapter:service-planning:figure:when-usage-of-the-exclusive-busway-by-lower-ranking-government-officials-becomes-commonplace-there-can-be-negative-impacts-on-the-efficiency-of-the-system}}{Lloyd Wright}
	}
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		\img{\hsize}{operations/assets/7dc6ff3f10146f59e66886be63e999fdcc5573f1.jpeg}
		\fignote{34}{In Quito, even garbage trucks take advantage of the exclusive busway.\label{chapter:service-planning:figure:in-quito-even-garbage-trucks-take-advantage-of-the-exclusive-busway}}{Lloyd Wright.}
	}
\fi

\subsection{2}{Overlap with the BRT Corridor}
\label{volume:operations:chapter:service-planning:section:determining-which-routes-to-include-inside-brt-infrastructure:subSection:overlap-with-the-brt-corridor}
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On most BRT corridors, some existing public transport routes overlap the corridor for a short segment. If the segment is very short, it may not be worth incorporating the service into the BRT system. Usually, incorporating a bus route into the BRT system requires buying special new vehicles for that route, and if the benefits of including the route in the BRT system are low because it only overlaps with the BRT for a short segment, these benefits may not outweigh the cost of buying a new BRT vehicle.\par
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In Table 6.1, existing routes are shown to the degree to which the route overlaps the planned BRT infrastructure. If the overlap is less than 20 percent of the total length of the route, it may not be worth incorporating it into the BRT service plan.\par
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In many cases, BRT service planners start by mapping the existing route and then exclude the routes that overlap the planned BRT corridor for less than 20 percent of their route. This is not a hard-and-fast rule; it is just what is normally done. In situations of low station saturation and high-frequency routes, the percentage may be as low as 10–15 percent, but in capacity-constrained settings, a range of 20–30 percent is more typical.\par
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If the part of the route that overlaps with the BRT corridor is downtown, on a highly congested road, or it includes some very high-demand stations, there may be significant benefits to incorporating the route into the BRT system, but in most cases 20 percent overlap is a reasonable rule of thumb for excluding a route. In case of doubt, the operational cost savings and time savings that would accrue from using the BRT infrastructure could be compared to the additional costs associated with buying special vehicles, if the BRT requires new vehicles. If the overlap is below 20 percent, but there is no particular need for the route to stop on the BRT corridor, one might consider allowing the route to use the BRT corridor for this short segment, while not stopping at any of the BRT station stops.\par
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\subsection{3}{Avoiding Station Saturation}
\label{volume:operations:chapter:service-planning:section:determining-which-routes-to-include-inside-brt-infrastructure:subSection:avoiding-station-saturation}
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Once the routes that have only a tangential relationship to the BRT trunk service have been excluded from the proposed BRT system services, ideally the BRT infrastructure should be designed to accommodate the demand from all of the remaining bus routes. However, this may be impossible. If the capacity of what can be designed is less than the remaining demand, it may be necessary to make further decisions about which routes to include in the BRT services, and which to leave in mixed traffic, or reroute off the corridor. In this sense, service planning is iterative with infrastructure planning. The next chapter provides the formulas needed to calculate the capacity and speed of a BRT corridor depending on \emphasis{The} \emphasis{BRT Standard} elements used. The normal situation where one needs to exclude some bus routes in the manner described in this section is when a single-lane BRT with no sub-stops or passing lanes has been designed.\par
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Having many routes is not a problem per se; it only becomes a problem if frequencies are high enough that stations begin to become saturated, and the speed of the BRT system begins to slow. Since new BRT infrastructure will allow vehicles to increase their speed, ideally as many customers as possible should be able to use it. Usually, a corridor will be chosen for BRT that already has a lot of bus or minibus services along it, and normally these preexisting services are a reasonable match to public transport demand patterns. As such, the first principle of service planning is to incorporate as many preexisting bus routes as possible into the services that will use the new BRT infrastructure. This will maximize the number of beneficiaries and minimize the disruption of service.\par
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In specific cases where current bus services already take up more than one mixed traffic lane, the BRT system may begin to become congested if too many routes are brought into the dedicated infrastructure, at which point the speeds will slow. Eventually, as saturation worsens, speeds inside the BRT system can drop to levels below the original mixed traffic speeds. Then, unless the design of the busway can be modified to accommodate all of the bus routes, the service planner will need to exclude some of the bus routes from the system.\par
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An example of this problem occurred with the Seoul BRT. The system was initially designed with insufficient capacity to handle the vehicle demand in the corridor. As a result, in the first several months of operation, the corridor became saturated, and vehicle speeds dropped below the pre-BRT speeds. After diverting some of the routes back to the mixed traffic lanes so the busway was not saturated, the overall system yielded significant user benefits. The methodology sketched out below should be used in similar circumstances when deciding which routes to put back into mixed traffic.\par
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The process of determining how many routes to include in the services for the planned BRT system has two basic steps. First, calculate which future BRT station or stations are most likely to become saturated. This will be the station projected to have the highest frequency and boarding and alighting volumes, because high frequency and high boarding and alighting volumes are the most likely causes of station saturation.\par
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In nearly all cases, BRT system saturation happens at stations where the capacity is too low to handle the frequency and boarding and alighting volumes, so vehicles begin to bunch. The formulas for calculating station saturation are covered in Chapter 7: Capacity and Speed.\par
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Second, a calculation should be performed to determine, given the characteristics of each route (demand, vehicle type, frequencies, and demand to that particular station, etc.), how many routes and which routes should be included as part of the new BRT services and which should be excluded. To do this, the routes should be ordered based on the seconds consumed at that specific station multiplied by the number of customers that are passing by that bottleneck station. In other words:\par
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\highlight{The first criteria used to select routes for inclusion in the BRT system is frequency and proportion of overlap with the BRT corridor. If the route only uses the BRT corridor for a short distance, or carries few customers, the benefits may not justify the cost of purchasing a BRT-infrastructure-compatible bus.}\par
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\highlight{For systems where there is a danger that the busway will become saturated and speeds will slow, a second method should be used: routes should be ranked based on the number of customers that a route can move through the bottleneck station for each second of dwell time they consume at the bottleneck station. Routes moving more customers per second of dwell time should continue to be included until the total delay caused to the busway of adding the last route is greater than the time savings benefits of adding the last route.}\par
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The existing bus route that uses the busway most efficiently will be the route that carries the most customers with the fewest customers getting off at the bottleneck station. For instance, if the bottleneck station in a BRT system is Times Square, and there is an express route, “T1,” that carries large numbers of customers through Times Square but does not stop at Times Square, it should certainly be included in the busway, as it does not contribute at all to the bottleneck at Times Square station. By contrast, a route that carries relatively few customers, yet all of them get off at Times Square, should be the first route to be excluded.\par
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In this section we provide formulas to determine how many and which vehicle routes to include in the BRT system. Given that every effort has already been made to design the system with a capacity that will avoid saturation, but, for one reason or another, design compromises had to be made, and the design has already been fixed in a way that does not accommodate all public transport customers who want to use the corridor. It is assumed that if some existing routes are not excluded, the bus speeds in the corridor will slow down. This is fairly common in the developing world, but not so common in the United States or Europe. Each scenario is progressively more complex—and more realistic; however, they do not cover every possibility. Service planners will need to understand the fundamentals laid out in this chapter and make modifications to fit a given situation.\par
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In these scenarios, there are two possible ways for running buses:\par
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\begin{enumerate}
\item BRT corridor: The BRT corridor is generally described in text as “BRT infrastructure” or “busway” and is indicated in formulas with the subscript “inside.”% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 263-265: code points 1-0
\item Mixed-traffic lane: The mixed-traffic lane is assumed to run parallel to the BRT corridor. The mixed-traffic lane is where bus routes that are excluded from the BRT infrastructure will run. The mixed-traffic lane is referred to in text as “outside the BRT corridor” and is indicated in formulas with the subscript “outside.” It is assumed that speeds in the mixed-traffic lane do not vary based on the number of buses in it, since buses generally constitute a relatively small share of total traffic, and it is generally possible for buses to pass each other in the mixed traffic lanes. If bus volumes in the mixed traffic lanes are likely to affect mixed traffic speeds, a more detailed analysis of the mixed traffic lanes should be made.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 265-272: code points 1-15
\end{enumerate}
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In the following scenarios, one should aim to minimize aggregate travel time for all customers ($ATT_\text{total}$), both inside and outside the BRT corridor. One assumes that there is a total number of bus routes, both inside and outside the BRT corridor operating at a combined total frequency, indicated by $Fi_\text{total}$. Bus routes operate as units, so that one cannot remove a few buses of the route “f” from the busway; the entire route must be removed.\par
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In all scenarios below, the part of the corridor that will receive BRT infrastructure is assumed to be 5 kilometers long and the speed in the mixed traffic lanes along this corridor is assumed to be 10 kph. The speed within the busway will vary by the scenario, while the speed in the mixed traffic lane will be assumed to stay at 10 kph.\par
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\tabletitle{17}{Example of Average Peak Hour Riders and Times}
\label{chapter:service-planning:table:example-of-average-peak-hour-riders-and-times}
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	\vtop{\sffamily\footnotesize\noindent\hsize=9\tablemodule#}\hbox to 0.5\tablemodule{}&
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	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\cr
	\color{gray75}\bfseries Departure& \color{gray75}\bfseries Arrival& \color{gray75}\bfseries Travel Time& \color{gray75}\bfseries Passengers \cr
	\noalign{\vskip 1mm} \hline \noalign{\vskip 2mm} 
	\color{gray50}6:00 a.m.&
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	\color{gray50}25\cr
	\noalign{\vskip 2mm 
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	\noalign{\vskip 2mm 
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	\noalign{\vskip 2mm 
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	\noalign{\vskip 2mm 
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	\color{gray50}25\cr
	\noalign{\vskip 2mm 
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	\noalign{\vskip 2mm 
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	\noalign{\vskip 2mm 
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	\noalign{\vskip 2mm 
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Further, the peak hour was already identified as between 6:15 and 7:14, the peak hour ridership is a hundred, and the peak hour travel time is two hours. It is assumed that all bus routes travelling through the corridor before the busway was introduced took a half hour to pass through the corridor. It means that at any given moment, with the hourly frequency of four, two buses of route A would be visible operating on the BRT corridor; the moment the bus ahead leaves the segment (after half an hour), another bus would get in at the beginning (being thirty minutes behind).\par
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Before the BRT system is implemented, all bus routes are operating “outside” the BRT. Therefore, during one hour we would have seen \emphasis{Aggregate Travel Time OUTSIDE the BRT}, operating along a planned BRT corridor, of two hours for this route. That is simply four bus trips per hour, each taking half an hour.\par
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If this route is included inside the BRT infrastructure where average speed (without congestion that is the aim) is 25 kph, it would take only 12.5 minutes to cross the corridor. In this case, the Aggregate Travel Time INSIDE the BRT is 12.5 times 4 or 50 minutes. This is a net improvement over the no-build scenario of one hour and ten bus minutes. Another way to think of this is that after only 12.5 minutes the first bus will exit the BRT, but the next bus would not appear on the segment for another 2.5 minutes, so if we look at the corridor once a minute over an hour, only 50 times in 60 times will we see a bus riding in the segment. In this situation the \emphasis{Aggregate Travel Time INSIDE the BRT} added 50 minutes for this route (or 5\slash{}6 of hour or 0.833 hour).\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 307-314: code points 1-46

For each of the examples, the total dwell time of each bus (Td) at a station inside the busway, assuming boarding and alighting through all doors will be a function of the fixed dwell time (T0), also known as dead time or the time the bus takes to pull up to the station, open and close its doors, and pull away, and the average boarding time per customer for buses with the given configuration (Tb) multiplied by the number of boarding customers and the average alighting time per customer for buses with the same configuration (Ta) times the number of alighting customers, or:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 316-321: code points 1-63

Eq. 6.22\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 323-323: code points 1-8

$ T_d=T_0+T_b+T_a  $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 325-325: code points 1-22

Or\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 327-327: code points 1-2

$ Td =T_0 + t_b * P_b + t_a * P_a $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 329-329: code points 1-37

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 331-332: code points 1-0

\begin{itemize}
\item $T_d$: Total dwell time;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 332-333: code points 1-0
\item $T_0$: Fixed dwell time (or “dead time”);% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 333-334: code points 1-0
\item $T_b$: Total boarding time per vehicle ((given by $tb * Pb$);% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 334-335: code points 1-0
\item $t_b$: Boarding time per customer;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 335-336: code points 1-0
\item $P_b$: Number of boarding customers;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 336-337: code points 1-0
\item $T_a$: Total alighting time per vehicle (given by $ta * Pa$);% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 337-338: code points 1-0
\item $t_a$: Alighting time per customer;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 338-339: code points 1-0
\item $P_a$: Number of alighting customers.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 339-339: code points 1-45
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 332-339: code points 1-45

As discussed in Chapter 7: Capacity and Speed, boarding and alighting times per customers are a function of bus configuration and bus station interface (number and width of doors, at-level boarding or boarding via several steps, internal or external fare collection, position of turnstiles, etc.) and bus occupancy at the station. A linear proxy, i.e., using average customers per second of surveyed boarding and alighting times under conditions similar to those being designed is a more accurate way of estimating dwell time per station than using a flat average dwell time per station, so long as the busway is not beginning to become saturated (saturation below 0.4). Avoiding saturation is the design goal of the examples. Outside the BRT infrastructure, it is assumed that buses’ speeds are the current commercial speed, which already include dwell times at station stops.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 341-349: code points 1-37

\subsubsection{1}{Scenario I: All Routes Are Similar}
\label{volume:operations:chapter:service-planning:section:determining-which-routes-to-include-inside-brt-infrastructure:subSection:avoiding-station-saturation:subSubSection:scenario-i-all-routes-are-similar}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 351-1240: code points 1-25

In this scenario, all vehicles, routes, and stations inside the BRT infrastructure have the same operational characteristics. In other words, they have roughly the same number of customers getting on and off at each stop; have the same number of doors; have the same frequency; use the same vehicle type; have floors level with the vehicle platform; and hence have the same dwell time per customer. As a result, one should not care which routes are included or excluded, one should only care about the number of routes one includes. In this simplified scenario, since all of the routes have the same dwell time per customer, and the same number of customers benefitting from the busway, there is no need to rank the bus routes. Given this uniform demand, all stations will become saturated equally. Vehicles operating inside the BRT infrastructure will become congested if there are too many vehicles using the bus lane. These assumptions allow for busway congestion to be isolated as the only factor that would cause a variance in total travel time when all else is constant.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 353-363: code points 1-26

In this scenario, given that all bus routes have the same demand and vehicle size, it is assumed that all routes have the same frequency. In later examples the frequency will vary by route. All routes are also assumed to have the same dwell time, since they have the same demand and vehicle size. It is assumed that the total dwell time Td is the same for all vehicle routes, because both the fixed and variable dwell times are the same for all vehicles:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 365-369: code points 1-42

$L_\text{corridor}$: Corridor length = 5 km;\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 372-372: code points 1-46

$V_\text{outside}$: Velocity outside the busway = 10 km\slash{}h;\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 374-374: code points 1-60

$V_\text{inside}$:Velocity inside BRT at free-flow speed = 25 km\slash{}h;\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 376-376: code points 1-69

$N_\text{stations}$ = 10;\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 378-378: code points 1-27

$F_\text{total}$: Total frequency of all services = 200 vehicles\slash{}h.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 380-380: code points 1-69

$T_d$: Dwell time per vehicle at each station = 18 seconds = 0.005 h\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 382-382: code points 1-70

$T_b$: Time per customer boarding = 3 seconds;\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 384-384: code points 1-48

$T_a$: Time per customer alighting = 2 seconds;\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 386-386: code points 1-49

$T_0$: Fixed dwell time per vehicle = 12 seconds.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 388-388: code points 1-51

To determine the optimal number of vehicle routes to include in a BRT corridor, as many buses as possible should be brought into the BRT corridor until the point where time-savings benefit for the last bus added to the corridor is less than the congestion delay it causes to the remaining vehicles in the busway.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 390-392: code points 1-100

By measuring the total vehicle travel time over the course of one hour for all vehicles on a single corridor ($ATT_\text{total}$) both inside ($ATT_\text{inside}$) and outside ($ATT_\text{outside}$) the BRT infrastructure, it is clear that it is often beneficial to leave some routes out of the BRT corridor. The ATT both inside and outside the BRT infrastructure will be the number of buses per hour ($ F_\text{inside} $ and Foutside) multiplied by the travel time per bus ($TT_\text{inside}$ and $TT_\text{outside}$ respectively). In all cases one will assume that the frequency outside the BRT corridor does not affect the travel time outside the corridor. Therefore, all of the total travel times (ATT) are expressed as a function of the frequency inside the busway ($F_\text{inside}$).\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 394-400: code points 1-110

Eq. 6.23\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 402-402: code points 1-8

$ATT_\text{total}=ATT_\text{outside}+ATT_\text{inside}$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 404-404: code points 1-57

Or:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 406-406: code points 1-3

$ATT_\text{total}=TT_\text{inside}*F_\text{inside}+TT_\text{outside}*F_\text{outside} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 408-408: code points 1-89

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 410-411: code points 1-0

\begin{itemize}
\item $ATT_\text{total}$:Total vehicle travel time over the course of one hour for all vehicles on a single corridor;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 411-412: code points 1-0
\item $ATT_\text{outside}$: Total vehicle travel time over the course of one hour for all vehicles on a single corridor outside of the BRT infrastructure ($ATT_\text{outside}=TT_\text{outside}*F_\text{outside}$);% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 412-414: code points 1-0
\item $ATT_\text{inside}$: Total vehicle travel time over the course of one hour for all vehicles on a single corridor inside of the BRT infrastructure($ATT_\text{inside}=TT_\text{outside}*F_\text{outside}$);% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 414-416: code points 1-0
\item $TT_\text{inside}$: Travel time per bus inside the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 416-417: code points 1-0
\item $F_\text{inside}$: Number of buses per hour inside the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 417-418: code points 1-0
\item $TT_\text{outside}:$ Travel time per bus outside the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 418-419: code points 1-0
\item $F_\text{outside}:$ Number of buses per hour outside the busway.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 419-419: code points 1-72
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 411-419: code points 1-72

Because $TT_\text{outside}$ is fixed, one can easily calculate it as:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 421-421: code points 1-71

Eq. 6.24a\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 423-423: code points 1-9

$TT_\text{outside}={L_\text{corridor} \over V_\text{outside}}$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 425-425: code points 1-64

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 427-428: code points 1-0

\begin{itemize}
\item $TT_\text{outside}$: Travel time per bus outside the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 428-429: code points 1-0
\item $L_\text{corridor}$: Length of the corridor;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 429-430: code points 1-0
\item $V_\text{outside}$: Velocity outside the busway.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 430-430: code points 1-56
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 428-430: code points 1-56

So, using the values defined above for the corridor:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 432-432: code points 1-52

$TT_\text{outside}={5\text{km} \over 10 \text{km/hr} } * 1 \text{hr} ={ 5 \over 10\text{hr} }  = 0.5 \text{hours} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 434-434: code points 1-117

$TT_\text{outside}$ will remain 0.5 hours (30 minutes) per bus no matter how many buses are operating outside the corridor.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 436-437: code points 1-13

Travel time inside the BRT infrastructure ($TT_\text{inside}$), however, varies in this simplified example as a simple function of frequency. That is, with each new vehicle added to the busway, a slight congestion is introduced and the total travel time inside increases.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 439-441: code points 1-57

Travel time for a bus within a busway is the sum of the time spent:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 443-444: code points 1-0

\begin{enumerate}
\item In motion (free running time);% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 444-445: code points 1-0
\item At intersections;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 445-446: code points 1-0
\item At stations;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 446-447: code points 1-0
\item In congestion.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 447-447: code points 1-22
\end{enumerate}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 444-447: code points 1-22

In most conditions, the stations become saturated long before the traffic signal or the busway itself is saturated, so generally one should assume that the bottleneck is the station and not the intersections or the busway. Even at quite low frequencies, it often occurs that one vehicle is unable to approach the station, because another vehicle is already occupying that location, and these delays can rapidly become very significant.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 449-453: code points 1-24

Design techniques for reducing dwell time at stations are discussed extensively in Chapter 7: Capacity and Speed. In this chapter, these design issues are not discussed; instead, one should assume that the best possible design has been used, so the boarding and alighting time at stations per passenger ($T_b 
+ T_a$) is already fixed by these design characteristics. In this scenario, the only factor that varies is (“In congestion”) and it varies based only on vehicle queuing at stations ($T_q$). Scenario II will consider variations in dwell times, but for now one should assume a fixed dwell time for all vehicles on the corridor.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 455-461: code points 1-16

So in this scenario the first three aspects of travel time in the busway are fixed and constitute the base speed ($_\text{Vinside-no-congestion}$) and travel time for any vehicle in the busway before the busway begins to become congested. Further, if only one vehicle is in the busway, there is no possibility of congestion, and that vehicle will experience this base travel time as:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 463-466: code points 1-58

Eq. 6.24b\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 468-468: code points 1-9

$TT_\text{inside-no-congestion}={L_\text{corridor} \over _\text{Vinside-no-congestion}}$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 470-470: code points 1-90

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 472-473: code points 1-0

\begin{itemize}
\item $TT_\text{inside-no-congestion}$: Travel time per bus inside the busway without delays at stations;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 473-474: code points 1-0
\item $L_\text{corridor}$: Length of the corridor;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 474-475: code points 1-0
\item $V_\text{inside-no-congestion}$: Velocity inside the busway, when there is no congestion delay at stations.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 475-475: code points 1-115
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 473-475: code points 1-115

If one wants to know the speed inside the busway without any vehicle congestion, one should calculate the initial value of $TT_\text{inside}$, with only one vehicle in the corridor:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 477-478: code points 1-81

$TT_\text{inside-no-congestion}={5\text{km} \over 25 \text{km/hr} }  = { 5 \over 25 \text{hr} }  = 0.2 \text{hours} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 480-480: code points 1-119

Usually, when performing this type of analysis, if one is planning to build a Silver or Gold Standard BRT, one would normally assume that the average speed of the BRT corridor before saturation would be around 20 kph in a dense urban area or downtown and around 25 on a major arterial, based on empirical observation of BRTs in different conditions. As soon as any additional vehicles are added to the busway, some possibility of queuing emerges. One should measure queuing delay on a per-station basis; however, in this scenario, it can be assumed that the queuing delay ($T_q$) will be the same at every station. One must thus expand Equation 6.17b to all vehicles as:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 482-488: code points 1-51

Eq. 6.24c\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 490-490: code points 1-9

$ TT_\text{inside}={ L_\text{corridor} \over V_\text{inside-no-congestion}}+T_q*N_\text{stations}$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 492-492: code points 1-100

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 494-495: code points 1-0

\begin{itemize}
\item $TT_\text{inside}$: Travel time per bus inside the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 495-496: code points 1-0
\item $L_\text{corridor}$: Length of the corridor;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 496-497: code points 1-0
\item $V_\text{inside-no-congestion}$: Velocity inside the busway without delay at stations;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 497-498: code points 1-0
\item $T_q$:Delay for a single vehicle at a single station due to queuing;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 498-499: code points 1-0
\item $N_\text{stations}$: Number of stations.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 499-499: code points 1-48
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 495-499: code points 1-48

Because queuing in a busway ($T_q$) is generally a direct result of station saturation, one should begin with the formula for station saturation. Detailed methodologies for calculating station saturation under different scenarios are provided in Chapter 7: Capacity and Speed, but for now one should use the basic consideration for station saturation under these extremely simplified conditions.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 501-504: code points 1-81

In this example, saturation at each station is expressed by the equation below.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 506-506: code points 1-79

Eq. 6.25\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 508-508: code points 1-8

$ x= T_d * F_\text{inside} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 510-510: code points 1-30

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 512-513: code points 1-0

\begin{itemize}
\item $x$: Saturation at each station for a specific frequency inside the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 513-514: code points 1-0
\item $T_d$: Dwell time per bus;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 514-515: code points 1-0
\item $F_\text{inside}$: Number of buses per hour inside the busway.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 515-515: code points 1-70
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 513-515: code points 1-70

If one includes 80 vehicles in the BRT corridor, and one knows the dwell time is 18 seconds (0.005 hours) per bus, station saturation, $x$, will be 40 percent.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 517-518: code points 1-62

$ x = 0.005 * 80 = 0.4 $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 520-520: code points 1-26

In this case, “$x$” is the average percentage of time that the station is occupied by vehicles loading and unloading, but it can be thought of as the probability that a vehicle approaching a station will find the station occupied. In our example, if a person (or a BRT vehicle) about whom we know nothing else arrives at the station, he\slash{}she\slash{}it has a 40 percent chance of finding a station with BRT vehicles using it and a 60 percent chance that no buses are there at that exact moment.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 522-526: code points 1-78

Let us now focus our attention on this 40 percent of time that the station is occupied, the probability of a BRT vehicle arriving at the station when another vehicle is already there is still 40 percent of the time the station is occupied, if nothing else is known. So the chance of a vehicle being a second vehicle queueing at the station is 40 percent of 40 percent (or 16 percent). This means that 16 percent of the time a bus will have to wait until the docking bay is cleared by at least one bus. Thus, 40 percent of these 16 percent, or 6.4 percent of the wait, will be for two or more buses to clear the station and so on.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 528-534: code points 1-6

Station saturation, as described above, begins to result in delay when vehicles are forced to queue up to the station waiting to dock. The probability that a vehicle will find the station occupied is approximately given by x, and the chance that the next vehicle will also face a queue is x2, and the vehicle after that would face a probability of x3. The average queue in such a situation would be given by:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 536-539: code points 1-93

Eq. 6.26\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 541-541: code points 1-8

$\text{Average Queue Size}={x^2 \over(1-x)} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 543-543: code points 1-47

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 545-546: code points 1-0

\begin{itemize}
\item $Average Queue Size$: Number of vehicles on average in queue;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 546-547: code points 1-0
\item $x$: Probability a vehicle will find the station occupied.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 547-547: code points 1-66
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 546-547: code points 1-66

If arrivals and departures are random, the average waiting time in queue per vehicle would be given by:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 549-550: code points 1-3

Eq. 6.27:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 552-552: code points 1-9

$ \text{Average Waiting time} = { x^2 \over (1-x) } * {1 \over F_\text{inside}} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 554-554: code points 1-83

Where\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 556-557: code points 1-0

\begin{itemize}
\item $\text{Average Queue Size}$: Number of vehicles on average in queue;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 557-558: code points 1-0
\item $x$: Probability a vehicle will find the station occupied;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 558-559: code points 1-0
\item $F_\text{inside}$: Number of buses per hour inside the busway.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 559-559: code points 1-69
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 557-559: code points 1-69

This is a derivation of what is known as Little’s Law: If the average waiting time in a queue is two hours and customers arrive at a rate of three per hour (Frequency) then, on average, there are six customers in the queue, or:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 561-563: code points 1-17

Eq. 6.28:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 565-565: code points 1-9

$ \text{Average Queue Size}=\text{Average Waiting Time}*\text{Frequency of Arrivals}$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 567-567: code points 1-87

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 569-570: code points 1-0

\begin{itemize}
\item $ \text{Average Queue Size} $: Number of vehicles on average in queue;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 570-570: code points 1-78
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 570-570: code points 1-78

\begin{itemize}
\item $ \text{Average Waiting Time} $: Average waiting time in a queue;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 572-572: code points 1-73
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 572-572: code points 1-73

\begin{itemize}
\item $ \text{Frequency of Arrivals} $: Number of customers arriving per a given amount of time.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 574-574: code points 1-98
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 574-574: code points 1-98

In our example, the average queue is known as 0.2667 vehicles (= 4\slash{}15 vehicle) and there are an average of 1.333 vehicles arriving per minute (80 vehicles per hour = 4\slash{}3 per minute), so in average they must be waiting 1\slash{}5 of a minute (= 12 seconds).\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 576-578: code points 1-42

Considering this distribution of arrivals and departures, theoretical queuing time per bus at each station would be given by:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 580-581: code points 1-26

Eq. 6.29\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 583-583: code points 1-8

$ T_q={0.5(Irr_\text{arrival}+ Irr_\text{departure})* x^2 \over 1-x }  {1 \over F_\text{inside}} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 585-585: code points 1-100

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 587-587: code points 1-6

\begin{itemize}
\item $ T_q $: One vehicle queueing time at each station;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 589-590: code points 1-0
\item $ x $: Saturation of the station;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 590-591: code points 1-0
\item $ F_\text{inside} $: Number of buses per hour inside the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 591-592: code points 1-0
\item $ Irr_\text{arrival} $: Irregularity of arrivals ($ Irr_\text{arrival}={\text{Variance}_\text{arrivals'intervals} \over \text{Mean}_\text{arrivals'intervals}^2}$);% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 592-593: code points 1-0
\item $ Irr_\text{departure} $: Irregularity of departures ($ Irr_\text{departure}={\text{Variance}_\text{departures'intervals} \over \text{Mean}_\text{arrivals'intervals}^2}$).% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 593-593: code points 1-181
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 589-593: code points 1-181

The mean of arrival and departure intervals is the headway and the variance would be similar to boarding and alighting variance if there were no traffic lights and starting schedules were followed to the letter. Equation 6.20 is the particular case where irregularities for arrival and departure are random ($Irr_\text{arrivals} = Irr_\text{departures} = 1)$.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 595-597: code points 1-149

Empirical observation shows that using the coefficient of 0.7 mimics the series of probabilities in high-frequency (above 80 vehicles per hour) busways in urban conditions. In fact, empirical observation of busways with full BRT characteristics do tend to saturate at around 80 vehicles per hour, and for a busway 0.4 is considered the beginning point of station saturation, so service planners will avoid designing services with frequencies where x > 0.4. In any case, queuing time per vehicle can be expressed (as a portion of an hour by):\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 599-604: code points 1-29

Eq. 6.30a\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 606-606: code points 1-9

$ T_q={0.7 * x^2 \over 1-x }  {1 \over F_\text{inside}} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 608-608: code points 1-59

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 610-611: code points 1-0

\begin{itemize}
\item $ T_q $: One vehicle queueing time at each station;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 611-612: code points 1-0
\item $ x $: Saturation of the station;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 612-613: code points 1-0
\item $ F_\text{inside} $: Number of buses per hour inside the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 613-613: code points 1-72
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 611-613: code points 1-72

Since empirical observation shows that this phenomenon is just as well captured by the much simpler formula above, it is not necessary to use the theoretical formula. It may also be interesting to note that this equation can also be written as a function of dwell time and saturation, or only as a function of dwell time and frequency inside the busway, as the three are related by Equation 6.25:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 616-619: code points 1-89

Eq. 6.25\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 621-621: code points 1-8

$ x=T_d*F_\text{inside}\Leftrightarrow Td= {x \over F_\text{inside}} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 623-623: code points 1-72

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 625-626: code points 1-0

\begin{itemize}
\item $ T_d $: Dwell time per bus;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 626-627: code points 1-0
\item $ x $: Saturation of the station;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 627-628: code points 1-0
\item $ F_\text{inside} $: Number of buses per hour inside the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 628-628: code points 1-72
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 626-628: code points 1-72

Eq. 6.30b\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 630-630: code points 1-9

$ T_q = {0.7 * x^2 \over 1-x }  {1 \over F_\text{inside}} = {0.7 * x \over 1-x }  {x \over F_\text{inside}} 
= {0.7 * x \over 1-x } * T_d $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 632-633: code points 1-31

$ T_q = {0.7 * (T_d*F_\text{inside})^2 \over 1-(T_d*F_\text{inside})}  {1 \over F_\text{inside}} = {0.7 * T_d ^2 * F_\text{inside} \over 1- (T_d *F_\text{inside} )} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 635-635: code points 1-168

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 637-638: code points 1-0

\begin{itemize}
\item $ T_q $: One vehicle queueing time at each station;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 638-639: code points 1-0
\item $ x $: Saturation of the station;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 639-640: code points 1-0
\item $ F_\text{inside} $: Number of buses per hour inside the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 640-640: code points 1-72
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 638-640: code points 1-72

Going back to Equation 6.24c\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 642-642: code points 1-28

Travel time inside the corridor can be expressed as function of the frequency inside the corridor:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 644-644: code points 1-98

Eq. 6.24c\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 646-646: code points 1-9

$ TT_\text{inside}={L_\text{corridor} \over V_\text{inside-no-congestion}}+T_q*N_\text{stations}$ $ TT_\text{inside}={L_\text{corridor} \over V_\text{inside-no-congestion}}+{0.7 * T_d ^2 * F_\text{inside} \over 1- (T_d *F_\text{inside} )}*N_\text{stations}$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 648-649: code points 1-161

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 651-652: code points 1-0

\begin{itemize}
\item $ TT_\text{inside} $: Travel time per bus inside the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 652-653: code points 1-0
\item $ L_\text{corridor} $: Length of the corridor;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 653-654: code points 1-0
\item $ V_\text{inside-no-congestion} $: Velocity inside the busway if there is no queueing at stations;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 654-655: code points 1-0
\item $ T_d $: Dwell time per bus at each station (equal for all buses in all stations in this scenario);% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 655-656: code points 1-0
\item $ F_\text{inside} $: Number of buses per hour inside the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 656-657: code points 1-0
\item $ N_\text{stations} $: Number of stations along the busway.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 657-657: code points 1-67
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 652-657: code points 1-67

Because it is assumed in this case that all stations will saturate equally (because the boarding and alighting customer volumes and frequencies are assumed to be constant), one can simply add the free-flow speed ($L_\text{corridor} \over  V_\text{inside-no-congestion}$) to the queue delay at each station and multiply it by the number of stations ($N_\text{stations}$). Later, it will be necessary to calculate the queue delay at each station and sum it across stations.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 659-663: code points 1-23

On the BRT corridor, if our sample frequency of 80 vehicles inside the corridor is tried, the travel time per vehicle inside the corridor is:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 665-666: code points 1-40

$ TT_\text{inside}(F_\text{inside}=80)=0.2 + ({ {0.7*0.4^2 \over (1-0.4)} \over 80}*10) = 0.2233 \text{hours}$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 668-668: code points 1-112

By fixing the other values in Equation 6.17 as proposed for our scenario ($L_\text{corridor} = 5 \text{km}, 
V_\text{inside-no-congestion}=25 \text{km/hour}, T_d = 18 \text{seconds (or 0.005 hour)} $ and $ N_\text{station}=10$), one can calculate the travel time per bus inside the corridor ($ TT_\text{inside} $ shown in the graphic on Figure 6.35), as a function of the bus frequency inside the corridor, up to the maximum $F_\text{total} = 200 $. By considering that $ F_\text{outside} = 200 – F_\text{inside}$ and using equations 6.16 and 6.17a, one may also calculate total aggregate time as a function of frequency inside as shown in Table 6.18.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 670-676: code points 1-14

On the figure, the orange line, $TT_\text{outside}$, remains constant at 0.5 hours, as described earlier, regardless of the frequency of buses outside the corridor. The blue line, however, increases as a function of bus frequency, from a minimum of 0.2 hours to a maximum reaching toward infinity (i.e., the vehicles are not moving at all) if all 200 vehicles are included in the BRT corridor.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 678-681: code points 1-72

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/6d4944a7181d6574cef8da8876d255a2211eefd6.png}
		\fignote{35}{Scenario I travel time inside the BRT corridor (blue line) and outside the BRT corridor (orange line) as a function of bus frequency brought inside the corridor.\label{chapter:service-planning:figure:scenario-i-travel-time-inside-the-brt-corridor-blue-line-and-outside-the-brt-corridor-orange-line-as-a-function-of-bus-frequency-brought-inside-the-corridor}}{Elebeta.}
	}
\fi

Figure 6.35 shows that the travel time within the bus lane reaches the travel time outside of the bus lane at approximately $F_\text{inside} = 179$. Thus, if 179 vehicles were included inside the corridor, there would be no benefit at all. Above 179 vehicles inside the busway, the travel time would be slower than the mixed traffic.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 686-689: code points 1-14

One should keep in mind that the travel times will affect all vehicles and that it is not actually the \emphasis{per bus} travel times we are interested in but rather the aggregate travel times inside and outside the corridor ($ATT_\text{inside}$ and $ATT_\text{outside}$). More precisely, we are most interested in the aggregate travel times \emphasis{for customers} inside and outside the corridor. However, in this simplified case, where customer volumes are the same from one bus to another, we leave customer volumes out of the equation with no consequence.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 691-695: code points 1-112

Aggregate travel times give the full picture of the overall benefit to all customers inside and outside the corridor each time a vehicle is added to the corridor. By optimizing the aggregate travel times inside and outside of the corridor so that the total aggregate travel time is minimized, we find the best $ F_\text{inside} $ for the corridor.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 697-700: code points 1-17

Continuing the example, one can now calculate the aggregate travel times both inside and outside the corridor, assuming that one will include 179 vehicles in the BRT corridor. The average travel time per vehicle when there are 179 vehicles in the corridor is 0.5 hours. So using Equation 6.23, one should multiply the per vehicle travel time inside the BRT corridor at a frequency of 179 vehicles by 179, to get the aggregate travel time for 178 vehicles inside the corridor. That is:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 702-706: code points 1-76

$ ATT_\text{inside}(F_\text{inside}=179)=0.5 \text{hours}*179=89.5 \text{hours} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 708-708: code points 1-83

If one includes 179 vehicles inside the BRT corridor, then 21 are left out. The travel time per bus outside of the BRT corridor ($TT_\text{outside}$) is fixed at 0.5 hours (again, equal to $TT_\text{inside} $ only in this case). So one should multiply the per bus travel time outside the BRT corridor by 21 to get the aggregate travel time for 21 buses outside the corridor. That is:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 710-713: code points 1-55

$ ATT_\text{outside}(F_\text{inside}=179)=0.5 \text{hours}*21=10.5 \text{hours} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 715-715: code points 1-83

Thus,\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 717-717: code points 1-5

$ ATT_\text{total}(F_\text{inside}=179)=89.5+10.5=100\text{hours}$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 719-719: code points 1-68

Exploring visually the properties of Equation 6.16, Figure 6.36 shows the aggregate travel times both inside and outside the BRT corridor when 179 vehicles are included inside the corridor ($ F_\text{inside} = 178$). Aggregate travel times are indicated by the blue ($TT_\text{inside}$) and orange ($TT_\text{outside}$) shaded areas. Note that the shaded areas are rectangular in shape. This is because every bus in either category ($ F_\text{inside} $ or $F_\text{outside}$) experiences a travel time equal to every other bus in its category.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 721-725: code points 2-92


			\ifxetex
				% disabled for now
			\else
				{  % group required to avoid fignote settings escaping
					\img{\hsize}{operations/assets/b08a28f10cd512c0cce57ef84a1d6ac5ad162e3e.png}
					\fignote{36}{Scenario I aggregated travel times, obtained by multiplying by the fixed travel time for all buses (0.5) by the number of buses inside the busway (179, represented by the blue shading) and outside the busway (21, represented by the orange shading), one should get $ATT_\text{inside}(F_\text{inside}=179) 
= 89.5 \text{hours} $ and $ ATT_\text{outside}(F_\text{inside}=179) = 10.5 \text{hours} $, respectively.\label{chapter:service-planning:figure:scenario-i-aggregated-travel-times-obtained-by-multiplying-by-the-fixed-travel-time-for-all-buses-05-by-the-number-of-buses-inside-the-busway-179-represented-by-the-blue-shading-and-outside-the-busway-21-represented-by-the-orange-shading-one-should-get-atttextinsideftextinside179895texthours-and-atttextoutsideftextinside179105texthours-respectively}}{Elebeta.}
				}
			\fi

One can already tell that $F_\text{inside} = 179 $ is not the optimal frequency for this corridor, since one knows that total area (an $ ATT_\text{total} $ of 100 hours) is not the lowest aggregate travel time that is achievable in this example and can be diminished. Figure 6.37 shows an example of a reduced area for $ F_\text{inside}= 150$ totaling 70.75 hours, i.e., $ ATT_\text{total} (F_\text{inside}=150) = 70.75 \text{hours} $.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 732-735: code points 1-94

\ifxetex
			% disabled for now
		\else
			{  % group required to avoid fignote settings escaping
				\img{\hsize}{operations/assets/df45f57e07729595c1fac05c4a7b36e813bbb68b.png}
				\fignote{37}{Scenario I aggregated travel times, obtained by multiplying by the fixed travel time for all buses inside the busway (0.305 hour) by the number of buses inside the busway (150, represented by the blue shading) added with the travel time outside the busway (0.50) multiplied by number of buses outside (50, represented by the orange shading), one should get $ AT_\text{Tinside} (F_\text{inside}=150) = 45.75 
\text{hours} $ and $ ATT_\text{outside} (F_\text{outside}=179) = 25 \text{hours} $, respectively.\label{chapter:service-planning:figure:scenario-i-aggregated-travel-times-obtained-by-multiplying-by-the-fixed-travel-time-for-all-buses-inside-the-busway-0305-hour-by-the-number-of-buses-inside-the-busway-150-represented-by-the-blue-shading-added-with-the-travel-time-outside-the-busway-050-multiplied-by-number-of-buses-outside-50-represented-by-the-orange-shading-one-should-get-attexttinsideftextinside1504575texthours-and-atttextoutsideftextoutside17925texthours-respectively}}{Elebeta.}
			}
		\fi

We determine the lowest aggregate travel time achievable by evaluating the time savings and time losses of shifting an additional bus route (or the bus frequencies of that route) onto the corridor. Each time a vehicle is added to the corridor, some time savings are realized to the customers on the vehicle that has been shifted, due to the higher speed of the bus lane. At the same time, delay is created for all the customers on vehicles already in the bus lane, which now suffer some new (marginal) congestion due to a larger number of vehicles travelling there.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 743-748: code points 1-48

In order to determine the savings, one should subtract the travel time for one vehicle inside the bus lane from the travel time for one bus outside the bus lane. When calculating the travel time per vehicle inside the bus lane, one does so based on congestion incurred by the \emphasis{new} frequency (i.e., $ F_\text{inside} + 
1 $), since the new travel time caused by that vehicle is ultimately the travel time that vehicle will experience. One therefore defines the benefit of adding one vehicle to the corridor as:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 750-754: code points 1-87

Eq. 6.31\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 756-756: code points 1-8

$ ATT_\text{savings}(1)=TT_\text{outside}–TT_\text{inside-after-shift} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 758-758: code points 1-74

$ ATT_\text{savings}(1)=TT_\text{outside}–TT_\text{inside}(F_\text{inside}=F_\text{inside-before}+1)$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 760-760: code points 1-103

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 762-763: code points 1-0

\begin{itemize}
\item $ ATT_\text{savings}(1) $: Benefit of adding one vehicle to the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 763-764: code points 1-0
\item $ TT_\text{outside} $: Travel time outside the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 764-765: code points 1-0
\item $ TT_\text{inside-after-shift} = TT_\text{inside}(F_\text{inside} = F_\text{inside-before} + 1)$: Travel time per bus inside the busway based on congestion incurred by the new frequency of adding one vehicle inside the busway.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 765-766: code points 1-90
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 763-766: code points 1-90

$ATT_\text{savings}(1)$ indicates that one vehicle is added to the corridor. Were one to be complete, one would multiply this benefit by the number of customers on the vehicle shifted into the bus lane. Again, since customer volumes are the same from one vehicle to another, this can be left out for now.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 768-770: code points 1-88

If expanded to shifting multiple vehicles ($N_\text{shift}$) to the corridor, one must calculate $TT_\text{inside}$ based on the old frequency plus the number of new vehicles (i.e., $ F_\text{inside}  + N_\text{shift}$). Additionally, the benefit is realized not just by the customers on one vehicle but by the customers on all the vehicles shifted to the corridor. So the entire savings calculation must be multiplied by the number of vehicles added (and by the number of customers shifted in later scenarios).\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 772-776: code points 1-60

Eq. 6.32\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 778-778: code points 1-8

$ATT_\text{savings}(N_\text{shift}) =TT_\text{outside}–TT_\text{inside-after-shift}*N_\text{shift}$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 780-780: code points 1-101

$ATT_\text{savings}(N_\text{shift}) =TT_\text{outside}–TT_\text{inside}( F_\text{inside} = F_\text{inside-before}+N_\text{shift})*N_\text{shift} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 782-782: code points 1-148

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 784-785: code points 1-0

\begin{itemize}
\item $ ATT_\text{saving}(N_\text{shift}) $: Aggregated travel time savings of adding Nshift vehicles to the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 785-786: code points 1-0
\item $ TT_\text{outside} $:Travel time per bus outside the busway (it does not change with frequency);% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 786-787: code points 1-0
\item $ TT_\text{inside-after-shift}( F_\text{inside} = F_\text{inside-before}+N_\text{shift}) $: Travel time per bus inside the busway based on the old frequency plus the number of new vehicles;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 787-789: code points 1-0
\item $ N_\text{shift}:$ Number of shifting vehicles inside the busway.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 789-789: code points 1-73
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 785-789: code points 1-73

The time losses of shifting one vehicle onto the busway are felt by all the customers on the other vehicles already travelling within the BRT infrastructure, since every new vehicle adds some congestion to the busway. This is calculated by subtracting the travel time before the shift from the travel time after the shift, as this is the marginal cost to each previously existing vehicle of shifting new vehicles. Next, one should multiply this by the total number of previously existing vehicles to get the full cost of adding new vehicles. The cost is defined as:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 791-796: code points 1-47

Eq. 6.33\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 798-798: code points 1-8

$ ATT_\text{losses}(N_\text{shift})=(TT_\text{inside-after-shift}–TT_\text{inside-before-shift}) * F_\text{inside-before-shift}$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 800-800: code points 1-130

$ ATT_\text{losses}(N_\text{shift})=(TT_\text{inside} (F_\text{inside}=F_\text{inside-after-shift})–TT_\text{inside}(F_\text{inside} = F_\text{inside-before-shift}))* F_\text{inside-before-shift}$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 802-802: code points 1-198

$ ATT_\text{losses}(N_\text{shift})=(TT_\text{inside} (F_\text{inside}=F_\text{inside-before-shift} + N_\text{shift})–TT_\text{inside}(F_\text{inside} = F_\text{inside-before-shift}))* F_\text{inside-before-shift}$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 804-804: code points 1-216

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 806-807: code points 1-0

\begin{itemize}
\item $ ATT_\text{losses} (N_\text{shift})$: Aggregated time losses by moving $N_\text{shift}$ vehicles onto the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 807-808: code points 1-0
\item $ TT_\text{inside-in-situation} $: Travel time per bus inside the busway as a function of the frequency inside the busway in given situation;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 808-810: code points 1-0
\item $ TT_\text{inside} (F_\text{inside} = K)$: Travel time per bus inside the busway based on a frequency of $K$ vehicles inside the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 810-812: code points 1-0
\item $ F_\text{inside-before-shift} $: Number of buses per hour inside the busway before moving vehicles;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 812-813: code points 1-0
\item $ F_\text{inside-after-shift} $: Number of buses per hour inside the busway after moving vehicles.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 813-813: code points 1-106
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 807-813: code points 1-106

Continuing the example, suppose the decision was initially made to include 80 vehicles in the corridor, and now one wants to know whether it would be better to include 90. So 10 vehicles are being shifted onto the corridor.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 815-817: code points 1-18

The aggregated time savings can be calculated using Equation 6.32:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 819-819: code points 1-66

$ATT_\text{savings}(10)=TT_\text{outside}–TT_\text{inside}(90)*10$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 821-821: code points 1-68

$TT_\text{outside}=0.5$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 823-823: code points 1-25

$TT_\text{inside}(90)={L_\text{corridor} \over V_\text{inside-no-congestion}}+({0.7 * T_d ^2 * F_\text{inside} \over 1- (T_d *F_\text{inside} )}*N_\text{stations})=0.2286$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 825-825: code points 1-173

So,$ATT_\text{savings}(10)=(0.5-0.2286)*10=2.714 \text{hours} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 827-827: code points 1-65

The aggregated travel time losses can be calculated using Equation 6.25:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 829-829: code points 1-72

$ATT_\text{losses}(10)=TT_\text{inside}(90)-TT_\text{inside}(80)*80 $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 831-831: code points 1-71

above, $TTinside(90)=0.2286 $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 833-833: code points 1-31

And from the first moment of this example (saturation):\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 835-835: code points 1-55

$ T_\text{Tinside}(80)=0.2233$.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 837-837: code points 1-33

So,$ATT_\text{losses10}=0.2286-0.2233*80=0.424 \text{hours}$.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 839-839: code points 1-63

On the corridor, the benefits of increasing the number of vehicles inside the busway from 80 to 90 outweigh the costs by a total of $ 2.714 - 0.424 = 2.29 \text{hours}$. The 10 buses should therefore be shifted in.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 841-843: code points 1-3

In Figure 6.38, the blue box shows the $ATT_\text{inside}$ for 80 vehicles and the light orange box shows the $ ATT_\text{outside} $ for the remaining 120 buses outside the corridor. If another 10 vehicles are added to the corridor, the blue box expands to 90, and the orange box shrinks to 110, with the purple area being transferred from one to the other. The benefit of including the 10 new vehicles in the corridor is shown by the green rectangle where the aggregate travel time savings is realized. This benefit is realized for the customers on the 10 new vehicles that can now use the bus lane.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 845-850: code points 1-53

Meanwhile, the “cost” of including 10 new vehicles in the corridor is shown in the yellow sliver between 0.2233 and 0.2286, where the 80 vehicles that previously travelled the corridor now need to accommodate an additional 10 vehicles, slowing down the travel time for all the customers on those buses. The cost is therefore on the customers on the 80 vehicles now suffering the new congestion.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 852-855: code points 1-82

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/ca97219abb88b68d4cd5465dc3f74da947ec173d.png}
		\fignote{38}{The losses to the buses inside the busway, $ATT_\text{loss}$ as represented by the light yellow rectangle, of shifting 10 buses into the corridor, amount to 0.424 hours. The aggregated time savings of those 10 buses, $ ATT_\text{savings} $ as represented by the green rectangle, amounts to 2.714 hours. Since the time savings are greater for those 10 buses than the losses to other buses already inside the corridor, it is still beneficial to shift in more buses.\label{chapter:service-planning:figure:the-losses-to-the-buses-inside-the-busway-atttextloss-as-represented-by-the-light-yellow-rectangle-of-shifting-10-buses-into-the-corridor-amount-to-0424-hours-the-aggregated-time-savings-of-those-10-buses-atttextsavings-as-represented-by-the-green-rectangle-amounts-to-2714-hours-since-the-time-savings-are-greater-for-those-10-buses-than-the-losses-to-other-buses-already-inside-the-corridor-it-is-still-beneficial-to-shift-in-more-buses}}{Elebeta.}
	}
\fi

To minimize aggregated travel time, the goal is to maximize the white area under the orange line for any given frequency inside the BRT in Figure 6.38, which in the shifting example includes the green area and loses the yellow area. So long as the area of the green rectangle (the time gains by customers on buses outside the BRT, or $ ATT_\text{savings} $) is greater than the yellow rectangle (the time lost to the customers on buses inside the BRT due to congestion, or $ ATT_\text{loss} $), more buses should be shifted in. For lower vehicle frequencies, the benefit of adding more vehicles to the BRT lane is even larger and the losses smaller. The benefit is larger than the cost because the new vehicles are going faster inside the BRT, and they are not yet adding much congestion to the bus lane (i.e., the curve is flatter at lower frequencies). Conversely, at higher frequencies, the benefit drops, and the costs increase. An optimal frequency is reached when the benefits equal the marginal costs of the last vehicle added, or where the area of the white rectangle is maximized.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 863-873: code points 1-29

The simplest way to make this determination is to include the formulas above in a table and simply calculate $ ATT_\text{total} $ at each frequency. One can do this in increments of 5. The resulting Table 6.18 is as follows:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 875-878: code points 1-0

\tabletitle{18}{Optimal Frequency inside a BRT Corridor}
\label{chapter:service-planning:table:optimal-frequency-inside-a-brt-corridor}
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	\noalign{\vskip 2mm 
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	\color{gray50}0.5&
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	\color{gray50}\highlight{124.36}\cr
	\noalign{\vskip 2mm 
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	\color{gray50}10&
	\color{gray50}0.86500&
	\color{gray50}0.5&
	\color{gray50}164.35&
	\color{gray50}5.00&
	\color{gray50}\highlight{169.35}\cr
	\noalign{\vskip 2mm 
}	\color{gray50}\highlight{199}&
	\color{gray50}1&
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	\color{gray50}0.5&
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	\noalign{\vskip 2mm 
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% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 878-1111: code points 1-9

Table 6.18 shows that the $ ATT_\text{total} $ reaches its minimum somewhere around $ F_\text{inside} = 135 $. At that point, $ ATT_\text{total} = 69.3 $. It is worth noting also that at $ F_\text{inside} = 199 $, $ ATT_\text{inside} $ suddenly skyrockets. This is because 200 is where saturation, $x$, reaches 1. At $ F_\text{inside} = 195$,$ x = 0.975$ and already $ ATT_\text{inside} $ is increasing more dramatically. But in the shift of the last five vehicles, the functioning of the busway breaks down, and at 200, it is saturated.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1113-1117: code points 1-28

One can also plot this in order to see graphically the point of the minimum aggregate travel time.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1119-1119: code points 1-98

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/730d1561893b7d01bce28da6755d2db03ac49036.jpeg}
		\fignote{39}{Plot of $ ATT_text{inside} $, $ ATT_text{outside} $, and $ATT_\text{Total}$ for each new bus added to the corridor. The minimum aggregate travel time is reached where $ATT_\text{Total}$ is the lowest, i.e., between 130 and 140 buses per hour.\label{chapter:service-planning:figure:plot-of-atttextinside-atttextoutside-and-atttexttotal-for-each-new-bus-added-to-the-corridor-the-minimum-aggregate-travel-time-is-reached-where-atttexttotal-is-the-lowest-ie-between-130-and-140-buses-per-hour}}{Elebeta.}
	}
\fi

So the approximate optimal frequency inside the busway is 135. However, one does not know whether it is precisely 135. At $ F_\text{inside} =130$, $ ATT_text{inside} = 69.5 $ and at $ F_\text{inside} =140 $, $ ATT_\text{inside} = 69.4$. It is possible that the minimum $ ATT_\text{inside} $ falls somewhere between $ F_\text{inside} =130 $ and $ F_\text{inside} =140 $. One should look more closely, and with a greater degree of precision, at $ ATT_\text{inside} $ for each of the values between $ F_\text{inside}  
(130) $ and $ F_\text{inside} (140)$.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1125-1129: code points 1-40

\tabletitle{19}{Optimal Frequency Inside the Busway}
\label{chapter:service-planning:table:optimal-frequency-inside-the-busway}
\halign to 30\tablemodule{%
	\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\hbox to 0.5\tablemodule{}&
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	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\cr
	\color{gray75}\bfseries \highlight{F inside (bus\slash{}hour)}& \color{gray75}\bfseries \highlight{F outside (bus\slash{}hour)}& \color{gray75}\bfseries \highlight{TT inside (hour\slash{}bus)}& \color{gray75}\bfseries \highlight{TT outside (hour\slash{}bus)}& \color{gray75}\bfseries \highlight{ATT inside (hour)}& \color{gray75}\bfseries \highlight{ATT outside (hours)}& \color{gray75}\bfseries \highlight{ATT total (hours)} \cr
	\noalign{\vskip 1mm} \hline \noalign{\vskip 2mm} 
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}	\color{gray50}\highlight{138}&
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% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1131-1228: code points 1-9

Table 6.19 confirms that the minimum aggregate travel time (69.31) is indeed at $ F_\text{inside} $ = 135.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1230-1230: code points 1-108

One can also zoom in to the graph from above to see that more clearly.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1232-1232: code points 1-70

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/8cda677ea6cdfa80f5ffc321967b0f7b617bdc8a.jpeg}
		\fignote{40}{Zoom-in of Figure 6.39 above to confirm minimum ATTTotal at 130 to 140 buses per hour. Image\label{chapter:service-planning:figure:zoom-in-of-figure-639-above-to-confirm-minimum-atttotal-at-130-to-140-buses-per-hour-image}}{Elebeta.}
	}
\fi

Therefore, as a first pass, if bus routes have similar levels of demand and fleet characteristics, services should be selected so that routes with a total frequency of about 135 vehicles per hour should be included in the BRT corridor, and routes with the remaining 55 vehicles per hour should be left to operate in mixed traffic.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1237-1240: code points 1-25

\subsubsection{2}{Scenario II: Dwell Times and Demand Vary from Route to Route, and All Stations Are Similar}
\label{volume:operations:chapter:service-planning:section:determining-which-routes-to-include-inside-brt-infrastructure:subSection:avoiding-station-saturation:subSubSection:scenario-ii-dwell-times-and-demand-vary-from-route-to-route-and-all-stations-are-similar}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1242-1472: code points 1-24

In this example, customer volumes, dwell times, vehicle type, and route frequencies all vary. In this case, maximizing total benefits will require deciding which bus routes to include in the BRT system and which routes to exclude. To do this, first calculate average passenger volumes and dwell times by route so that the variation is between routes, rather than between buses. For this example we will assume that stations become saturated equally. Although this seems a too hypothetical situation, a central BRT section with high renovation factor could look somewhat like this and still keep the same loads along the section. As load is relevant to this example and we are assuming it is constant through all stations, to visualize this situation one should imagine that the number of boardings is similar to the number of alightings in every station. In this example, it is assumed that one is unable, due to lack of political will, to take sufficient road space to build stations with the necessary passing lane and sub-stops to avoid station saturation. The following is also assumed:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1244-1254: code points 1-42

$L_\text{corridor}$: Corridor length = 5 km;\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1256-1256: code points 1-46

$V_\text{outside}$: Velocity outside the busway = 12 km\slash{}h;\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1258-1258: code points 1-60

$V_\text{inside}$:Velocity inside BRT at free-flow speed = 25 km\slash{}h;\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1260-1260: code points 1-69

$N_\text{stations}$ = 10;\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1262-1262: code points 1-27

In this scenario, besides varying demand levels at stations, bus types are also different. Because it is not always possible to replace the entire fleet of buses with BRT vehicles all at once, the vehicles are going to vary in size and configuration in ways that will change the dwell time per customer. Because of this varying dwell time per customer, the BRT infrastructure will saturate to different degrees depending on which routes are incorporated into the BRT system. This will be one important change from Scenario I. Now, rather than simply determining how many routes to include, it is possible to determine \emphasis{which }routes to include. This requires using a time savings formula to be applied to the number of customers instead of to the vehicles.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1264-1271: code points 1-27

The service planner would have collected two types of data about each route:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1273-1274: code points 1-0

\begin{itemize}
\item \emphasis{Frequency and occupancy surveys}, which will give the system planner the number of vehicles per route per hour, and their estimated occupancy;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1274-1276: code points 1-0
\item \emphasis{Boarding and alighting data} per route, which will give the number of passengers boarding and alighting at each station stop.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1276-1277: code points 1-31
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1274-1277: code points 1-31

Table 6.20 provides an example showing thirteen bus routes with varying dwell times and customer volumes. This example will be used to demonstrate the methodology for determining which routes to include.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1279-1280: code points 1-97


			\ifxetex
				% disabled for now
			\else
				{  % group required to avoid fignote settings escaping
					\tabletitle{20}{Example of Route Choice}
\label{chapter:service-planning:table:example-of-route-choice}

					\img{\hsize}{operations/assets/24711cd4df53aef47c54419c5d1afd239f6931e3.jpeg}
				}
			\fi

In Table 6.20 the fixed dwell time (or “dead time”) per bus is varied in a very simple way: either the bus is a large bus with a time of 12 seconds, it is a smaller bus with a time of 10 seconds, or there is one very small bus with a time of four seconds. The projected boarding and alighting time per bus route also only varies based on the vehicle type. For those new BRT-type buses with at-level boarding and three or four wide doors, one should estimate that the boarding and alighting time per customer will be one second, while for typical older buses one should assume the boarding or alighting time per passenger will be three seconds. These are reasonable values. The boarding and alighting passenger volumes are collected from the boarding and alighting survey for the bottleneck station. By adding the fixed dwell time ($T_0$) to the boarding and alighting time per route ($T_b + T_a$), the total dwell time per bus ($T_d$) can be calculated and is shown in the table above.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1308-1317: code points 1-73

Using the results of the occupancy survey, one can now define a new variable, Pax(i). This refers to the average occupancy on each bus within a single route “i,” in the peak hour passing the station most likely to face a bottleneck. With this, a “priority index” can be calculated in order to determine which routes to include first:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1319-1322: code points 1-24

Eq. 6.34\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1324-1324: code points 1-8

$ \text{Priority}(i)={\text{Pax}(i) \over T_d(i)} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1326-1326: code points 1-53

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1328-1329: code points 1-0

\begin{itemize}
\item $ \text{Priority}(i)$: Priority index of route “i”; Passengers per second of dwell time on route “i” at the bottleneck station;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1329-1330: code points 1-0
\item $  \text{Pax}(i)$: Average occupancy of each bus on route “i” as the bus passes the station;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1330-1331: code points 1-0
\item $ T_d(i)$: Total dwell time in seconds of each bus on route “i”.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1331-1331: code points 1-72
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1329-1331: code points 1-72

In other words, priority should be given to those bus routes where the most passengers are able to benefit from the busway for each second used at the bottleneck station. Bus routes should be listed in descending order of this priority index, so that routes with more customers per second of dwell time consumed at the bottleneck station are included first, and so on. In Table 6.21, the routes are ranked based on the priority index listed in the column labeled “Priority index.”\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1333-1337: code points 1-74


			\ifxetex
				% disabled for now
			\else
				{  % group required to avoid fignote settings escaping
					\tabletitle{21}{Ranking of Routes for Route Choice}
\label{chapter:service-planning:table:ranking-of-routes-for-route-choice}

					\img{\hsize}{operations/assets/c9e38eb0236df7aa11e96427c0b37b13d028e30b.jpeg}
				}
			\fi

Each row in Table 6.21 represents a new route to be included in the BRT infrastructure. Starting with the empty busway, the last column shows the benefit in customers-hours (during one hour of operation) for including the route and all routes in rows above. After route “j,” the row in blue, overall benefits start to decrease, so no more routes should be included.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1365-1368: code points 1-90

Now one can proceed with the methodology used in Scenario I, noting some differences. One should begin by calculating saturation. In this case, the dwell times should still be added up per route, but since dwell times vary from route to route, one cannot simply multiply one dwell time by total frequency inside the busway. Instead, one should multiply dwell time per route by frequency per route and then perform the full summation. So, in this case, the saturation formula should be written as:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1370-1374: code points 1-82

Eq. 6.35 $ x = \sum_{\text{route-inside}} (T_{d i} * F_i) / 3600 $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1376-1377: code points 1-59

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1379-1380: code points 1-0

\begin{itemize}
\item $ x $: Saturation at station;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1380-1381: code points 1-0
\item $ T_{d i} $: Total dwell time at station for route “i” in seconds;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1381-1382: code points 1-0
\item $ F_i $: Frequency of route “i” in vehicles\slash{}hour.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1382-1382: code points 1-57
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1380-1382: code points 1-57

In Table 6.21, station saturation ($x$) is recalculated each time a new route is added. So saturation when only Route B is part of the BRT service plan, is the number of seconds of an hour (the peak hour) that Route B consumes in total dwell time ($=(T_0 * \text{Freq})/3600 = 10 * 20/3600 = 0.056$), meaning that Route B uses 5.6 percent of available station time in an hour.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1384-1387: code points 1-56

If Route F is added, the BRT service plan includes Routes B and F. The station saturation that is contributed by Route F (calculated in the same manner as above) is simply added to the saturation contributed by Route B, or in this case 8.3 percent, and so on.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1389-1391: code points 1-48

As is discussed in Chapter 7: Capacity and Speed, a busway starts to saturate when $x = 0.4$, so routes where $ x > 0.4 $ should probably be excluded, pending further analysis.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1393-1394: code points 1-74

The average queue time (average for all buses using the station) is calculated using the same formula from Scenario I (Eq. 6.30a):\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1396-1397: code points 1-28

Eq. 6.30a\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1399-1399: code points 1-9

$ T_q={0.7 * x^2 \over 1-x }  {1 \over F_\text{inside}} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1401-1401: code points 1-59

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1403-1403: code points 1-6

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1405-1406: code points 1-0

\begin{itemize}
\item $ T_q $: One vehicle queueing time at each station;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1406-1407: code points 1-0
\item $ x $: Saturation of the station;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1407-1408: code points 1-0
\item $ F_\text{inside} $: Number of buses per hour inside the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1408-1408: code points 1-72
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1406-1408: code points 1-72

So going back to including only Route B, the queuing delay is simply:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1410-1410: code points 1-69

$T_q = {0.7* 0.056 ^ 2 \over (1-0.056)} * { 1 \over 20} = 0.00114  \text{hours}=0.4 \text{seconds} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1412-1412: code points 1-102

For this low frequency, 20 vehicles\slash{}hour, the average delay is less than 0.5 seconds, virtually no delay; as we add more vehicles this increases visibly.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1414-1415: code points 1-54

For a more refined analysis, the additional time savings and losses of shifting a route is done per customer. The final piece of information that is needed in order to determine benefits for customers is the customer load passing the station. Load is calculated by multiplying the frequency times the observed customer occupancy per bus on the link approaching the bottleneck station. In the case of including only Route B, the load is 1,000. In the case where both Routes B and F are included in the BRT service, the load is the load for both Route B and Route F, or 1,000 + 500 = 1,500. Load is the sum of all occupancies on all routes included in the BRT infrastructure.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1417-1423: code points 1-49

Eq. 6.36\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1425-1425: code points 1-8

$ \text{Load}_\text{inside} = \sum_\text{routes-inside} (O_{\text{route }i} * F_{\text{route }i} )$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1427-1427: code points 1-101

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1429-1429: code points 1-6

\begin{itemize}
\item $ \text{Load}_\text{inside} $: Customer load inside the BRT infrastructure;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1431-1432: code points 1-0
\item $ \text{routes-inside} $: Number of routes inside the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1432-1433: code points 1-0
\item $ O_{\text{route }i}$: Occupancy on route i (inside the busway);% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1433-1434: code points 1-0
\item $ F_{\text{route }i}$: Frequency of route i (inside the busway).% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1434-1434: code points 1-72
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1431-1434: code points 1-72

We then calculate the total aggregated time savings for including each additional route, using the same benefit formula from Scenario I, as the calculus is cumulative, i.e., started from the reference situation where there are no routes inside the busway, there is no time loss to be computed due to the addition of the new route. The time savings must be multiplied by the passenger load instead of the vehicles to determine actual benefits to passengers, by using Equations 6.24a, 6.24c, and a variant of 6.24 (6.30 below):\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1436-1441: code points 1-7

Eq. 6.24a\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1443-1443: code points 1-9

$TT_\text{outside}={L_\text{corridor} \over V_\text{outside}}$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1445-1445: code points 1-64

Eq. 6.24c\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1447-1447: code points 1-9

$ TT_\text{inside}={L_\text{corridor} \over V_\text{inside-no-congestion}}+T_q*N_\text{stations}$\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1449-1449: code points 1-99

Eq. 6.37\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1451-1451: code points 1-8

$ ATT_\text{savings} = (TT_\text{outside} – T_\text{Tinside}) * \text{Load}_\text{inside} $\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1453-1453: code points 1-93

Where:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1455-1456: code points 1-0

\begin{itemize}
\item $ ATT_\text{savings} $: Aggregated Travel Time savings for including selected routes in the BRT infrastructure;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1456-1457: code points 1-0
\item $ \text{Load}_\text{inside} $: Customer load inside the BRT infrastructure;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1457-1458: code points 1-0
\item $ TT_\text{inside} $: Travel time per bus inside the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1458-1459: code points 1-0
\item $ TT_\text{outside}$: Travel time per bus outside the busway;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1459-1460: code points 1-0
\item $ L_\text{corridor}$: Length of the corridor;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1460-1461: code points 1-0
\item $ V_\text{outside}$: Velocity outside the busway.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1461-1462: code points 1-0
\item $ V_\text{inside-no-congestion} $: Velocity inside the busway without delay at stations;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1462-1463: code points 1-0
\item $ T_q $: Average delay for each vehicle at a single station due to queuing;% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1463-1464: code points 1-0
\item $ N_\text{stations} $: Number of stations along the busway.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1464-1464: code points 1-67
\end{itemize}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1456-1464: code points 1-67

We do not need, in fact, to look at the aggregate travel time outside the corridor to determine which routes must be included. Aggregated travel time savings alone can answer for the utility of the inclusion of each additional route, and the point where the benefits are highest should be selected. In this case, benefits reach a maximum in the scenario where the following routes are included in the BRT services plan: B, F, K, H, D, M, G, J, and Routes A, I, E, L, and C are left to operate in mixed traffic. The result is almost the same as simply cutting off new routes when the saturation level reaches 0.4, except one more route is added.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1466-1472: code points 1-24

\subsubsection{3}{Scenario III: Dwell Time and Occupancies Vary from One Bus Stop to the Next}
\label{volume:operations:chapter:service-planning:section:determining-which-routes-to-include-inside-brt-infrastructure:subSection:avoiding-station-saturation:subSubSection:scenario-iii-dwell-time-and-occupancies-vary-from-one-bus-stop-to-the-next}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1474-1687: code points 1-74

In this example, it is assumed that different bus routes are causing the saturation problem at different stations, and multiple stations face bottlenecks. This is the most typical of real-world situations. In this case, there may be more than one bottleneck station, and the bus routes causing the bottleneck might vary by station. This scenario attempts to include all bus routes that need to use the infrastructure based on their rankings and, like the previous scenarios, leaves out those routes for which the cost of including them is greater than the benefit.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1476-1481: code points 1-46

Considering a situation of 13 routes as the previous example, there are 8,191 possible combinations of routes to include inside the busway, and one could write a program to try them all to find which one yields the maximum aggregated travel time savings. If the number of routes doubles (26 routes), the number of possibilities increases to 67 million, which can still be tested in a feasible computational time. For 30 routes there are more than 1 billion combinations and for 40 routes, there are 1 trillion combinations, which computer brute force certainly cannot test.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1483-1488: code points 1-49

For determining an optimal solution in this case, one should use the simplified methodology presented here, which alone is likely to yield the ideal result or a limited and manageable number of alternatives. This is mostly because the demand profile from one route to another is usually not completely random. High levels of vehicle occupation and high dwell times are often clustered in the same areas and at the same stops across many routes.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1490-1494: code points 1-30

Here is a new example to demonstrate this methodology. Let’s say the corridor has three BRT stations (X, Y, and Z), and four potential bus routes (A, B, C, and D). The average dwell time and average occupancy on each route vary between stations.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1496-1499: code points 1-0

\begin{enumerate}
\item {For each station, make a table of bus routes including average occupancy and dwell time, and calculate the priority index, Priority (station), using Equation 6.26 from Scenario II. Using the new example, one will have three tables:\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1499-1502: code points 9-0

\tabletitle{22}{Route Characteristics at Station W}
\label{chapter:service-planning:table:route-characteristics-at-station-w}
\halign to 30\tablemodule{%
	\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=7\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=6\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=9\tablemodule#}\cr
	\color{gray75}\bfseries Route& \color{gray75}\bfseries Dwell time& \color{gray75}\bfseries Occupancy& \color{gray75}\bfseries PriorityiY \cr
	\noalign{\vskip 1mm} \hline \noalign{\vskip 2mm} 
	\color{gray50}&
	\color{gray50}TdiW&
	\color{gray50}OiW&
	\color{gray50}= OiY\slash{} TdiW\cr
	\noalign{\vskip 2mm 
}	\color{gray50}&
	\color{gray50}seconds\slash{}bus&
	\color{gray50}pax\slash{}bus&
	\color{gray50}pax\slash{}second\cr
	\noalign{\vskip 2mm 
}	\color{gray50}A&
	\color{gray50}10&
	\color{gray50}43&
	\color{gray50}4.3\cr
	\noalign{\vskip 2mm 
}	\color{gray50}B&
	\color{gray50}6&
	\color{gray50}20&
	\color{gray50}3.3\cr
	\noalign{\vskip 2mm 
}	\color{gray50}C&
	\color{gray50}10&
	\color{gray50}48&
	\color{gray50}4.8\cr
	\noalign{\vskip 2mm 
}	\color{gray50}D&
	\color{gray50}12&
	\color{gray50}55&
	\color{gray50}4.6\cr
	\noalign{\vskip 2mm 
}	\color{gray50}&
	\color{gray50}&
	\color{gray50}&
	\color{gray50}\cr
	\noalign{\vskip 2mm 
}}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1502-1543: code points 1-9

\tabletitle{23}{Route Characteristics at Station Y}
\label{chapter:service-planning:table:route-characteristics-at-station-y}
\halign to 30\tablemodule{%
	\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=7\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=6\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=9\tablemodule#}\cr
	\color{gray75}\bfseries Route& \color{gray75}\bfseries Dwell time& \color{gray75}\bfseries Occupancy& \color{gray75}\bfseries PriorityiW \cr
	\noalign{\vskip 1mm} \hline \noalign{\vskip 2mm} 
	\color{gray50}&
	\color{gray50}TdiY&
	\color{gray50}OiY&
	\color{gray50}= OiY\slash{} TdiY\cr
	\noalign{\vskip 2mm 
}	\color{gray50}&
	\color{gray50}seconds\slash{}bus&
	\color{gray50}pax\slash{}bus&
	\color{gray50}Pax\slash{}second\cr
	\noalign{\vskip 2mm 
}	\color{gray50}A&
	\color{gray50}10&
	\color{gray50}35&
	\color{gray50}3.5\cr
	\noalign{\vskip 2mm 
}	\color{gray50}B&
	\color{gray50}9&
	\color{gray50}20&
	\color{gray50}2.2\cr
	\noalign{\vskip 2mm 
}	\color{gray50}C&
	\color{gray50}8&
	\color{gray50}30&
	\color{gray50}3.8\cr
	\noalign{\vskip 2mm 
}	\color{gray50}D&
	\color{gray50}12&
	\color{gray50}40&
	\color{gray50}3.3\cr
	\noalign{\vskip 2mm 
}	\color{gray50}&
	\color{gray50}&
	\color{gray50}&
	\color{gray50}\cr
	\noalign{\vskip 2mm 
}}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1544-1585: code points 1-9

\tabletitle{24}{Route Characteristics at Station Z}
\label{chapter:service-planning:table:route-characteristics-at-station-z}
\halign to 30\tablemodule{%
	\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=7\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=6\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=9\tablemodule#}\cr
	\color{gray75}\bfseries Route& \color{gray75}\bfseries Dwell time& \color{gray75}\bfseries Occupancy& \color{gray75}\bfseries PriorityiY \cr
	\noalign{\vskip 1mm} \hline \noalign{\vskip 2mm} 
	\color{gray50}&
	\color{gray50}TdiZ&
	\color{gray50}OiZ&
	\color{gray50}= OiY\slash{} TdiZ\cr
	\noalign{\vskip 2mm 
}	\color{gray50}&
	\color{gray50}seconds\slash{}bus&
	\color{gray50}pax\slash{}bus&
	\color{gray50}pax\slash{}second\cr
	\noalign{\vskip 2mm 
}	\color{gray50}A&
	\color{gray50}15&
	\color{gray50}55&
	\color{gray50}3.7\cr
	\noalign{\vskip 2mm 
}	\color{gray50}B&
	\color{gray50}11&
	\color{gray50}33&
	\color{gray50}3.0\cr
	\noalign{\vskip 2mm 
}	\color{gray50}C&
	\color{gray50}7&
	\color{gray50}22&
	\color{gray50}3.1\cr
	\noalign{\vskip 2mm 
}	\color{gray50}D&
	\color{gray50}11&
	\color{gray50}30&
	\color{gray50}2.7\cr
	\noalign{\vskip 2mm 
}}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1586-1622: code points 1-9

}
\item {Determine the best priority order by averaging priority (station) for each route.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1624-1625: code points 10-0

\tabletitle{25}{Average Priority across Stations W, Y, Z}
\label{chapter:service-planning:table:average-priority-across-stations-w-y-z}
\halign to 30\tablemodule{%
	\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=24\tablemodule#}\cr
	\color{gray75}\bfseries Route& \color{gray75}\bfseries Average Priority \cr
	\noalign{\vskip 1mm} \hline \noalign{\vskip 2mm} 
	\color{gray50}&
	\color{gray50}= (OiY + OiW + OiZ)\slash{}3\cr
	\noalign{\vskip 2mm 
}	\color{gray50}&
	\color{gray50}pax\slash{}second\cr
	\noalign{\vskip 2mm 
}	\color{gray50}A&
	\color{gray50}3.8\cr
	\noalign{\vskip 2mm 
}	\color{gray50}B&
	\color{gray50}2.9\cr
	\noalign{\vskip 2mm 
}	\color{gray50}C&
	\color{gray50}3.9\cr
	\noalign{\vskip 2mm 
}	\color{gray50}D&
	\color{gray50}3.5\cr
	\noalign{\vskip 2mm 
}}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1625-1647: code points 1-9

And then reorder the routes in descending order based on the average priorities, one table per station.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1649-1650: code points 1-0

\tabletitle{26}{Routes Ordered by Average Priority}
\label{chapter:service-planning:table:routes-ordered-by-average-priority}
\halign to 30\tablemodule{%
	\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=24\tablemodule#}\cr
	\color{gray75}\bfseries Route& \color{gray75}\bfseries Average Priority \cr
	\noalign{\vskip 1mm} \hline \noalign{\vskip 2mm} 
	\color{gray50}&
	\color{gray50}= (OiY + OiW + OiZ)\slash{}3\cr
	\noalign{\vskip 2mm 
}	\color{gray50}&
	\color{gray50}pax\slash{}second\cr
	\noalign{\vskip 2mm 
}	\color{gray50}C&
	\color{gray50}3.9\cr
	\noalign{\vskip 2mm 
}	\color{gray50}A&
	\color{gray50}3.8\cr
	\noalign{\vskip 2mm 
}	\color{gray50}D&
	\color{gray50}3.5\cr
	\noalign{\vskip 2mm 
}	\color{gray50}B&
	\color{gray50}2.9\cr
	\noalign{\vskip 2mm 
}}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1650-1672: code points 1-9

}
\item Maintaining the priority order obtained above, add routes to the system as in Scenario II and obtain saturation and queue time per station, travel time inside the corridor, and aggregated time savings.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1674-1676: code points 1-0
\item For each station, assume corridor length as the distance (or half the distance) to the previous and next station and real observed speed outside the corridor to determine where the total aggregate travel time savings for that section reaches its minimum. Look in greater detail at the levels of saturation at critical stations, and if they are far from the individual optimum using the average priority, consider changing the route priority from the average route priority to something that more closely optimizes the route priority around the bottleneck station.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1676-1682: code points 1-0
\item Re-create the tables by station and see if the change results in a higher total benefit (sum of benefit of all stations calculated as in Scenario II): if yes, make the change; if not, try another.% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1682-1683: code points 1-100
\end{enumerate}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1499-1683: code points 1-100

These steps essentially replicate in a crude way what linear programming would do in a systematic way, and if the planner has data, time, and a deep understanding of these formulas, she or he can put all equations and restrictions into a system and look for an optimal solution.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1685-1687: code points 1-74

\subsubsection{4}{Conclusion of BRT Route Inclusion}
\label{volume:operations:chapter:service-planning:section:determining-which-routes-to-include-inside-brt-infrastructure:subSection:avoiding-station-saturation:subSubSection:conclusion-of-brt-route-inclusion}
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1689-1702: code points 1-0

In conclusion, when designing BRT services for a BRT corridor with constrained capacity, the inclusion of routes into BRT services should be based on ensuring that the aggregated travel time gains that accrue to the last route included in the BRT system outweigh the losses that its inclusion imposes on the other routes already included in the BRT system. This loss results from the additional bus route to the BRT system slowing down the speeds of the vehicles already inside the system.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1691-1695: code points 1-73

Further, the frequency and amount of overlap with the BRT corridor should be taken into consideration. Additionally, in order to help make decisions about which routes should be included in a new BRT service, a “priority” index could be created to measure the following: total customers on board the bus as it approaches the bottleneck stations divided by the total dwell time that that bus route uses at the bottleneck stations.\par
% @ guide/06-service_planning/65-determining-which-routes-to-include-inside-brt-infrastructure.src: lines 1697-1702: code points 1-0

\section{6}{Direct Services, Trunk-and-Feeder Services, or Hybrids}
\label{volume:operations:chapter:service-planning:section:direct-services-trunk-and-feeder-services-or-hybrids}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 3-1246: code points 1-0

\quotation{Paths cross all the time in this world of ours, sometimes in the strangest places.}{Stephen King, writer, 1947–}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 5-6: code points 1-29

When designing new services for a BRT system, the project team must decide which preexisting bus routes that continue beyond the BRT corridor should be incorporated into the new BRT service plan as “direct” services that enter and exit the BRT corridor, and which should be split into trunk routes operating inside the BRT infrastructure and feeder routes operating in mixed traffic and “feeding” the trunk stations. Whether and when to do this has been the subject of debate among BRT service planners. This section provides some basic guidance on how to make this determination in specific cases.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 8-13: code points 1-72

In general, most customers would prefer to take a bus directly from where their trip begins to where it ends. New BRT infrastructure on one corridor is not going to fundamentally change people’s trip origins and destinations in the short term. The new BRT infrastructure is likely to be built on a corridor with multiple preexisting public transport services that not only run up and down the corridor, but also continue beyond the corridor. Chances are that many people will not have destinations within walking distance of the new BRT stations, so if the preexisting services are discontinued, and only one BRT trunk service is running up and down the BRT infrastructure, many customers will be forced to use feeder services and transfer to trunk in stations along the corridor or at larger terminals. In the worst case, this transfer delay may be greater than the time benefit of using the BRT system.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 15-23: code points 1-67

The most important differences in the costs and benefits of direct services versus trunk-and-feeder services are as follows (listed here and described in detail below):\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 25-27: code points 1-0

\begin{itemize}
\item Fleet requirements: When demand is peaked, as is generally the case, more fleet is required for trunk-and-feeder services than for direct services. When demand is flat, fleet requirements are basically equivalent;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 27-30: code points 1-0
\item Vehicle sizes: When the trunk portion of the route is longer than the feeder portion, and many routes share the trunk corridor, larger vehicles can be used on the trunk routes, providing a cost savings for trunk-and-feeder services over direct services;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 30-33: code points 1-0
\item {Transfer costs: The greater the delay caused by the introduction of the new transfer, the greater the additional cost of trunk-and-feeder services, including:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 33-35: code points 8-0

\begin{itemize}
\item Running time;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 35-36: code points 1-0
\item Boarding and alighting delay;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 36-37: code points 1-0
\item Suboptimal terminal location;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 37-38: code points 1-0
\item Suboptimal terminal design on walking time;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 38-39: code points 1-0
\item Land acquisition and terminal construction costs.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 39-39: code points 1-55
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 35-39: code points 1-55

}
\item Station saturation: The greater the risk of trunk corridor station platform saturation, the greater the benefit of trunk-and-feeder services.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 40-41: code points 1-41
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 27-41: code points 1-41

This section systematically analyzes these key factors. Factors that did not vary significantly between trunk-and-feeder and direct service modes were not further considered. For instance, while some claim to prefer trunk-and-feeder systems to reduce irregularity of service inside the BRT trunk corridor, there is little empirical evidence to suggest any significant overall system-wide benefit of this. Having irregular arrivals of feeder buses at transfer terminals where conditions can become severely overcrowded, as frequently happens in Bogotá’s TransMilenio, is as problematic as having irregular direct services with a dispersed impact along the BRT trunk corridor.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 43-49: code points 1-36

The following sections provide some formulas based on the above criteria that should assist in making decisions about which bus routes to retain as direct services and which to cut into trunk-and-feeder services. As there are many variables to consider, alternatives should ideally be tested using a public transport demand model, and this should be complemented by an analysis of saturation and delays of each proposal at critical points such as at stations and signals.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 51-55: code points 1-60

\subsection{1}{Fleet Requirements for Direct Versus Trunk-and-Feeder Services}
\label{volume:operations:chapter:service-planning:section:direct-services-trunk-and-feeder-services-or-hybrids:subSection:fleet-requirements-for-direct-versus-trunk-and-feeder-services}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 57-360: code points 1-20

All other things being equal, trunk-and-feeder systems tend to require larger fleets than direct service systems, and the amount of extra fleet needed will vary based in large part on the degree to which the demand is concentrated in peak periods. This subsection explains the reasons for this effect, and uses the method of calculating fleet requirements in specific conditions.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 59-62: code points 1-68

As was discussed above in Section 6.4, the fleet size per route is generally determined by the fleet required to satisfy the maximum load that accumulates on the critical link during the course of the route cycle time during the peak period (Eq. 6.18: $ \text{Fleet}_\text{route} = {\text{MaxLoad}_\text{route} 
\over \text{VSize} * \text{LoadFactor}} $ ). Below, a series of scenarios illustrate the point, each with more complicated assumptions.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 64-68: code points 1-34

First, the fleet requirements for direct services with uniform demand throughout the day will be discussed. Then, calculating the fleet if demand varies between peak and off peak will be reviewed. Finally, some of the direct routes are split into trunk-and-feeder routes using the principles from the previous scenarios and fleet needs are compared between direct services and trunk-and-feeder services. In order to do this, one should have a BRT corridor with services that look like the diagram in Figure 6.41.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 70-74: code points 1-87

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/420452afb882e3a7e27f51bad38b215d6c414695.jpeg}
		\fignote{41}{Service pattern used for fleet calculations in Scenarios 1–3 below. Image\label{chapter:service-planning:figure:service-pattern-used-for-fleet-calculations-in-scenarios-13-below-image}}{ITDP.}
	}
\fi

We make the following additional assumptions:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 79-80: code points 1-0

\begin{itemize}
\item \emphasis{A} One should have already determined that the bus capacity (VSize), for the examples being considered have a design load factor of 85 percent, so in these examples the bus capacity is 60 passengers, though the real BRT vehicle capacity is 70 passengers;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 80-83: code points 1-0
\item \emphasis{B} All the bus routes operate on full BRT infrastructure between Downtown and the Terminal (as in diagram Figure 6.41), and all services operate in mixed traffic beyond the Terminal;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 83-85: code points 1-0
\item \emphasis{C} There is no overlap of routes until they reach the common point, Terminal;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 85-86: code points 1-0
\item \emphasis{D} The critical link with the maximum aggregate load (i.e., the load for all routes combined) occurs somewhere near the Terminal and continues at a similar level to Downtown;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 86-88: code points 1-0
\item \emphasis{E} The peak hour, in the cases where it exists, occurs earlier in the day on the link before the Terminal and later between the Terminal and Downtown.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 88-89: code points 1-53
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 80-89: code points 1-53

\subsubsection{1}{Comparative Fleet Advantages under Flat Demand with Uniform Routes}
\label{volume:operations:chapter:service-planning:section:direct-services-trunk-and-feeder-services-or-hybrids:subSection:fleet-requirements-for-direct-versus-trunk-and-feeder-services:subSubSection:comparative-fleet-advantages-under-flat-demand-with-uniform-routes}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 91-260: code points 1-98

In this situation, two service patterns are compared:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 93-94: code points 1-0

\begin{enumerate}
\item \emphasis{Direct Services}: A service pattern where multiple bus routes run in mixed traffic on local streets and then continue onto the BRT corridor (Figure 6.42).% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 94-96: code points 1-0
\item \emphasis{Trunk-and-Feeder Services}: A service pattern where multiple bus routes run in mixed traffic on local streets and terminate at a single terminal. Another bus route with higher frequency operates up and down the BRT corridor, and customers travelling between one and the other must transfer.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 96-98: code points 1-95
\end{enumerate}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 94-98: code points 1-95

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/80894b83e913041a38a4b20cc8f01f5db73be40f.jpeg}
		\fignote{42}{Service Pattern A—Direct Services: A service pattern where multiple bus routes run in mixed traffic on local streets and then continue onto the BRT corridor.\label{chapter:service-planning:figure:service-pattern-adirect-services-a-service-pattern-where-multiple-bus-routes-run-in-mixed-traffic-on-local-streets-and-then-continue-onto-the-brt-corridor}}{ITDP.}
	}
\fi

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/1887bdf3221b46ce9b201a4accfc7e81ccbc97b7.jpeg}
		\fignote{43}{Service Pattern B—Trunk-and-Feeder Services: A service pattern where multiple bus routes run in mixed traffic on local streets and terminate at a single terminal. Another bus route with higher frequency operates up and down the BRT corridor, and customers travelling between one and the other must transfer.\label{chapter:service-planning:figure:service-pattern-btrunk-and-feeder-services-a-service-pattern-where-multiple-bus-routes-run-in-mixed-traffic-on-local-streets-and-terminate-at-a-single-terminal-another-bus-route-with-higher-frequency-operates-up-and-down-the-brt-corridor-and-customers-travelling-between-one-and-the-other-must-transfer}}{ITDP.}
	}
\fi

When designing a BRT system, normally one could assume a reasonable BRT speed to be the equivalent of the speed of a vehicle operating during off-peak conditions, or one could assume a Gold Standard BRT system speed will be roughly 20 kph in a downtown area and about 25 kph on a major urban arterial. For this analysis, the cycle time (TC) of a direct service route will be the time spent on the trunk (at off-peak speeds) plus the time spent on the mixed traffic portion of the route at existing peak-hour mixed traffic speeds. For the trunk-and-feeder alternative, the TC of the trunk route will just be the time spent on the trunk portion of the route at off-peak speeds, and the feeder portion of the route will be the feeder portion of the route at existing peak-hour mixed traffic speeds. Therefore, one should define three types of TCs:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 108-116: code points 1-26

Eq. 6.38\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 118-118: code points 1-8

$ TC_\text{Trunk}=(L_\text{Trunk}*V_\text{Trunk Outbound})+(L_\text{Trunk}*V_\text{Trunk Inbound}) $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 120-120: code points 1-102

Where:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 122-123: code points 1-0

\begin{itemize}
\item $ TC_\text{Trunk} $: Cycle time in hours for a vehicle to complete one circuit of the trunk;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 123-124: code points 1-0
\item $ L_\text{Trunk} $: Length of the trunk;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 124-125: code points 1-0
\item $ V_\text{Trunk Outbound} $: Velocity on the outbound trunk;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 125-126: code points 1-0
\item $ V_\text{Trunk Inbound} $: Velocity on the inbound trunk.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 126-126: code points 1-66
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 123-126: code points 1-66

Eq. 6.39\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 128-128: code points 1-8

$ TC_\text{Feeders}=L_\text{Feeders}*V_\text{Feeders Outbound}+L_\text{Feeders}*V_\text{Feeders Inbound}$\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 130-130: code points 1-107

Where:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 132-133: code points 1-0

\begin{itemize}
\item $ TC_\text{Feeders} $: Cycle time in hours for a vehicle to complete one circuit of the feeders;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 133-134: code points 1-0
\item $ L_\text{Feeders} $: Length of the feeders;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 134-135: code points 1-0
\item $ V_\text{Feeders Outbound}$: Velocity on the outbound feeder;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 135-136: code points 1-0
\item $ V_\text{Feeders Inbound}$: Velocity on the inbound feeder.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 136-136: code points 1-68
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 133-136: code points 1-68

For our analysis, it is assumed that the cycle time for the trunk routes plus the cycle time for the feeder routes is as short as possible, being equivalent to the cycle time for the direct service routes or:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 138-140: code points 1-3

Eq. 6.40\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 142-142: code points 1-8

$ TC_\text{direct}=TC_\text{trunk}+TC_\text{feeder} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 144-144: code points 1-55

Where:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 146-147: code points 1-0

\begin{itemize}
\item $ TC_\text{Direct} $: Cycle time in hours for a vehicle to complete one circuit of the trunk-and-feeder services;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 147-148: code points 1-0
\item $ TC_\text{Trunk} $: Cycle time in hours for a vehicle to complete one circuit of the trunk service;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 148-149: code points 1-0
\item $ TC_\text{Feeder} $: Cycle time in hours for a vehicle to complete one circuit of the feeder service;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 149-149: code points 1-110
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 147-149: code points 1-110

Under these conditions, the benefit of a direct service will be the difference in the fleet requirements between Service Plan A and Service Plan B:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 151-152: code points 1-42

Eq. 6.41\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 154-154: code points 1-8

$ \text{Fleet}_\text{benefit direct}=\text{Fleet}_\text{trunk}+\text{Fleet}_\text{feeder}–\text{Fleet}_\text{direct} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 156-156: code points 1-120

Where:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 158-158: code points 1-6

\begin{itemize}
\item $ \text{Fleet}_\text{benefit direct} $: Benefit of a direct service in terms of the fleet;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 160-161: code points 1-0
\item $ \text{Fleet}_\text{trunk} $: Fleet requirement for the trunk service;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 161-162: code points 1-0
\item $ \text{Fleet}_\text{feeder} $: Fleet requirement for the feeder service;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 162-163: code points 1-0
\item $ \text{Fleet}_\text{direct} $: Fleet requirement for the direct service.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 163-163: code points 1-81
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 160-163: code points 1-81

Recall Equation 6.18 from Section 6.4, which shows that the fleet size is determined by the maximum load of passengers that accumulates over the course of the cycle time for a given bus size.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 165-166: code points 1-91

Equation 6.18 applied:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 168-168: code points 1-22

$ \text{Fleet}_\text{direct} = {\text{MaxLoadperCycle}_\text{direct} \over \text{VSize} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 170-170: code points 1-112

$ \text{Fleet}_\text{trunk} = {\text{MaxLoadperCycle}_\text{trunk} \over \text{VSize} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 172-172: code points 1-110

$ \text{Fleet}_\text{feeder} = {\text{MaxLoadperCycle}_\text{feeder} \over \text{VSize} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 174-174: code points 1-112

Where:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 176-177: code points 1-0

\begin{itemize}
\item $ \text{Fleet}_\text{trunk} $: Fleet requirement for the trunk service;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 177-178: code points 1-0
\item $ \text{Fleet}_\text{Feeder} $: Fleet requirement for the feeder service;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 178-179: code points 1-0
\item $ \text{Fleet}_\text{direct} $: Fleet requirement for the direct service.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 179-180: code points 1-0
\item $ \text{MaxLoadperCycle}_\text{trunk} $: Maximum load on the trunk service for one cycle time;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 180-181: code points 1-0
\item $ \text{MaxLoadperCycle}_\text{feeder} $: Maximum load on the feeder service for one cycle time;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 181-182: code points 1-0
\item $ \text{MaxLoadperCycle}_\text{direct} $: Maximum load on the direct service for one cycle time;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 182-183: code points 1-0
\item $ \text{VSize} $: Vehicle capacity;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 183-184: code points 1-0
\item $ \text{LoadFactor}$: Design load factor (usually 0.85), which is the same for all routes.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 184-184: code points 1-98
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 177-184: code points 1-98

The main assumption of this scenario, that the demand is uniform throughout the day, implies that the maximum load in the critical link (MaxLoad) is equal at any time. So the maximum load considered per cycle time (MaxLoadperCycle) for any given cycle time would be equal to the sum of two “maximum load per cycle” of smaller cycles times that add up to the same time, or, starting from Eq. 6.6a.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 186-189: code points 1-92

Eq. 6.6a\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 191-191: code points 1-8

$ \text{MaxLoadperCycle}=\text{MaxLoad}*TC $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 193-193: code points 1-46

$ \text{MaxLoadperCycle}_{T1}=\text{MaxLoad}*T1  $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 195-195: code points 1-52

$ \text{MaxLoadperCycle}_{T2}=\text{MaxLoad}*T2  $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 197-197: code points 1-52

$ \text{MaxLoadperCycle}_{T1+T2}=\text{MaxLoad}*(T1+T2) $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 199-199: code points 1-59

Eq. 6.42\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 201-201: code points 1-8

$ \text{MaxLoadperCycle}_(T1+T2)= \text{MaxLoadperCycle}T1 + \text{MaxLoadperCycle}_T2 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 203-203: code points 1-90

Where:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 205-206: code points 1-0

\begin{itemize}
\item $ \text{MaxLoadperCycle}_(T1+T2) $: Maximum load considered for the sum of cycle times 1 and 2;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 206-207: code points 1-0
\item $ \text{MaxLoadperCycle}_T1 $: Maximum load considered for cycle time 1;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 207-208: code points 1-0
\item $ \text{MaxLoadperCycle}_T2 $: Maximum load considered for cycle time 2.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 208-208: code points 1-80
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 206-208: code points 1-80

Therefore, as long as $ TC_\text{direct}=TC_\text{trunk}+TC_\text{feeder} $ the benefit of direct service is zero, as we show below:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 210-210: code points 1-135

$ \text{Fleet}_\text{benefitdirect}=(\text{Fleet}_\text{trunk}+\text{Fleet}_\text{feeder})–\text{Fleet}_\text{direct} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 212-212: code points 1-121

$ = ( {\text{MaxLoadperCycle}_\text{trunk} \over \text{VSize} * \text{LoadFactor}}+{\text{MaxLoadperCycle}_\text{feeder} \over \text{VSize} * \text{LoadFactor}}) - {\text{MaxLoadperCycle}_\text{direct} \over \text{VSize} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 214-214: code points 1-245

$ = {\text{MaxLoadperCycle}_\text{trunk} + \text{MaxLoadperCycle}_\text{feeder} - \text{MaxLoadperCycle}_\text{direct} \over \text{VSize} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 216-216: code points 1-162

$ = {\text{MaxLoadperCycle}_\text{trunk} + \text{MaxLoadperCycle}_\text{feeder} - \text{MaxLoadperCycle}_\text{trunk+feeder} \over \text{VSize} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 218-218: code points 1-168

$ = {\text{MaxLoadperCycle}_\text{trunk} + \text{MaxLoadperCycle}_\text{feeder} - (\text{MaxLoadperCycle}_\text{trunk} + \text{MaxLoadperCycle}_\text{feeder} )  \over \text{VSize} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 220-220: code points 1-204

$ = 0 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 222-222: code points 1-9

As an example we use a cycle time (TC) on the trunk of one hour, as well as a cycle time on the feeders in mixed traffic of one hour. So:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 224-225: code points 1-33

$ TC_\text{trunk}=1 \text{hour} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 227-227: code points 1-35

$ TC_\text{feeder}=1 \text{hour} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 229-229: code points 1-36

$ TC_\text{direct}=2 \text{hour} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 231-231: code points 1-36

This example assumes that the optimal vehicle capacity was already determined (see previous introduction subsection) to be sixty passengers.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 233-234: code points 1-35

The $ \text{MaxLoadperCycle} $ for two hours is precisely double the maximum load for a cycle time of one hour, or:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 236-237: code points 1-3

$ \text{MaxLoadperCycle}_\text{2 hours} = 2 * \text{MaxLoadperCycle}_\text{1 hour} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 239-239: code points 1-86

In this case, one should assume that $ \text{MaxLoad} = 225 \text{pax}/\text{hour} $, and one knows that demand is flat throughout the day, so the $ \text{PHtoCC} = 0 $, therefore:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 241-242: code points 1-51

$ \text{MaxLoadperCycle}_\text{direct} = 225 * 2 = 450 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 244-244: code points 1-58

And the fleet required for the trunk-and-feeder scenario is:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 246-246: code points 1-60

$ \text{Fleet}_\text{direct} = 450 \over 60 = 7.5 (ROUNDUP) = 8 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 248-248: code points 1-67

In the trunk-and-feeder scenario,\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 250-250: code points 1-33

$\text{MaxLoadperCycle}_\text{trunk} =  \text{MaxLoadperCycle}_\text{feeder} = 225 *2 = 450 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 252-252: code points 1-95

$ \text{Fleet}_\text{trunk} = 225 \over 60 = 3.75 (ROUNDUP) = 4 $ $ \text{Fleet}_\text{feeder} = 225 \over 60 = 3.75 (ROUNDUP) = 4 $ $ \text{Fleet}_\text{direct benefit} = (4+4) - 8 =0 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 254-256: code points 1-55

In this case, the fleet needed for the direct service scenario is the same as the fleet needed for the trunk-and-feeder service option. If there were a rounding error, the trunk-and-feeder option may require a slightly larger fleet due to rounding, but the additional fleet is not that significant.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 258-260: code points 1-98

\subsubsection{2}{Comparative Fleet Advantages under Peaked Demand with Uniform Routes}
\label{volume:operations:chapter:service-planning:section:direct-services-trunk-and-feeder-services-or-hybrids:subSection:fleet-requirements-for-direct-versus-trunk-and-feeder-services:subSubSection:comparative-fleet-advantages-under-peaked-demand-with-uniform-routes}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 262-360: code points 1-20

If the demand is peaked, but the routes remain uniform, the fleet requirements change, and direct services have a distinct advantage over trunk-and-feeder services. The advantage is proportional to double the peak hour to cycle correction factor (PHtoCC).\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 264-266: code points 1-46

Remembering that and (Eq. 6.6b) the fleet benefit for using a direct route will be given by:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 268-268: code points 1-93

Eq. 6.43\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 270-270: code points 1-8

$ \text{Fleet}_\text{benefitdirect}=(\text{Fleet}_\text{trunk}+\text{Fleet}_\text{feeder})–\text{Fleet}_\text{direct} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 272-272: code points 1-121

$ = {\text{MaxLoadperCycle}_\text{trunk} + \text{MaxLoadperCycle}_\text{feeder} - (\text{MaxLoadperCycle}_\text{trunk} + \text{MaxLoadperCycle}_\text{feeder} )  \over \text{VSize} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 274-274: code points 1-204

$ = {\text{MaxLoad}*TC_\text{trunk} * [1 - \text{PHtoCC} * (\text{TC}_\text{trunk} -1) ] + \text{MaxLoad}*TC_\text{feeder} * [1 - \text{PHtoCC} * (\text{TC}_\text{feeder} -1) ] 
\over \text{VSize} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 276-277: code points 1-42

$ - {\text{MaxLoad}*(TC_\text{trunk} + TC_\text{feeder}) * [1 - \text{PHtoCC} * ((TC_\text{trunk} + TC_\text{feeder}) -1) ]  \over \text{VSize} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 279-279: code points 1-168

$ = {\text{MaxLoad}*TC_\text{trunk} * [1 - \text{PHtoCC} * (\text{TC}_\text{trunk} -1) ] + \text{MaxLoad}*TC_\text{feeder} * [1 - \text{PHtoCC} * (\text{TC}_\text{feeder} -1) ] 
\over \text{VSize} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 281-282: code points 1-42

$ - {\text{MaxLoad}*TC_\text{trunk}  * [1 - \text{PHtoCC} * ((TC_\text{trunk} + TC_\text{feeder}) -1) ]  \over \text{VSize} * \text{LoadFactor}} $ $ - {\text{MaxLoad}*TC_\text{feeder} * [1 - \text{PHtoCC} * ((TC_\text{trunk} + TC_\text{feeder}) -1) ]  \over \text{VSize} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 284-285: code points 1-148

$ = {\text{MaxLoad}*TC_\text{trunk} *  \{[1 - \text{PHtoCC} * (\text{TC}_\text{trunk} -1) ] - [1 - \text{PHtoCC} * ((TC_\text{trunk} + TC_\text{feeder}) -1) ]\} 
\over \text{VSize} * \text{LoadFactor}} $ $ + {\text{MaxLoad}*TC_\text{feeder} *  \{[1 - \text{PHtoCC} * (\text{TC}_\text{feeder} -1) ] - [1 - \text{PHtoCC} * ((TC_\text{trunk} + TC_\text{feeder}) -1) ]\} 
\over \text{VSize} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 287-290: code points 1-42

$ = {\text{MaxLoad}*TC_\text{trunk} *  \{[1 - \text{PHtoCC} * \text{TC}_\text{trunk} + \text{PHtoCC}  ] - [1 - \text{PHtoCC} * TC_\text{trunk} -\text{PHtoCC} * TC_\text{feeder} + \text{PHtoCC} ]\} 
\over \text{VSize} * \text{LoadFactor}} $ $ + {\text{MaxLoad}*TC_\text{feeder} *  \{[1 - \text{PHtoCC} * \text{TC}_\text{feeder} + \text{PHtoCC}  ] - [1 - \text{PHtoCC} * TC_\text{trunk} -\text{PHtoCC} * TC_\text{feeder} + \text{PHtoCC} ]\} 
\over \text{VSize} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 292-295: code points 1-42

$ = {\text{MaxLoad}*TC_\text{trunk} *  \{TC_\text{feeder} + \text{PHtoCC} \} \over \text{VSize} * \text{LoadFactor}} 
+ {\text{MaxLoad}*TC_\text{feeder} *  \{TC_\text{trunk} + \text{PHtoCC} \} \over \text{VSize} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 297-298: code points 1-117

$ =  2* {\text{MaxLoad}*TC_\text{trunk} * TC_\text{feeder} * \text{PHtoCC}  \over \text{VSize} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 300-300: code points 1-119

Where\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 302-303: code points 1-0

\begin{itemize}
\item {$\text{PHtoCC}$: Nonnegative correction factor, the calibration of which is based on survey data, is discussed in Box 6.2. The usual value is near 0.1;\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 303-304: code points 7-0

\begin{itemize}
\item If $\text{TC}$ is larger than one hour: correction $ 1 - \text{PHtoCC} * (\text{TC} -1) $ will result smaller than one;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 304-305: code points 1-0
\item If $\text{TC}$ is smaller than one hour: correction $ 1 - \text{PHtoCC} * (\text{TC} -1) $ will result larger than one;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 305-306: code points 1-0
\item If $\text{TC}$ is equal one hour: correction $   1 - \text{PHtoCC} * (\text{TC} -1) $ will result in one;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 306-307: code points 1-0
\item If $\text{PHtoCC}$ is equal zero, there will be no correction, and the formula is equal to the previous formula.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 307-307: code points 1-120
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 304-307: code points 1-120

}
\item $ \text{MaxLoad}$: Maximum hourly load on the critical link;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 308-309: code points 1-0
\item $ \text{TC}$: Cycle time in hours.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 309-310: code points 1-0
\item $ TC_\text{Direct} $: Cycle time in hours for a vehicle to complete one circuit of the trunk-and-feeder services;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 310-311: code points 1-0
\item $ TC_\text{Trunk} $: Cycle time in hours for a vehicle to complete one circuit of the trunk service;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 311-312: code points 1-0
\item $ TC_\text{Feeder} $: Cycle time in hours for a vehicle to complete one circuit of the feeder service;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 312-313: code points 1-0
\item $ Fleet_\text{trunk} $: Fleet requirement for the trunk service;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 313-314: code points 1-0
\item $ VSize $: Vehicle capacity;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 314-315: code points 1-0
\item $ LoadFactor$: Design load factor (usually 0.85), which is the same for all routes.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 315-315: code points 1-91
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 303-315: code points 1-91

As an example, we keep the same assumptions from the previous case, but consider a peaked demand of 265 where the correction factor is given by 0.15 (see Box 6.2 How to determine correction factor from hour to cycle time ($PHtoCC$) based on load observations):\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 317-319: code points 1-60

$ \text{MaxLoadperCycle}_\text{direct}  $ $ = \text{MaxLoad} * (TC_\text{direct}*(1 - \text{PHtoCC} * (\text{TC}_\text{direct} -1))) $ $ = 265     *   2  *  (           1         -0.15   *            2            -1)))     =   450 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 321-323: code points 1-99

$ \text{MaxLoadperCycle}_\text{feeder} =  \text{ MaxLoadperCycle}_\text{trunk} $ $ = \text{MaxLoad} * (TC_\text{feeder}*(1 - \text{PHtoCC} * (\text{TC}_\text{feeder} -1))) $ $ = 265     *   1  *  (           1         -0.15   *            1            -1)))     =   265 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 325-327: code points 1-99

In the case of the direct service option,\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 329-329: code points 1-41

$ \text{Fleet}_\text{direct} = {\text{MaxLoadperCycle}_\text{direct} \over \text{VSize} * \text{LoadFactor}} = 
{450 \over 60} = 7.5 (ROUNDUP) = 8 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 331-332: code points 1-37

In the case of the trunk-and-feeder option:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 334-334: code points 1-43

$ \text{Fleet}_\text{trunk} = {\text{MaxLoadperCycle}_\text{trunk} \over \text{VSize} * \text{LoadFactor}} = 
{265 \over 60} = 4.417 (ROUNDUP) = 5 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 336-337: code points 1-39

$ \text{Fleet}_\text{feeder} = {\text{MaxLoadperCycle}_\text{feeder} \over \text{VSize} * \text{LoadFactor}} = 
{265 \over 60 } = 4.417 (ROUNDUP) = 5 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 339-340: code points 1-40

So:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 342-342: code points 1-3

$ \text{Fleet}_\text{directbenefit} = 
(\text{Fleet}_\text{trunk}+\text{Fleet}_\text{feeder})–\text{Fleet}_\text{direct} 
=(5+5) – 8 = 2 \text{vehicles} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 344-346: code points 1-33

We save two vehicles by using direct services over a trunk-and-feeder service plan on this route. One way to think about this is that the peak demand in the mixed traffic section of the routes occurs earlier in the day, so the same vehicles in a direct services service plan needed to serve the peak-hour demand on the mixed traffic “feeder” portion of the route can continue past the terminal and serve the peak-hour demand, occurring slightly later, on the trunk. With the trunk-and-feeder service plan, buses need to serve the peak demand on the feeder routes at close to the same time as on the trunk. So, while it is peak time for the feeders, the trunk vehicles are waiting, and then, as the peak demand shifts toward the trunk, some of the feeder vehicles will be unused. A direct services service plan therefore uses a smaller fleet because it optimizes the fleet by serving the demand as it moves through the corridor.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 348-356: code points 1-102

In this example, the benefit was evaluated for just one route. If one does the analysis for ten equivalent routes, and all have the same TC, the difference in fleet would be multiplied by ten, and the difference becomes significant.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 358-360: code points 1-20

\subsection{2}{Vehicle Size Optimization Benefits for Trunk-and-Feeder versus Direct Services}
\label{volume:operations:chapter:service-planning:section:direct-services-trunk-and-feeder-services-or-hybrids:subSection:vehicle-size-optimization-benefits-for-trunk-and-feeder-versus-direct-services}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 362-851: code points 1-7

The main advantage of a trunk-and-feeder service is that the demand on the feeder routes, which in isolation would be served by small vehicles with high operating costs per customer, can be combined on the trunk portion of the route, so that customers from multiple feeder routes can all use a much larger trunk vehicle. Because large vehicles at high occupancy levels have lower operating costs per customer than smaller vehicles, there is a benefit of lower vehicle operating costs with trunk-and-feeder services in appropriate conditions. This section identifies easy ways of spotting what those conditions are, to conclude the following:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 364-370: code points 1-23

\highlight{The greater the number of routes being combined into a trunk route, and the greater the proportion of the total trip that is taken up by the trunk portion of the trip, the greater the benefit.}\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 372-374: code points 1-1

Applying the formulas presented before, the benefits of optimal fleet size can be compared under different service plan alternatives as applied to some typical conditions. In both scenarios simplified examples are first introduced to illustrate general principles, and then the general formulas are applied to more real-world situations.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 376-379: code points 1-22

\subsubsection{1}{Vehicle size optimization with several similar feeder routes:}
\label{volume:operations:chapter:service-planning:section:direct-services-trunk-and-feeder-services-or-hybrids:subSection:vehicle-size-optimization-benefits-for-trunk-and-feeder-versus-direct-services:subSubSection:vehicle-size-optimization-with-several-similar-feeder-routes}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 381-608: code points 1-7

In this example, one looks at the benefits of trunk-and-feeder systems from using bigger vehicles on the trunk portion of the route for BRT projects where the following conditions apply:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 383-385: code points 1-0

\begin{itemize}
\item \emphasis{A} All routes have similar demand;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 385-386: code points 1-0
\item \emphasis{B} All routes extend beyond the trunk corridor for a similar distance and at similar speeds, and all routes leave the trunk corridor at roughly the same place;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 386-388: code points 1-0
\item \emphasis{C} The peak-hour load ($MaxLoad$) for the trunk is similar to the peak-hour load for all of the combined feeders;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 388-390: code points 1-0
\item \emphasis{D} No transfer time is required to get from the feeder vehicle to the trunk vehicle, just waiting time;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 390-392: code points 1-0
\item \emphasis{E} No extra time is required for vehicles to pull off the BRT trunk corridor and enter a transfer terminal;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 392-394: code points 1-0
\item \emphasis{F} There is no peak in the demand (i.e., $\text{PHtoCC} = 0$). In other words, demand is constant throughout the day, such that the effect of the peak factor on the overall fleet size does not apply.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 394-395: code points 1-90
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 385-395: code points 1-90

The following is assumed:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 397-398: code points 1-0

\begin{itemize}
\item There are five routes that have the same itineraries on the BRT corridor, with the same characteristics, $ N_\text{routes}$: number of routes $ = 5$ ;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 398-400: code points 1-0
\item The cycle time on the part of the service that overlaps the BRT trunk infrastructure is assumed to be two hours. $ TC_\text{trunk} = 2 $;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 400-402: code points 1-0
\item The cycle time on the part of the service that operates in mixed traffic beyond the trunk corridor is 0.6 hours; $ TC_\text{feeder} = 0.6 $ ;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 402-404: code points 1-0
\item {Other variables determinant to the optimal bus size and waiting costs are equal for all routes, in the two alternatives (direct service and trunk-and-feeder service):\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 404-406: code points 8-0

\begin{itemize}
\item Bus FixedCost = US\$30\slash{}per bus-hour;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 406-407: code points 1-0
\item Renovation factor = 1.5;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 407-408: code points 1-0
\item (Frequency) Irregularity = 0.3;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 408-409: code points 1-0
\item Waiting cost per passenger = US\$12\slash{}hour;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 409-410: code points 1-0
\item Design Load Factor = 0.85.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 410-410: code points 1-32
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 406-410: code points 1-32

}
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 398-410: code points 1-33

We also assume that the total fixed operating costs are simply the sum of the fixed operating cost per vehicle times the fleet (i.e., no other fixed costs are being considered), or:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 412-413: code points 1-82

Eq. 6.9:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 415-415: code points 1-8

$\text{RouteFixedCost} = \text{BusFixedCost} * \text{Fleet}_\text{route} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 417-417: code points 1-76

Where:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 419-420: code points 1-0

\begin{itemize}
\item $ \text{RouteFixedCost}$: Total fixed operational cost for the route;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 420-421: code points 1-0
\item $ \text{BusFixedCost}$: Fixed operating costs per vehicle;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 421-422: code points 1-0
\item $ \text{Fleet}_\text{route}$: Number of buses needed to operate the route.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 422-422: code points 1-82
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 420-422: code points 1-82

It is also assumed that the maximum load on the trunk route is the same as the number of routes times the maximum load of each route combined; for each route we will assume a MaxLoad of a hundred passengers per hour:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 424-426: code points 1-9

Eq. 6.44\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 428-428: code points 1-8

$ \text{MaxLoad}_\text{trunk} = N_\text{routes} * \text{MaxLoad}_\text{iroute} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 430-430: code points 1-82

Where:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 432-433: code points 1-0

\begin{itemize}
\item $ \text{MaxLoad}_\text{trunk}$: MaxLoadtrunk = Maximum hourly load on the trunk;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 433-434: code points 1-0
\item $ N_\text{routes} $: Number of routes;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 434-435: code points 1-0
\item $ \text{MaxLoad}_\text{iroute} $: Maximum hourly load on the “i” route.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 435-435: code points 1-79
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 433-435: code points 1-79

As was explained earlier, the optimal vehicle size depends on the point where the combined value of people’s time waiting (which is lower with higher frequency and smaller vehicles) and the total fixed costs (which are lower with larger vehicles) are minimized, as laid out by Equation 6.16. We therefore need two more variables:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 437-440: code points 1-24

$ \text{VSize}_\text{optimum}*\text{LoadFactor} = \sqrt{\text{BusFixedCost}*\text{MaxLoadperCycle}_\text{route} \over {\text{Ren}_\text{route}*\text{Costwait} * 0.5 (1+Irr_\text{route})} } $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 443-443: code points 1-192

For this case, where demand is flat ($ \text{MaxLoadperCycle} = \text{MaxLoad}_\text{route} * TC $), this means:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 445-445: code points 1-114

$ \text{VSize}_\text{optimum}*\text{LoadFactor} = \sqrt{\text{BusFixedCost}*\text{MaxLoad}_\text{route} * TC  \over {\text{Ren}_\text{route}*\text{Costwait} * 0.5 (1+Irr_\text{route})} } $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 447-447: code points 1-190

To determine whether, in this scenario, the direct service option or the trunk-and-feeder service option is better, the total waiting and fixed costs of the two scenarios (given by Equations 6.12 and 6.13 below) need to be compared. Equations 6.12 and 6.15:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 449-451: code points 1-45

$ \text{WaitCost}_\text{route} =  \text{Ren}_\text{route} * \text{Cost}_\text{wait} * 0.5 * (1+ Irr_\text{route}) *\text{LoadFactor} * \text{VSize} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 453-453: code points 1-151

$ \text{FixedCost}_\text{route} = {\text{BusFixedCost} * \text{MaxLoadperCycle}_\text{route} \over { \text{VSize}_\text{route}*\text{LoadFactor}}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 455-455: code points 1-150

For the formulas above:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 457-458: code points 1-0

\begin{itemize}
\item $\text{WaitCost}_\text{route} $: Total waiting time cost generated to the route users (in \$);;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 458-459: code points 1-0
\item $ \text{VSize}_\text{route}$: Vehicle serving the route capacity;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 459-460: code points 1-0
\item $ \text{LoadFactor}$: Design load factor (usually 0.85).% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 460-461: code points 1-0
\item $ \text{MaxLoadperCycle}_\text{route}$: Maximum demand across the critical segment of the route that will accumulate for the duration of one cycle during the busiest moment of the typical day (see Subsection 6.3.13);% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 461-462: code points 1-0
\item $\text{MaxLoad}$: Maximum demand across the critical segment of the route;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 462-463: code points 1-0
\item $ \text{TC} $:Cycle time of the route;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 463-464: code points 1-0
\item $ \text{FixedCost}_\text{route} $: Total fixed operating cost for the route (in US\$\slash{}hour) ($=\text{WaitCostRoute}$ when $\text{VSize}$ is optimum)% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 464-465: code points 1-0
\item $ \text{Ren}_\text{route}$: Renovation factor of the route;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 465-466: code points 1-0
\item $ \text{Costwait}$ Average user waiting cost (\$\slash{}time);% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 466-467: code points 1-0
\item $ \text{Irr}\text{route}$: Irregularity index of the route; measure of the variance between the actual headways and the scheduled headways (usually near 0.3, see Section 6.3.9);% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 467-468: code points 1-61
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 458-468: code points 1-61

\highlight{Direct services}:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 470-470: code points 1-28

$ \text{VSize}_\text{opt-direct}*\text{LoadFactor} = \sqrt{\text{BusFixedCost}*\text{MaxLoad}_\text{direct} * TC  \over \text{Ren}_\text{route}*\text{Costwait} * 0.5 (1+Irr_\text{direct}) }  $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 472-472: code points 1-194

$ \text{VSize}_\text{opt-direct}* 0.85 = \sqrt{30*100 *2.6  \over 1.5 * 12  * 0.5 (1+0.3)} = 25.82 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 474-474: code points 1-102

$ \text{VSize}_\text{opt-direct} = 30 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 476-476: code points 1-41

\highlight{Trunk-and-feeder option}\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 478-478: code points 1-35

$ \text{VSize}_\text{opt-trunk}*\text{LoadFactor} = \sqrt{\text{BusFixedCost}*\text{MaxLoad}_\text{trunk} * TC  \over \text{Ren}_\text{route}*\text{Costwait} * 0.5 (1+Irr_\text{trunk}) }  $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 480-480: code points 1-191

$ \text{VSize}_\text{opt-trunk}* 0.85 = \sqrt{30*500 *2.0  \over 1.5 * 12  * 0.5 (1+0.3)} = 50.64 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 482-482: code points 1-101

$ \text{VSize}_\text{opt-trunk} = 60 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 484-484: code points 1-40

$ \text{VSize}_\text{opt-feeder}*\text{LoadFactor} = \sqrt{\text{BusFixedCost}*\text{MaxLoad}_\text{feeder} * TC  \over \text{Ren}_\text{route}*\text{Costwait} * 0.5 (1+Irr_\text{feeder}) }  $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 486-486: code points 1-194

$ \text{VSize}_\text{opt-feeder}* 0.85 = \sqrt{30*100 *0.6  \over 1.5 * 12  * 0.5 (1+0.3)} = 12.40 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 488-488: code points 1-102

$ \text{VSize}_\text{opt-direct} = 15 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 490-490: code points 1-41

The comparative cost of the two scenarios can now be calculated for both alternatives; when the vehicle size is optimal, the total cost of waiting is equal to the total fixed costs (see Section 6.4.3); as such, it is enough to double either one:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 492-494: code points 1-40

$ \text{WaitCost}_\text{direct} =  \text{Ren}_\text{route} * \text{Cost}_\text{wait} * 0.5 * (1+ Irr_\text{direct}) *\text{LoadFactor} * \text{VSize}_\text{direct} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 496-496: code points 1-167

$ \text{WaitCost}_\text{direct} =  1.5*12* 0.5*(1+0.3)*0.85* 30=298.35 \$ $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 498-498: code points 1-77

As there are 5 direct routes, the wait cost plus the fixed costs for this alternative is 10 times the wait cost, i.e., US\$2,983.50.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 500-501: code points 1-29

$ \text{WaitCost}_\text{trunk} =  \text{Ren}_\text{route} * \text{Cost}_\text{wait} * 0.5 * (1+ Irr_\text{trunk}) *\text{LoadFactor} * \text{VSize}_\text{trunk} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 503-503: code points 1-164

$ \text{WaitCost}_\text{trunk} =  1.5*12* 0.5*(1+0.3)*0.85* 60=596.70\$ $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 505-505: code points 1-75

$ \text{WaitCost}_\text{feeder} =  \text{Ren}_\text{route} * \text{Cost}_\text{wait} * 0.5 * (1+ Irr_\text{feeder}) *\text{LoadFactor} * \text{VSize}_\text{feeder} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 507-507: code points 1-167

$ \text{WaitCost}_\text{feeder} =  1.5*12* 0.5*(1+0.3)*0.85* 15=149.17\$ $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 509-509: code points 1-76

As there are five feeder routes, the wait cost plus the fixed costs for the trunk-and-feeder alternative is 10 times the feeder wait cost plus two times the trunk wait cost, i.e., US\$2,685.15 US\$ (1,491.75 + 1,193,40).\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 511-513: code points 1-26

In this example, the trunk-and-feeder system yields about a 13 percent benefit in total costs over the direct service alternative. This is entirely due to the savings made possible by the returns to scale from using larger vehicles.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 515-517: code points 1-27

\beginbox{3}{Estimating the range of benefit from vehicle size optimization due to trunk-and-feeder operations}
\label{chapter:service-planning:box:estimating-the-range-of-benefit-from-vehicle-size-optimization-due-to-trunk-and-feeder-operations}
If one runs several scenarios, one finds that there is a pattern to the conditions in which there will be benefits from fleet optimization from a trunk-and-feeder system over a direct service system.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 521-521: code points 1-199

It turns out that two parameters determine the degree of benefit likely to happen from conversion of a direct service into a trunk-and-feeder service purely from the perspective of the vehicle size optimization: cycle times for each part of the service. So one must consider the proportion of time spent on the feeder portion of the route vis-à-vis the time spent on the trunk portion of the route ($Fpr$) as follows:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 523-523: code points 1-419

$ F_pr= {TC_\text{feeder} \over TC_\text{trunk}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 525-525: code points 1-52

Eq. 6.45\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 527-527: code points 1-8

${TC_\text{feeder} = F_pr * TC_\text{trunk}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 530-530: code points 1-48

Where:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 533-534: code points 1-0

\begin{itemize}
\item $ F_pr $: Proportion of time spent on the feeder portion of the route vis-à-vis the time spent on the trunk portion of the route;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 534-535: code points 1-0
\item $ TC_\text{Trunk} $: Cycle time in hours for a vehicle to complete one circuit of the trunk service;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 535-536: code points 1-0
\item $ TC_\text{Feeder}  $: Cycle time in hours for a vehicle to complete one circuit of the feeder service.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 536-536: code points 1-111
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 534-536: code points 1-111

After some reformulation where only Nroute and Fpr determine the outcome, it turns out that, if the assumptions for this section hold, trunk-and-feeder services will yield benefits in a condition where:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 538-538: code points 1-202

Eq. 6.46\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 540-540: code points 1-8

$ F_pr < {  (N_\text{route} - 1) ^2 \over 4 * N_\text{route}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 542-542: code points 1-65

Where:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 544-545: code points 1-0

\begin{itemize}
\item $ F_pr $: Proportion of time spent on the feeder portion of the route vis-à-vis the time spent on the trunk portion of the route;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 545-546: code points 1-0
\item $ N_\text{route}$: Number of routes being combined into the same trunk part of the service.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 546-546: code points 1-99
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 545-546: code points 1-99

In other words, with just the number of feeder routes and their cycle time as a proportion of the trunk, one can already have a reasonable sense of the degree of benefit from shifting to a trunk–feeder system (if one ignores all the other costs and benefits associated with trunk-and-feeder services versus direct services).\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 548-548: code points 1-324

In this ideal case, there will be a generalized cost reduction from shifting from a direct service to a trunk-and-feeder service. This is shown in the next figure. The line below shows the slope ofi $ F_{pr}= { (N-1) ^2 \over (4*N_\text{route})} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 550-550: code points 1-249

For any combination above the line there is no benefit, and for any combination below the line there is a benefit to shifting to trunk-and-feeder under these conditions.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 552-552: code points 1-169

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/0ec8c61eb074294d0d69e3782c8715a75004419f.jpeg}
		\fignote{44}{Conditions under which benefits can be accrued from vehicle size optimization in a trunk-and-feeder system: The blue line above shows the points at which the benefits and costs of direct services and trunk-and-feeder services are equal, determined by two variables: the proportion of the total trip time that takes place on the feeder route (y axis) and the total number of feeder routes that share the trunk demand (x axis). Image\label{chapter:service-planning:figure:conditions-under-which-benefits-can-be-accrued-from-vehicle-size-optimization-in-a-trunk-and-feeder-system-the-blue-line-above-shows-the-points-at-which-the-benefits-and-costs-of-direct-services-and-trunk-and-feeder-services-are-equal-determined-by-two-variables-the-proportion-of-the-total-trip-time-that-takes-place-on-the-feeder-route-y-axis-and-the-total-number-of-feeder-routes-that-share-the-trunk-demand-x-axis-image}}{Pedro Szász.}
	}
\fi

If all the possible outcomes are plotted as different combinations of the number of routes ($ N_\text{route} 
= n $ in the figure) and the feeder portion cycle time as a proportion of total cycle time $F_pr$. It would be found that the benefits fall in the ranges shown in Figure 6.45.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 565-567: code points 1-58

The yellow line, for instance, indicates that the maximum benefit for a system where the direct service originally had only three routes ($ n = 3 $), and the cycle time beyond the trunk is only 20 percent of the total cycle time ($Fpr = 0.1$).\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 569-570: code points 1-110

The maximum total cost benefit is only 5 percent. In such circumstances, it will be nearly impossible to recover the other losses associated with trunk-and-feeder services from the benefits of optimizing the vehicle size.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 572-574: code points 1-17

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/9cc501a631acc368aae5c280ea21d6d76e96906a.jpeg}
		\fignote{45}{Range of possible benefits from vehicle size optimization from for trunk-and-feeder systems, depending on the number of routes (each line) and the share of the total trip time accounted for by the feeder route (x axis).\label{chapter:service-planning:figure:range-of-possible-benefits-from-vehicle-size-optimization-from-for-trunk-and-feeder-systems-depending-on-the-number-of-routes-each-line-and-the-share-of-the-total-trip-time-accounted-for-by-the-feeder-route-x-axis}}{Pedro Szász.}
	}
\fi

This points to the fact that, if there are a lot of small direct service routes that overlap for a long distance with the trunk corridor, each route will have a relatively low demand and will optimally use small vehicles. If the small direct routes along the trunk route are turned into trunk-and-feeder services, customers on each low-demand route would share the use of a much larger vehicle, realizing returns to scale in the fixed cost of vehicles.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 582-590: code points 1-47

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/4ef1bc769bad834b989660d0cd3cf256564e872e.jpeg}
		\fignote{46}{Visual comparison of situations that can yield more benefits from the shift from direct service to trunk-and-feeder services.\label{chapter:service-planning:figure:visual-comparison-of-situations-that-can-yield-more-benefits-from-the-shift-from-direct-service-to-trunk-and-feeder-services}}{ITDP.}
	}
\fi

If the number of routes is low, the demand will be split among a smaller number of routes, so the original routes will already be using larger buses. Further, if the routes share only a short section of the trunk, the distance available for larger vehicles to reap benefits would be smaller, so there would be less benefit.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 595-598: code points 1-8

The smaller services with low demand have the greater benefits from joining the trunk-and-feeder system to achieve returns to scale. As with any collective, the more people who join, and the longer they remain members, the greater the benefit.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 600-602: code points 1-33

In summary, a corridor that has a long trunk and short feeder extensions and more routes, rather than fewer sharing the total demand, the greater the chances that a trunk-and-feeder system will bring benefits.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 604-605: code points 1-107

\endbox
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 519-608: code points 1-7

\subsubsection{2}{Calculating the Benefits of a Trunk-and-Feeder System for Corridors with Multiple Routes of Different Characteristics}
\label{volume:operations:chapter:service-planning:section:direct-services-trunk-and-feeder-services-or-hybrids:subSection:vehicle-size-optimization-benefits-for-trunk-and-feeder-versus-direct-services:subSubSection:calculating-the-benefits-of-a-trunk-and-feeder-system-for-corridors-with-multiple-routes-of-different-characteristics}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 611-851: code points 1-7

Usually, when planning a BRT system, most of the routes using a BRT corridor are different, and determining the benefits of a trunk-and-feeder operation in those conditions is complicated. This section outlines a methodology that will be applicable in some real-world conditions. In this scenario, to make things simpler, some of the same assumptions from the previous scenario still hold.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 613-617: code points 1-0

\begin{itemize}
\item \emphasis{A} Trunk segment (and time) is the same for all routes.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 617-618: code points 1-0
\item \emphasis{B} No transfer time is required to get from the feeder vehicle to the trunk vehicle, just waiting time.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 618-620: code points 1-0
\item \emphasis{C} No extra time is required for vehicles to pull off the BRT trunk corridor and enter a transfer terminal.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 620-622: code points 1-0
\item \emphasis{D} PHtoCC = 0, there is no peak factor. In other words, it can be assumed that the demand is constant throughout the day, such that the effect of the peak factor index on the overall fleet size does not apply, so there is no fixed operating costs (Cf) disadvantage to converting to trunk-and-feeder services related to smaller fleet size.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 622-625: code points 1-30
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 617-625: code points 1-30

However, in this case, each bus route is allowed to vary in the length that it overlaps the trunk corridor and in the cycle time.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 627-628: code points 1-22

In these conditions, one explores how to answer the following questions:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 630-631: code points 1-0

\begin{enumerate}
\item Knowing that shifting all routes from direct services to a trunk-and-feeder system yields benefits, will there still be benefits if only some of the routes are changed to trunk-and-feeder?% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 631-633: code points 1-0
\item Is the maximum benefit obtained when all routes are converted to trunk-and-feeder, or when routes are selectively converted based on their demand profile?% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 633-635: code points 1-0
\item How is the optimum case determined?% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 635-635: code points 1-43
\end{enumerate}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 631-635: code points 1-43

We approach these questions in a similar manner to the subsection: \emphasis{Scenario II: Dwell Times and Demand Vary from Route-to-Route, and All Stations Are Similar}, to decide which routes should be included in the busway, by calculating the benefits generated by shifting successive routes to trunk-and-feeder service starting from the condition where all routes are direct services. In order to analyze the theoretical behavior, the exercise allows for every possible bus size. In real operation planning, one has to select among the existing bus capacities (accepting design load factors up to 0.9 also comes into play) and calculate fixed costs and waiting costs (no longer equal) based on the resulting number of buses.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 637-643: code points 1-97

Each route has two basic characteristics that vary in this example:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 645-646: code points 1-0

\begin{itemize}
\item Maximum Load for route “i” $ = \text{MaxLoad}_i$;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 646-647: code points 1-0
\item Cycle time on feeder part of route “i” $ = TC_{i\text{-feeder}} $% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 647-647: code points 1-73
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 646-647: code points 1-73

With these two parameters, the following equations are obtained:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 649-649: code points 1-64

$ \text{MaxLoadperCycle}_{i\text{-direct}} =\text{MaxLoad} * TC_i$;\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 651-651: code points 1-69

$ \text{MaxLoadperCycle}_{i\text{-trunk}} =\text{MaxLoad} * TC_{i\text{-trunk}}$\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 653-653: code points 1-82

$ \text{MaxLoadperCycle}_{i\text{-feeder}} =\text{MaxLoad} * TC_{i\text{-feeder}}$\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 655-655: code points 1-84

Where:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 657-658: code points 1-0

\begin{itemize}
\item $ \text{MaxLoad}_i $: Maximum hourly load for route “i” in the critical link;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 658-659: code points 1-0
\item $  \text{MaxLoadperCycle}_{i\text{-direct}} $: Maximum load (or the number of passenger places required) on the direct service per cycle time for route “i”;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 659-661: code points 1-0
\item $ \text{MaxLoad}_{i\text{-trunk}}$: Maximum load (or the number of passenger places required) on the trunk part of service per trunk cycle time ($TC_{i\text{-trunk}}$) for route “i”;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 661-663: code points 1-0
\item $\text{MaxLoadperCycle}_{i\text{-feeder}} $: Maximum load (or the number of passenger places required) on the trunk part of service per trunk cycle time ($ TC_{i\text{-feeder}}$) for route “i”;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 663-665: code points 1-0
\item $  TC_i$: cycle time for route “i,” could be also represented as TCi-direct;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 665-666: code points 1-0
\item $ TC_{i\text{-feeder}}$: Cycle time in hours for a vehicle to complete one circuit of the feeder part of route “i”;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 666-668: code points 1-0
\item $ TC_{i\text{-trunk}}$: Cycle time in hours for a vehicle to complete one circuit of the trunk part of route “i.”% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 668-668: code points 1-121
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 658-668: code points 1-121

This means that the feeder services should supply places during the peak hour to meet the maximum load on the critical link of the feeder route, which is assumed to be close to the terminal.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 670-671: code points 1-87

Our example considers eight routes as defined in Table 6.27 where the trunk part of all routes needs 1.3 hours and the assumption that $ TC_{i\text{-direct}} =TC_{i\text{-trunk}} + TC_{i\text{-feeder}} $ is still valid.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 673-674: code points 1-121


			\ifxetex
				% disabled for now
			\else
				{  % group required to avoid fignote settings escaping
					\tabletitle{27}{Example of Routes to Be Considered for Trunk-and-Feeder Service}
\label{chapter:service-planning:table:example-of-routes-to-be-considered-for-trunk-and-feeder-service}

					\img{\hsize}{operations/assets/b11db28880c6be171792de45fe49fbcb1da1c480.jpg}
				}
			\fi

Other variables that determine the optimal bus size and waiting costs are equal for all routes in the two alternatives (direct service and trunk-and-feeder service):\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 680-682: code points 1-0

\begin{itemize}
\item BusFixedCost = US\$30\slash{}per bus-hour;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 682-683: code points 1-0
\item Renovation factor = 1.5;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 683-684: code points 1-0
\item (Frequency) Irregularity = 0.3;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 684-685: code points 1-0
\item Wait cost per passenger = US\$12\slash{}hour;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 685-686: code points 1-0
\item Design Load Factor = 0.85.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 686-686: code points 1-32
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 682-686: code points 1-32

The equations are the same: Eq. 6.16a, Eq. 6.12, and Eq. 6.18 (taking into account the fixed operating costs per vehicle, $\text{BusFixedCost}$):\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 688-689: code points 1-44

$ \text{VSize}_\text{optimum}*\text{LoadFactor} = \sqrt{\text{BusFixedCost}*\text{MaxLoad}_\text{route} * TC  \over {\text{Ren}_\text{route}*\text{Costwait} * 0.5 (1+Irr_\text{route})} } $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 691-691: code points 1-190

$ \text{WaitCost}_\text{route} =  \text{Ren}_\text{route} * \text{Cost}_\text{wait} * 0.5 * (1+ Irr_\text{route}) *\text{LoadFactor} * \text{VSize} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 693-693: code points 1-151

$ \text{FixedCost}_\text{route} = {\text{BusFixedCost} * \text{MaxLoadperCycle}_\text{route} \over { \text{VSize}_\text{route}*\text{LoadFactor}}} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 695-695: code points 1-150

Where:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 697-698: code points 1-0

\begin{itemize}
\item $ \text{VSize}_\text{optimum}$: Optimum vehicle size;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 698-699: code points 1-0
\item $ \text{LoadFactor}$: Design load factor (usually 0.85).% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 699-700: code points 1-0
\item $ \text{BusFixedCost} $: Fixed operating costs per vehicle;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 700-701: code points 1-0
\item $ \text{WaitCost}_\text{route} $: Total waiting time cost generated to the route users (in \$);;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 701-702: code points 1-0
\item $ \text{MaxLoad}_\text{route} $: Route demand on the critical link;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 702-703: code points 1-0
\item $ \text{TC} $:Cycle time of the route;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 703-704: code points 1-0
\item $ \text{Ren}_\text{route}$: Renovation factor of the route;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 704-705: code points 1-0
\item $ \text{Costwait}_\text{route} $ Average user waiting cost (\$\slash{}time);% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 705-706: code points 1-0
\item $ \text{Irr}\text{route}$: Irregularity index of the route; measure of the variance between the actual headways and the scheduled headways (usually near 0.3, see Section 6.3.9);% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 706-708: code points 1-0
\item $ \text{VSize}$: Vehicle capacity;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 708-709: code points 1-0
\item $ \text{FixedCost}_\text{route} $: Total fixed operating cost for the route (in US\$\slash{}hour) ($=\text{WaitCostRoute}$ when $\text{VSize}$ is optimum)% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 709-710: code points 1-0
\item $ \text{MaxLoadperCycle}_\text{route}$: Maximum demand across the critical segment of the route that will accumulate for the duration of one cycle during the busiest moment of the typical day (see Subsection 6.3.13);% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 710-710: code points 1-224
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 698-710: code points 1-224

In order to decide which should be changed, the routes should be situated in ascending order of places ($ \text{MaxLoadperCycle}_\text{feeder}$) that each feeder route brings to the trunk service. Routes bringing fewer places to the trunk corridor will benefit more from being integrated into the trunk-and-feeder system, because these routes, in a direct service arrangement, will have the smallest vehicles.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 712-715: code points 1-79

Then the following should be calculated for each route:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 717-718: code points 1-0

\begin{itemize}
\item Optimal bus size and the sum of fixed plus waiting costs for operation as direct service;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 718-719: code points 1-0
\item Optimal bus size and sum of fixed plus waiting costs for the feeder part of the route as if operated as trunk-and-feeder;% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 719-721: code points 1-0
\item Optimal bus size and sum of fixed plus waiting costs for the trunk assuming all routes classified as if operated as trunk-and-feeder.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 721-722: code points 1-35
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 718-722: code points 1-35

With that, the overall benefits of fixed plus waiting costs of each alternative from splitting an additional route into separate feeder-and-trunk services can be calculated. The steps for the example are shown in Table 6.28.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 724-726: code points 1-14


			\ifxetex
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					\tabletitle{28}{Route Selection to Shift from Direct to Trunk-and-Feeder Service}
\label{chapter:service-planning:table:route-selection-to-shift-from-direct-to-trunk-and-feeder-service}

					\img{\hsize}{operations/assets/08891f3751f1227c129e1923a2b0b1602d43d41e.jpg}
				}
			\fi

On the table, one can now compare scenarios. The first column “F” is a scenario where only the former direct service Route “F” has been converted to a trunk route and a feeder route. Then it is assumed that the remainder of the service is direct. The cost of servicing the remainder of the demand in the corridor with direct services is calculated thus:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 732-735: code points 1-70

- Total cost of waiting and fixed operating costs on the remaining direct service routes equals total cost of all direct service routes less the route converted to trunk-and-feeder, or:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 737-738: code points 1-83

$ Cwf_\text{remaining direct lines} = Cwf_\text{all routes direct} - Cwf_\text{direct route F} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 740-740: code points 1-98

$ =  11,355 – 918 = 10,437 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 742-742: code points 1-30

The total cost of a scenario where only Route F is converted to a trunk-and-feeder service, and all the remaining routes remain direct service routes, is just the cost of the trunk service, plus the cost of the feeder service, plus the cost of the remaining direct services, or:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 744-746: code points 1-74

$ Cwf_\text{total Scenario F} = 854+335+10,437=11,627 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 748-748: code points 1-57

In the second scenario, row “B,” both Route F and Route B are converted to a trunk-and-feeder services, and all the other routes remain direct services. All of the columns are calculated in the same manner.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 750-751: code points 1-102

Unlike the costs of the feeder routes and the direct service routes, which will not change depending on how many routes there are, the trunk route will have decreasing costs the more routes that join the trunk-and-feeder service, as the maximum load and hence the vehicle size will increase the more small routes that join. The trunk-and-feeder system, under this specific set of assumptions, becomes more efficient than the direct-service-only system once the three best routes for conversion (F, B, and A) are added to the trunk-and-feeder service, as the total costs of the direct-service-only scenario (11,355) are greater than the trunk-and-feeder with F, B, and A scenario (11,342). The benefits continue to accrue as more routes are converted to trunk-and-feeder until Route H is added. Route H is particularly unsuited to trunk-and-feeder operations, because it has a very high demand on its own; has a very high frequency on its own; uses a very large vehicle size on its own; and continues well beyond the trunk corridor for some distance. With these characteristics, it is a prime candidate for a route that should continue to function as a direct service.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 753-764: code points 1-29

Figure 6.47 is a graph of the overall cost structure of each alternative:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 766-766: code points 1-73

\ifxetex
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\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/3d86a7c80228f7c22f8d08559d0072610980a4d9.jpeg}
		\fignote{47}{This is one possible set of cost curves that represents the total system costs as more preexisting direct service routes are converted to trunk-and-feeder routes, once all preexisting direct services are ranked based on the number of potential customers the feeder route brings to the trunk corridor. As more routes are converted to trunk-and-feeder, the cost of operating the trunk and the feeder routes increases, the cost of operating the remaining direct routes decreases, and the total system cost in this example continues to fall until the routes bringing the largest volume of customers to the trunk are converted, at which point total system costs increase.\label{chapter:service-planning:figure:this-is-one-possible-set-of-cost-curves-that-represents-the-total-system-costs-as-more-preexisting-direct-service-routes-are-converted-to-trunk-and-feeder-routes-once-all-preexisting-direct-services-are-ranked-based-on-the-number-of-potential-customers-the-feeder-route-brings-to-the-trunk-corridor-as-more-routes-are-converted-to-trunk-and-feeder-the-cost-of-operating-the-trunk-and-the-feeder-routes-increases-the-cost-of-operating-the-remaining-direct-routes-decreases-and-the-total-system-cost-in-this-example-continues-to-fall-until-the-routes-bringing-the-largest-volume-of-customers-to-the-trunk-are-converted-at-which-point-total-system-costs-increase}}{Pedro Szász.}
	}
\fi

So as expected trunk-and-feeder system costs are growing, and normal route costs are decreasing. Figure 6.48 shows just the total cost:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 776-777: code points 1-31

\ifxetex
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		\img{\hsize}{operations/assets/36185fd9cb522915ca4a787cf40b579b9440a393.jpeg}
		\fignote{48}{Close up of total system costs only from Figure 6.47.\label{chapter:service-planning:figure:close-up-of-total-system-costs-only-from-figure-647}}{Pedro Szász.}
	}
\fi

\beginbox{4}{Exercise to demonstrate the effectiveness of a trunk-and-feeder system}
\label{chapter:service-planning:box:exercise-to-demonstrate-the-effectiveness-of-a-trunk-and-feeder-system}
Continuing with the same methodology from above, one finds that if the trunk route is very long and carries a lot of demand, the costs will continue to fall as more routes are converted to trunk-and-feeder.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 783-785: code points 1-92

\ifxetex
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	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/086f8556e28cceeaaa5b2cf5b81dbbc6ab1a45b2.jpeg}
		\fignote{49}{Likely total system cost curve if there are many feeder routes and the feeders only constitute a short portion of total trip time. Graph\label{chapter:service-planning:figure:likely-total-system-cost-curve-if-there-are-many-feeder-routes-and-the-feeders-only-constitute-a-short-portion-of-total-trip-time-graph}}{Pedro Szász.}
	}
\fi

Conversely, if the trunk portion of the total route is very short, and most of the customers are going well beyond the trunk corridor, converting more routes to trunk-and-feeder will only increase overall system costs.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 797-801: code points 1-13

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	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/9a464994bdee3b9996c0fa30cbccb77396c17e94.jpeg}
		\fignote{50}{Likely total system cost curve if feeder route travel time is greater than trunk travel time. Graph\label{chapter:service-planning:figure:likely-total-system-cost-curve-if-feeder-route-travel-time-is-greater-than-trunk-travel-time-graph}}{Pedro Szász.}
	}
\fi

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/b1ee81f0279fe98a7f21bf62286171a1ed136b39.jpeg}
		\fignote{51}{Likely cost curve if there are feeder routes of varying length but in general the time spent on the feeder route is long relative to the time spent on the trunk route. Graph\label{chapter:service-planning:figure:likely-cost-curve-if-there-are-feeder-routes-of-varying-length-but-in-general-the-time-spent-on-the-feeder-route-is-long-relative-to-the-time-spent-on-the-trunk-route-graph}}{Pedro Szász.}
	}
\fi

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/85df3c529f572acfc60f0a5cc9cf579834e502ce.jpeg}
		\fignote{52}{Likely cost curve for feeder routes of various travel times but where in general feeder route travel times are short relative to total travel time.\label{chapter:service-planning:figure:likely-cost-curve-for-feeder-routes-of-various-travel-times-but-where-in-general-feeder-route-travel-times-are-short-relative-to-total-travel-time}}{Pedro Szász.}
	}
\fi

This exercise, while simplified from real-world conditions by a number of assumptions, demonstrates the general concept that the effectiveness of a trunk-and-feeder system depends on whether it makes sense for a critical mass of routes. Once it makes sense to convert a critical mass of routes to a trunk-and-feeder system, it becomes easier and easier to add more routes to the system profitably. Once trunk-and-feeder reaches critical mass, only very high volume routes continuing well beyond the trunk system are likely to still be profitably excluded from the trunk feeder system and retained as direct services. As such, there are mathematical reasons why there is a tendency toward systems with all direct services or all trunk-and-feeder services.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 835-849: code points 1-26

\endbox
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 781-851: code points 1-7

\subsection{3}{Transfer and Terminal Delay}
\label{volume:operations:chapter:service-planning:section:direct-services-trunk-and-feeder-services-or-hybrids:subSection:transfer-and-terminal-delay}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 853-1013: code points 1-52

Splitting an existing direct service route into a trunk route and a feeder route will add several types of additional delay relating to the new required transfer. First, if transfer facilities are not located in an optimal location, or if access to the facility is poorly designed, vehicles will have to go out of their way to make the transfer possible, described as “negative distances,” increasing vehicle cycle times, and hence fleet requirements and operating costs. Second, transfers add significantly to customer travel times and discomfort since customers must walk from one bus route to the next. Avoiding transfer delays is often one of the main reasons discretionary riders elect not to use a system. Further, if transfers involve any form of physical hardship, such as stairs, tunnels, or exposure to rain, cold, or heat, then the system’s acceptability is even more compromised.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 855-863: code points 1-52

Not all transfers are equal. On one extreme are transfers located far from the trunk corridor involving slow and circuitous detours for both trunk routes and feeder routes to reach the transfer station, and lengthy walks across intersections and other obstacles unprotected from rain and sun. At the other extreme there are transfers made directly on a trunk corridor where many feeder services converge, with excellent terminal design involving minimal vehicle diversion and a simple few meters to walk across a comfortable, safe, and weather-protected platform. The quality of the transfer depends largely on the infrastructure and route design.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 865-871: code points 1-17

When considering whether to implement a trunk-and-feeder service, a direct service, or some combination, it is critical to calculate the likely delays caused by the forced transfer under the specific conditions being proposed for the system.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 873-875: code points 1-30

\subsubsection{1}{Additional Passenger Delay Waiting for the Trunk Vehicle or Feeder Vehicle and Boarding and Alighting Again}
\label{volume:operations:chapter:service-planning:section:direct-services-trunk-and-feeder-services-or-hybrids:subSection:transfer-and-terminal-delay:subSubSection:additional-passenger-delay-waiting-for-the-trunk-vehicle-or-feeder-vehicle-and-boarding-and-alighting-again}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 877-888: code points 1-10

When customers on a former direct service route now need to take a feeder vehicle and transfer at some point to a trunk vehicle, and this transfer point tends to be near where the bus route is at its maximum load, the maximum load of customers will now have to wait for the trunk vehicle in the morning and the feeder vehicle in the afternoon. These customers will face a waiting cost of half the headway of the trunk, or half the headway on their feeder route, depending on which direction they are going.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 879-883: code points 1-94

Since customers have to alight from the first vehicle and board a second one, there is an additional boarding and alighting delay per customer who needs to transfer. This additional delay will simply be the total boarding and alighting delay at the transfer station multiplied by the total number of transferring customers.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 885-888: code points 1-10

\subsubsection{2}{Extended Vehicle Running Time Due to Route Modifications Required by the Suboptimal Location of the Transfer Terminal}
\label{volume:operations:chapter:service-planning:section:direct-services-trunk-and-feeder-services-or-hybrids:subSection:transfer-and-terminal-delay:subSubSection:extended-vehicle-running-time-due-to-route-modifications-required-by-the-suboptimal-location-of-the-transfer-terminal}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 890-943: code points 1-89

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/8b83c186dbdc7251f5fe69e8aa4abccb38a63f4f.jpeg}
		\fignote{53}{An illustration of why additional route kilometers would be added to a route if it were converted to a trunk-and-feeder route and the point where the new transfer takes place (a new transfer facility) is beyond the point where the original route diverged from the trunk route. Typical terminal observations of additional customer travel times are shown in the box. Image\label{chapter:service-planning:figure:an-illustration-of-why-additional-route-kilometers-would-be-added-to-a-route-if-it-were-converted-to-a-trunk-and-feeder-route-and-the-point-where-the-new-transfer-takes-place-a-new-transfer-facility-is-beyond-the-point-where-the-original-route-diverged-from-the-trunk-route-typical-terminal-observations-of-additional-customer-travel-times-are-shown-in-the-box-image}}{Arthur Szász.}
	}
\fi

In all of the examples of trunk-and-feeder systems proposed in this section, all the routes pass a common point where they would diverge, so the location of a transfer terminal was simple and caused no additional travel time penalty. However, in most cases, the location of the terminal will serve some routes better than others. There will be some routes that will be pulled off their original route to reach a new common terminal point. In Figure 6.53, one of three vehicle routes is diverted from its original path because the terminal is not located where it originally departed the BRT corridor. This causes additional delay for all customers and additional operating time and cost for the vehicle operator. Some empirically observed ranges of additional minutes of running time on a route have been shown, but this will need to be measured on a route-by-route basis.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 898-906: code points 1-41

In addition, there is often no land readily available directly on the trunk corridor, so the terminal will need to be located where lower-cost land is available at some larger distance from the original trunk route. Terminals typically require a lot of land. In addition to accommodating other feeder services, terminals are places where vehicles turn around or park during off-peak periods (staging areas), and that requires space, too.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 908-912: code points 1-25

In most real-world cases, instead of placing a terminal at the natural convergence point of the existing bus routes, the terminal is located some blocks away on a piece of land owned by the municipality or that can be acquired otherwise at low cost. This adds two types of additional delay. It creates extra travel distance, possibly for both the trunk and the feeder vehicles, and it doubles the cycle time for vehicles traveling from the original corridor.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 914-918: code points 1-46

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/35d1ffe0faa2da87a26c8c88bfea4b06904ce653.jpeg}
		\fignote{54}{An illustration of additional route kilometers that are generated if a direct service is replaced by a trunk-and-feeder alternative where the point of transfer takes place at a facility off the BRT infrastructure. Typical terminal observations of additional customer travel times are shown in the box. Image\label{chapter:service-planning:figure:an-illustration-of-additional-route-kilometers-that-are-generated-if-a-direct-service-is-replaced-by-a-trunk-and-feeder-alternative-where-the-point-of-transfer-takes-place-at-a-facility-off-the-brt-infrastructure-typical-terminal-observations-of-additional-customer-travel-times-are-shown-in-the-box-image}}{Arthur Szász.}
	}
\fi

If the BRT trunk infrastructure is not extended all the way to the terminal, as is sometimes the case, the reduced speeds of the additional travel distance also need to be factored into the additional delay caused by the terminal being off corridor. Often, these access and egress roads around the terminal require complex new multiphase traffic signals, narrow, congested streets and other causes of slow speeds that did not affect the original direct service route that operated entirely on a major arterial.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 925-929: code points 1-92

As an example of this situation, in León, Guanajuato, Mexico, the terminal is 600 meters away from the main trunk corridor on Lopez Mateos Avenue (Figure 6.55). In addition to the delay due to the 600-meter diversion, the speeds on the terminal access road are lower than on the original arterial, and additional signal delay was introduced in order to provide turning access to enter and exit the terminal.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 931-934: code points 1-94

Another example is on Corridor 9 de Julho\slash{}Santo Amaro, in São Paulo, where the transfer terminal is 500 meters away from the natural connection point (Figure 6.56).\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 936-937: code points 1-64

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/156b48c7fa32878c35221d3ee07972406ba7cb4c.png}
		\fignote{55}{The addition of the trunk-and-feeder terminal in León, Guanajuato, Mexico, introduced considerable delay in travel times. Image\label{chapter:service-planning:figure:the-addition-of-the-trunk-and-feeder-terminal-in-len-guanajuato-mexico-introduced-considerable-delay-in-travel-times-image}}{Arthur Szász.}
	}
\fi

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/1139ab9603887a466cd43fd1d82877c3c4cd3fb4.jpeg}
		\fignote{56}{Trunk-and-feeder terminal Santo Amaro in São Paulo is poorly located and accesses are poorly designed, causing additional travel times. Image\label{chapter:service-planning:figure:trunk-and-feeder-terminal-santo-amaro-in-so-paulo-is-poorly-located-and-accesses-are-poorly-designed-causing-additional-travel-times-image}}{Arthur Szász.}
	}
\fi

\subsubsection{3}{Internal Circulation within the Transfer Terminal}
\label{volume:operations:chapter:service-planning:section:direct-services-trunk-and-feeder-services-or-hybrids:subSection:transfer-and-terminal-delay:subSubSection:internal-circulation-within-the-transfer-terminal}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 945-966: code points 1-85

The art of high-quality terminal design is not well known nor has it been systematized. In this planning guide, Chapters 25: Stations and 28: Multi-Modal Integration provide some very preliminary guidance, but optimizing a transfer terminal design is a critical area for further work.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 947-949: code points 1-78

Buses entering a transfer terminal often face significant delays caused by bus queues. Transfer terminals often include multiple platforms, as they are generally designed to accommodate multiple bus routes converging in one location. When poorly designed, there can be significant additional delays involved with vehicles entering the terminal and reaching their assigned platforms.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 951-954: code points 1-60

Transferring customers also face walks of varying distances and comfort depending on the quality of the terminal design. The best-designed trunk-and-feeder systems have feeder platforms immediately across from the trunk platforms, but not all terminals are so well designed. It is quite typical for a transfer terminal to require customers to needlessly climb up and down multiple stairways to reach their allotted boarding platform, when grade crossing would work just fine. If the terminal is large enough, it is of course impossible for all the feeder routes to be located immediately across the platform from a trunk platform, and the more feeder routes there are, the greater the likelihood that the customers will have to walk significant distances to reach their transfer route. Ideally, routes should be restructured and designed so that transfers can be made in several different stations, instead of concentrating all of them in just one location. Chapter 25: Stations and Chapter 28: Multi-Modal Integration also provide some preliminary guidelines for terminal design that can minimize this walking delay.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 956-966: code points 1-85

\subsubsection{4}{Range of Likely Delays from Empirical Observations}
\label{volume:operations:chapter:service-planning:section:direct-services-trunk-and-feeder-services-or-hybrids:subSection:transfer-and-terminal-delay:subSubSection:range-of-likely-delays-from-empirical-observations}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 968-1013: code points 1-52

Taking into account all six forms of transfer delay described in the previous four items, Table 6.29 provides some typical ranges for each variable.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 970-971: code points 1-47


			\ifxetex
				% disabled for now
			\else
				{  % group required to avoid fignote settings escaping
					\tabletitle{29}{Typical Ranges of Additional Terminal Delays}
\label{chapter:service-planning:table:typical-ranges-of-additional-terminal-delays}

					\img{\hsize}{operations/assets/0f8cd69fc622c559f8343bb331553c873096612f.jpeg}
				}
			\fi

Some variables affect both the bus operating cost and the waiting time of customers, and other variables only affect customer waiting times. If a terminal is located directly on a trunk corridor and at a natural point of divergence for the feeder routes, there could be zero delay for customers and operators due to bad terminal location, but at worst both operators and customers could face very significant delays. Internal and external circulation time for the bus at the terminal virtually always adds some delay. Additional boarding and alighting time due to the transfer delays both customers and vehicles in all cases within predictable ranges.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 977-983: code points 1-52

The additional walking times inside the terminal will vary depending on the quality of the terminal design, and the additional waiting time due to the transfer will vary with the frequency of the trunk service and the feeder service within somewhat predictable ranges.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 985-987: code points 1-66

The total time in minutes per customer adds up with these causes of delay. The “equivalent time” per customer multiplies walking time by three, because people generally do not like to walk, and it multiplies waiting time by two, because people generally do not like to wait. In other words, following standard cost-benefit analysis practice, these two types of delay are weighted based on customers’ empirically observed willingness to pay to avoid these types of delay.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 989-993: code points 1-58

As a result of this transfer penalty, an average trunk-and-feeder system starts with a disadvantage of twenty-three minutes of customer travel time per route converted. These additional delays also translate into increased cycle time ($TC$), which directly translates into increased fleet needs and increased operating costs. When added to the extra fleet needed to compensate for the peak hour correction factor and extra fleet required at the terminal for scheduling adjustments in real-world conditions, it is typical for trunk feeder systems to require from 11 percent to 66 percent additional fleet. In most cases, these extra costs will total something in the range of 34 percent of an additional cost for the trunk-and-feeder service, while the benefits from the larger vehicle use are going to be generally in a similar range only when the trunk is very long relative to the feeder route, and there are many very small routes converging.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 995-1003: code points 1-111

While the general benefits of many elements of BRT accrue primarily during the peak period, the time lost at terminals has an adverse impact on cycle times and customer travel times throughout the day. As a result, the benefits of a trunk-and-feeder BRT system exist mainly during peak hours. From a cost-benefit perspective, the terminal losses are rarely possible to recover from the benefits of being able to use larger vehicles on the trunk corridor.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1005-1009: code points 1-38

In summary, an excellent terminal project, located directly on the BRT trunk corridor at a natural convergence point, is a necessary but insufficient precondition for achieving any benefit from the conversion from a direct service to a trunk-and-feeder service.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1011-1013: code points 1-52

\subsection{4}{Avoiding Station and Platform Saturation}
\label{volume:operations:chapter:service-planning:section:direct-services-trunk-and-feeder-services-or-hybrids:subSection:avoiding-station-and-platform-saturation}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1015-1167: code points 1-80

There are two additional factors to consider when deciding on whether to convert a direct service route to a trunk-and-feeder route: station saturation and platform saturation.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1017-1018: code points 1-72

\subsubsection{1}{Avoiding Station Saturation}
\label{volume:operations:chapter:service-planning:section:direct-services-trunk-and-feeder-services-or-hybrids:subSection:avoiding-station-and-platform-saturation:subSubSection:avoiding-station-saturation}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1020-1048: code points 1-19

It may be the case that some existing bus routes using a planned BRT corridor operate with very small vehicles that are not compatible with BRT trunk infrastructure, usually because the roads they use are too narrow or in too deteriorated a condition for BRT vehicle operation. In this situation, including this route as a direct service on a BRT trunk corridor is likely to be ill advised. This is because providing a direct service for a minibus, for instance, is likely to more rapidly saturate the trunk corridor.\par
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If the methodology is followed as suggested in subsection \emphasis{Scenario II: Dwell Times and Demand Vary from Route-to-Route, and All Stations Are Similar}, where routes are included inside the BRT infrastructure based on a metric that gives priority to those bus routes where the customers using that route consume the least time at the bottleneck station, then it is likely that a route in which only minibuses can operate due to the operational conditions off the trunk route would be excluded because that type of bus would consume a lot of time at the bottleneck station.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1029-1034: code points 1-58

In Section 6.5, it was assumed that such a route would operate in parallel to the BRT infrastructure in mixed traffic. However, such a solution has two disadvantages. The first is that the demand from the route is lost to the BRT system, and the second is that the mixed traffic lanes on the BRT corridor are more likely to face saturation. As such, in those conditions, it may be desirable to convert that direct service route into a trunk route and a feeder route.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1036-1040: code points 1-52

The degree to which that specific route is likely to congest the bottleneck station can be calculated using the formulas provided in Chapter 7: Capacity and Speed on capacity and speed. The determination of whether the route should be simply cut, converted to a feeder, or allowed to continue to operate in the mixed traffic lanes will depend on the availability of land for a transfer location; the importance of the route to the level of demand on the trunk route; the level of congestion in the mixed traffic lanes; and the degree to which the trunk route can handle the additional demand without saturating the bottleneck station.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1042-1048: code points 1-19

\subsubsection{2}{Avoiding Station Platform Saturation}
\label{volume:operations:chapter:service-planning:section:direct-services-trunk-and-feeder-services-or-hybrids:subSection:avoiding-station-and-platform-saturation:subSubSection:avoiding-station-platform-saturation}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1050-1167: code points 1-80

Another possible reason to convert a direct service route to a trunk-and-feeder service is if there is a risk that the trunk station platforms would become overcrowded with waiting customers, though in this case the less drastic and more practical option would be simply to reconfigure the routes.\par
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Lower frequency, direct service buses can cause more customers to have to wait on station platforms than high-frequency trunk services. For low-demand systems this does not cause any significant problem. However, at high levels of demand, the station platform can become overcrowded and become saturated.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1056-1058: code points 1-100

As such, there are limitations to the number of direct routes that can operate on the same trunk bus stop unless stations can be sized to handle the required volumes of waiting customers. While external fare collection, at-level boarding, multiple and large doors, and large vehicles have increased station capacity markedly (the subject of the next chapter), these features have not made any progress in reducing the space consumed by waiting customers.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1061-1065: code points 1-40

In order to show the difference, begin by calculating the average number of passengers waiting for one route ($Pwait_i$) by:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1067-1068: code points 1-27

Eq. 6.47\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1070-1070: code points 1-8

$ P_{w i}= {P_{b i} \over F_i}  * {(1+Irr_i) \over 2} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1072-1072: code points 1-57

Where:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1074-1074: code points 1-6

\begin{itemize}
\item $ P_{w i} $: Passengers waiting for route i at given station (passengers\slash{}hour);% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1076-1077: code points 1-0
\item $ P_{b i} $: Boarding passengers in route i at given station (passengers\slash{}hour);% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1077-1078: code points 1-0
\item $ F_i $: Frequency of route “i” (vehicles\slash{}hour);% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1078-1079: code points 1-0
\item $ Irr_i $: Irregularity index of route i.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1079-1079: code points 1-49
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1076-1079: code points 1-49

Then, the total number of passengers waiting at the station (Pwait) is given by:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1081-1081: code points 1-80

Eq. 6.48\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1083-1083: code points 1-8

$ P_{w total} = \sum_i {Pb_i \over F_i} *  {(1+Irr_i) \over 2} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1085-1085: code points 1-66

Where i is all the routes that use the station.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1087-1087: code points 1-47

In other words, the number of customers that are likely to end up waiting on a platform will be the sum total of all of the boarding passengers per route per hour at that station divided by the frequency and then multiplied by the risk of irregular arrival of the bus.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1089-1091: code points 1-64

For example:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1093-1093: code points 1-12

$ P_{b i} $: 120 passengers\slash{}hour ;\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1095-1095: code points 1-36

$ F_i $: 6 vehicles\slash{}hour;\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1097-1097: code points 1-27

$ Irr_i $: 0.3 .\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1099-1099: code points 1-18

$ P_{w i} = { {120 \over 6}  * (1+0.3) \over 2} =13 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1101-1101: code points 1-55

It might be expected that at any given time there would be 13 passengers accumulating for boarding in route i.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1103-1104: code points 1-11

If there are 20 similar direct routes using the same sub-stop, there will be on average 13 passengers at that bus stop for each route at any given time.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1106-1107: code points 1-50

So,:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1109-1109: code points 1-4

$ P_{w\ \text{direct}} = P_{w\ \text{total}} = 20 * 13 =  260 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1111-1111: code points 5-69

There will be 260 passengers on the station platform at any given time.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1113-1113: code points 1-71

To accommodate these passengers, normally one would want at least one square meter for every 2 passengers waiting. Also consider usable platform width minus 1 meter (0.5 m “buffer” on both sides), minus 1 meter for circulation space for up to 2,000 passengers per hour (1 meter of width is required per 2,000 circulating passengers per hour) to be the usable waiting space. Usually the length of the docking bay is considered the usable length.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1115-1119: code points 1-18

Therefore, to accommodate just the waiting area for 260 passengers, and assuming circulating passengers are less than 2,000 per hour, one would need 260\slash{}2 = 130 square meters, or a platform 6 meters wide and 33 meters long, or 7 meters wide and 26 meters long, or 9 meters wide and 22 meters long, and so on.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1121-1123: code points 1-100

If these 20 direct services routes (120 buses) were converted into just one trunk route with a frequency of 60 articulated buses per hour (cutting the frequency in half by doubling the size of the buses), the number of boarding passengers per hour into the one trunk route would be:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1126-1128: code points 1-73

$ P_{b i} =  120 * 20 = 2400 $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1130-1130: code points 1-32

And the average number of waiting passengers at each trunk station will be:\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1132-1132: code points 1-75

$ P_{w\ \text{trunk}} = P_{w\ \text{total}} = { {2400 \over 60}  * (1+0.3) \over 2} = 26 \text{passengers} $\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1134-1134: code points 1-110

As people can take the first bus that comes along, fewer passengers accumulate on the platform waiting for their bus. In this scenario, trunk-and-feeder reduces the number of passengers waiting on each platform by 90 percent (from 260 to just 26) due to the frequency and size of the vehicles. Thus, the station platform only needs to be 13 meters long and 4 meters wide to comfortably accommodate the waiting passengers. Indeed, this is the more common situation, where the station length is determined not by the number of waiting passengers, but by consideration of the BRT station saturation from stopping buses, since the platform length required for 60 large buses per hour will be at least 40 meters. If there is limited space along the trunk route and sufficient space at the terminals, there will be some advantage to relocating these waiting passengers from a congested trunk platform to a transfer terminal.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1136-1144: code points 1-80

When designing BRT stations, calculate the expected density of waiting customers based on the proposed service plan, and ensure that the length and width is adequate to serve both vehicle movements and waiting customer requirements. As the Guangzhou BRT is the highest capacity direct service BRT system in the world, it is worth looking at the station-sizing ramifications of its direct service in Figure 6.57.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1146-1149: code points 1-100

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/49e599c7b4a204c32d652141a39163644e6f89da.jpeg}
		\fignote{57}{On the Guangzhou BRT, the highest capacity direct service BRT system in the world, there are stations with up to four sub-stops and twelve docking bays (two to three docking bays per sub stop) per direction. Image\label{chapter:service-planning:figure:on-the-guangzhou-brt-the-highest-capacity-direct-service-brt-system-in-the-world-there-are-stations-with-up-to-four-sub-stops-and-twelve-docking-bays-two-to-three-docking-bays-per-sub-stop-per-direction-image}}{Bing Maps.}
	}
\fi

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/dca86121e2cfc833c92b9346a4f083831452734d.jpeg}
		\fignote{58}{With only direct services in the Guangzhou BRT System, Shidajida station has four sub-stops and was designed with ample platforms and customer waiting space. Image\label{chapter:service-planning:figure:with-only-direct-services-in-the-guangzhou-brt-system-shidajida-station-has-four-sub-stops-and-was-designed-with-ample-platforms-and-customer-waiting-space-image}}{Karl Fjellstrom, Far East BRT.}
	}
\fi

In Guangzhou, the design parameter was to provide for two passengers per square meter. Each docking bay has 5 meters of platform width, of which 2.5 is usable for a waiting area, and each waiting area per docking bay is 20 meters long. As such, each waiting area per bus is $ 20 \text{m} * 2.5 \text{m} = 50 {\text{m}}^2 $. With eight docking bays, the station can support up to 100 passengers per docking bay, and 800 passengers in total.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1159-1162: code points 1-104

It was not easy, however, to convince the authorities to allocate 5 meters of road right-of-way to the station platform, although 5 meters is the average. A station narrower than 4 meters is not recommended for a bidirectional station. In very space-constrained locations, a small station with just 3 meters of width and 20 meters in length can only support around 60 passengers per hour.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1164-1167: code points 1-80

\subsection{5}{Conclusion: When to Consider Converting Direct Services to Trunk-and-Feeder Services}
\label{volume:operations:chapter:service-planning:section:direct-services-trunk-and-feeder-services-or-hybrids:subSection:conclusion-when-to-consider-converting-direct-services-to-trunk-and-feeder-services}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1169-1246: code points 1-0

The large number of variables to consider when deciding whether to split existing direct services into trunk-and-feeder services makes it difficult to provide a single unified formula for making such a determination. Commercial public transport simulation software is not equipped to handle the sorts of multivariate analyses presented here either. The number of possible alternative service plan scenarios to test is so great that service planners need to follow some basic rules of thumb to create a set of scenarios for testing with a public transport demand model. As such, most of these decisions will need to continue to rely on good judgment assisted with the basic approaches and tools provided, aided by public transport software models only after many of the critical decisions have already been made.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1171-1178: code points 1-72

The following provides a brief summary of these rules, based on the preceding discussions.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1180-1181: code points 1-0

\begin{itemize}
\item Trunk-and-feeder systems require additional fleet due to the peaked nature of demand.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1181-1181: code points 1-91
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1181-1181: code points 1-91

Trunk-and-feeder systems require larger fleets to accommodate the same number of customers. The more peaked the demand, the more additional fleet that the trunk- and-feeder service will require. In normal operating conditions, real-world observations indicate that the additional fleet required to convert a direct service into a trunk-and-feeder service will be in the range of 11 to 15 percent. If demand is heavily peaked, slightly more vehicles may be needed. If demand is less peaked, slightly fewer additional vehicles will be required.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1183-1189: code points 1-0

\begin{itemize}
\item Trunk-and-feeder systems allow the use of larger buses with lower operating costs per customer on trunk routes, assuming high occupancy levels.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1189-1190: code points 1-48
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1189-1190: code points 1-48

The main benefit of the trunk-and-feeder system is the ability to use larger buses with lower operating costs per customer along high-volume trunk corridors. By consolidating the demand from a number of lower demand direct service routes, a trunk BRT might be able to operate very large articulated or even bi-articulated buses along the trunk corridor, allowing for potential operating cost savings. This savings is likely to be in the 15 to 30 percent range if the trunk portion of the route is long relative to the feeder portion (say, the length of most of the feeder routes are considerably less than 50 percent of the length of the trunk corridor), and a large number of direct service routes (say, greater than five) originally shared the demand along the trunk corridor.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1192-1200: code points 1-0

\begin{itemize}
\item Trunk-and-feeder systems impose additional costs related to the required additional transfers.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1200-1200: code points 1-100
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1200-1200: code points 1-100

Trunk-and-feeder systems impose a lot of additional costs on BRT services related to the need for an additional transfer. These additional costs manifest themselves during the peak hour as well as throughout the day.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1202-1204: code points 1-8

First, if it is not possible to locate the transfer terminal very near to the trunk corridor at a natural point of route divergence, the buses and their customers will need to go out of their way to get to the transfer terminal. This directly increases both customer travel time and cost and vehicle operating time and cost.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1206-1209: code points 1-9

Circulation within and around the terminal also tends to cause delays. Poor circulation might involve problems with buses approaching and operating within the terminal, or it might involve the way customers move within the terminal. Poor terminal design is common in public transport system design, and the number of skilled terminal designers is limited.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1211-1214: code points 1-41

This transfer terminal-related delay is likely to add between 11 and 66 percent to the fleet required in a trunk-and-feeder service plan. In addition, in a well-designed terminal, customers could face five-minute delays, and in a badly designed terminal, an additional 48 minutes per transferring customer has been observed.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1216-1219: code points 1-9

Transfer terminals also tend to have large construction costs and may require land acquisition and resettlement. Once constructed, the transfer terminals need personnel to manage, operate, clean, and maintain them, adding to operating costs.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1221-1224: code points 1-0

\begin{itemize}
\item Trunk-and-feeder systems can mitigate against station saturation and station platform saturation.% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1224-1224: code points 1-103
\end{itemize}
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1224-1224: code points 1-103

If some bus routes cannot easily use buses that are fully compatible with BRT trunk infrastructure (such as minibus routes operating on narrow, poorly maintained roads), incorporating them into the trunk corridor as direct service routes will increase the risk that the trunk corridor stations will become saturated. It may be better to turn such routes into feeder routes.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1226-1229: code points 1-67

Direct services also require customers on the trunk corridor to wait longer for their bus than trunk services. This results in more customers accumulating inside the station waiting for their buses. Trunk-and-feeder services will reduce the number of accumulating customers waiting for their buses, because more customers can take more of the routes operating on the trunk. This problem is more likely to manifest itself in high-demand systems.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1231-1235: code points 1-20

The conditions under which the conversion of direct services to trunk-and-feeder services will bring overall benefits are fairly limited. Until recently, trunk-and-feeder systems were proliferating in conditions inappropriate to their use, and direct service options were being neglected. This can probably be attributed to the similarity of trunk-and-feeder services to rail services, and the application of service plans developed in Gold Standard systems like Bogotá to cities with different conditions, where trunk-and-feeder operations may make less sense. In the future, with more full-featured direct service and hybrid (i.e., Direct + Trunk-and-Feeder) BRT systems coming into existence, such as the new system in Lanzhou, Yichang, and other cities, more real-world data will become available for comparison of the relative merits of the two basic service planning approaches.\par
% @ guide/06-service_planning/66-direct-services,-trunk-and-feeder-services,-or-hybrids.src: lines 1237-1246: code points 1-0

\section{7}{Deciding on Stop Elimination and Express Services}
\label{volume:operations:chapter:service-planning:section:deciding-on-stop-elimination-and-express-services}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 3-1032: code points 1-0

\quotation{If you want a happy ending that depends, of course, on where you stop your story.}{Orson Welles, actor, director, producer, and writer, 1915–1985}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 5-6: code points 1-64

This section addresses the question of whether a new BRT service should retain the same stations as preexisting services, and whether limited-stop services should be created. Creating limited-stop services is done by means of selecting a proportion of the trips on an existing service and changing the programming to skip stops at certain stations: the unchanged service will be referred as the local service and the other one or more as a limited-stop service (or express service).\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 8-12: code points 1-65

While eliminating stops from the system increases the walking time required by some customers to reach a stop, it also increases the average BRT vehicle speed (or “commercial speed”) by removing the fixed dwell times at the station. Fixed dwell time (T0 or dead time) is the time associated with the bus pulling up to the station, docking, opening and closing its doors, and pulling out of the station.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 14-17: code points 1-90

In this chapter, the impact of stop removal on variable dwell time is not considered, as it is assumed there will not be much change with the elimination of stops, as the ridership will just redistribute among the remaining stations.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 19-21: code points 1-29

Including limited-stop service or services has a variety of impacts. The main advantages of limited-stop and express services are:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 23-25: code points 1-0

\begin{itemize}
\item Fixed dwell time is eliminated on the express routes so customers whose origins and destinations lie on the limited-stop route will benefit. This is discussed in this section;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 25-27: code points 1-0
\item On high-demand corridors, by dividing a route into local and limited stop, the frequency per route is reduced, but also the irregularity of arrivals. This is also treated in this section;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 27-29: code points 1-0
\item By increasing overall system speed, overall system capacity can be increased. This is covered in Chapter 7: Capacity and Speed.% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 29-30: code points 1-33
\end{itemize}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 25-30: code points 1-33

However, these services also introduce some costs:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 32-33: code points 1-0

\begin{itemize}
\item Customer waiting times on local routes increase, as the frequency on the original route is reduced;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 33-34: code points 1-0
\item Vehicles must be able to pass one another at stations.% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 34-34: code points 1-60
\end{itemize}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 33-34: code points 1-60

Adding additional services must balance the benefits of removing fixed dwell time with the costs of adding customer waiting time, and the costs of deteriorated mixed traffic level of service resulting from the need to introduce passing lanes at all stations skipped by limited-stop services.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 36-38: code points 1-90

This section provides guidance to service planners to make decisions about which stations to eliminate or add when introducing a BRT system. The first subsection provides a basic methodology for deciding when to eliminate a station. It is a simple cost-benefit equation that compares the additional walking time to the reduction in fixed dwell time and provides some simple rules of thumb.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 40-43: code points 1-82

The remainder of the section assumes that the local service will be retained, but that additional limited-stop services will be created. In all these examples, walking time is no longer an issue, as the local service is retained, but at a lower frequency. Rather, it is an issue of balancing the waiting time associated with reduced frequencies per route and with the increased bus speeds. It is also a matter of optimizing frequencies to reduce the irregularity of service.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 45-49: code points 1-50

Normally, service planners will look at the demand profile of the corridor (an internal O\slash{}D to the system that also provides the number of customers on board at each link), and using a simulation model, will run alternative scenarios to test its benefits and its costs (operation and travel times). Service planners generally do not try an infinite number of possible alternatives; they use certain basic approaches to determine which scenarios are likely to perform the best, and limit themselves to a reasonable number of scenarios. This chapter is aimed at making more transparent the basic thinking that service planners use when defining scenarios to test using their simulation models.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 51-57: code points 1-66

\subsection{1}{Station Spacing and Station Elimination}
\label{volume:operations:chapter:service-planning:section:deciding-on-stop-elimination-and-express-services:subSection:station-spacing-and-station-elimination}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 59-153: code points 1-100

When deciding whether to eliminate or add stations, it is necessary to determine what constitutes optimal spacing. If stations are spaced very far apart in the manner of a metro system, it is possible to reach very high vehicle speeds and system capacities. However, the disadvantage of such an approach is the additional time customers must spend to reach the nearest station. Therefore, BRT station spacing should try to strike an optimal balance between convenience for walking trips to popular destinations, and convenience for customers in the form of higher speed and capacity.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 61-66: code points 1-55

If the origins of customer trips are randomly distributed along a BRT corridor, a standard optimal distance between stations can be calculated. In most contexts, it ends up being between 450 meters and 500 meters, or roughly a quarter mile.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 68-70: code points 1-38

In Figure 6.59 the optimum station spacing distance is where the total travel time (blue line) is minimized. From the figure, this point occurs in the range of a station separation of 400 meters to 500 meters.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 72-73: code points 1-100

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/38cc7e738d19db112a068c71542c6e663db9abac.png}
		\fignote{59}{Optimizing total travel time as a function of station separation, this graph illustrates the trade-off faced by customers for increasing distances between station stops. As station stop distances increase, in-vehicle time falls as BRT vehicle speeds increase, but walking times also increase. Total travel time in a typical urbanized corridor tends to become minimal with stop distances around 450 meters. Image\label{chapter:service-planning:figure:optimizing-total-travel-time-as-a-function-of-station-separation-this-graph-illustrates-the-trade-off-faced-by-customers-for-increasing-distances-between-station-stops-as-station-stop-distances-increase-in-vehicle-time-falls-as-brt-vehicle-speeds-increase-but-walking-times-also-increase-total-travel-time-in-a-typical-urbanized-corridor-tends-to-become-minimal-with-stop-distances-around-450-meters-image}}{Arthur Szász.}
	}
\fi

The following formulas can be used to calculate the optimal distance between stations, where the total walking cost and travel cost is minimized, or where:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 82-83: code points 1-52

Eq. 6.49\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 85-85: code points 1-8

$ \text{Distance}_\text{optimum} = MIN({C_\text{walk} + C_\text{travel}}) $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 87-87: code points 1-77

Where:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 89-89: code points 1-6

\begin{itemize}
\item $ \text{Distance}_\text{optimum} $: Optimal distance between stations;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 91-92: code points 1-0
\item $ C_\text{walk}:$ Walking cost;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 92-93: code points 1-0
\item $ C_\text{travel}:$ Travel cost.% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 93-93: code points 1-40
\end{itemize}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 91-93: code points 1-40

Table 6.30 provides an example comparing general travel times for varying station spacings (from 210 meters to 500 meters) for an average customer trip. In this example, the average customer trip on a corridor is 4.35 kilometers. The trade-off between additional walking distances due to fewer stations and time spent waiting at stations due to more stations is compared on a per customer basis.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 95-98: code points 1-83


			\ifxetex
				% disabled for now
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					\tabletitle{30}{Comparison of General Travel Times for Varying Station Spacings}
\label{chapter:service-planning:table:comparison-of-general-travel-times-for-varying-station-spacings}

					\img{\hsize}{operations/assets/3d8f83e96611cb844f5d5e78ea6c77f7972a99df.png}
				}
			\fi

In Table 6.30, the average number of stations per customer trip on the corridor is derived by dividing the average trip length by the average distance between stations. This is then multiplied by the average fixed dwell time per station to get the average delay per customer from the selected station distance.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 104-107: code points 1-35

It is then assumed that each customer walks on average one-quarter of the distance between stations at a walking speed of 1.3 meters per second. Boarding customers then have to walk to the station, and alighting customers have to walk from the station. This combined walking time then should be weighted by a factor of two, because most people dislike walking more than they dislike sitting on a moving bus. When these are compared for different stopping distances, the minimum total cost of walking and transiting customers occurs at an optimal distance of around .4 or .45 kilometers between stations. This turns out to be the optimal spacing when demand along a corridor is relatively uniform.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 109-115: code points 1-77

\emphasis{The} \emphasis{BRT Standard} gives 2 points for a system where the average stopping distance between stations is 0.3 kilometers and 0.8 kilometers (or between 0.2 miles and 0.5 miles), with 450 being a typical appropriate distance between stations. Note, however, that in high-capacity systems with large stations, BRT stations may cover an area around 100–250 meters long, and in this case a more reasonable station spacing is around 600 meters.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 117-121: code points 1-11

Of course, this calculation has been made per customer, rather than for customers in aggregate. Where there are large volumes of boarding and alighting customers, more frequent stations will be optimal, because more people will be affected by the long walking times than will benefit from the faster vehicle speeds. In areas with very few boarding and alighting customers, greater distances between stations will be optimal, because fewer people will benefit from the shorter walking distances, and more will benefit from the faster vehicle speeds. For this reason, it is fairly typical to have stations spaced at a greater distance apart farther from the city center, where demand is lower, and closer together downtown, where both demand and the density of trip attractors or generators are higher. Figure 6.59 visually summarizes the trade-off between walking times and BRT travel times in relation to the distance between stations.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 123-131: code points 1-102

Further, the optimal distance is not a constant, but will vary depending on a number of factors, including: the average trip length (assumed to be 4.35 kilometers in the table above), the average walking speed (used 1.2 m\slash{}s as a design speed to accommodate the range of walking speeds, but this can vary from city to city), the weight that people attribute to walking and urban density. In the table above, a weight of two was used, but if, for example, a lot of people are elderly or disabled, or if the walking environment is very bad, people might pay more to avoid walking.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 134-139: code points 1-52

A reasonable average stopping distance is around 450 meters for low-capacity stations and 600 meters for larger, high-capacity stations. This spacing is the best way to minimize walking distances, while keeping vehicle speeds at a reasonable level. BRT stations are typically located near major destinations such as commercial centers, large office or residential buildings, educational institutions, major junctions, or any concentration of trip origins and destinations. Usually this siting is done based on intuitive local knowledge and space availability. The station area will typically consume more right-of-way than other parts of the BRT infrastructure. As such, station location may look for places where the right-of-way can be most easily widened; mid-block rather than at intersections where road space is at a premium; locations where small parcels of public land, variances in the road right-of-way, or the presence of low-cost land such as surface parking lots adjacent to the corridor.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 141-150: code points 1-68

Reducing the number of stations does not reduce variable dwell time, as in most cases the vast majority of boarding and alighting delay will just redistribute to other stations if a station is eliminated.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 152-153: code points 1-100

\subsection{2}{Implementing Limited-Stop Services}
\label{volume:operations:chapter:service-planning:section:deciding-on-stop-elimination-and-express-services:subSection:implementing-limited-stop-services}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 155-456: code points 1-9

As discussed in the previous subsection, every station adds delay to customers on board, a BRT vehicle usually needs from 12 to 30 seconds of dead time per station, and an average can be readily calculated for a specific corridor by observation. The idea of introducing limited and express services into a BRT system is to reduce this fixed dwell time.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 157-160: code points 1-42

The introduction of a new, limited-stop service usually implies reducing frequencies on the local service. While the new limited-stop service will travel at a higher speed, the demand on the corridor is now divided between the local route or routes and the new limited route. The frequency of the original route therefore goes down, and the drop in frequency introduces some additional delay to local route customers making trips not served by the express route, as they have to wait longer for their vehicle to arrive.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 162-166: code points 1-95

Generally, routes should have a frequency of at least 10 vehicles per hour. If adding a limited route drops the frequency of the local service below 10 vehicles per hour, the chances are that the longer waiting time faced by the customers who cannot take the limited as an alternative will outweigh the time savings for those who can take the limited. There are, of course, exceptions.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 168-171: code points 1-77

This reduced frequency may also have an extra benefit in some cases because too high service frequencies commonly lead to service irregularity. Consider, for example, a vehicle that is a minute behind schedule in a service with 5-minute headways (12 vehicles per hour) service: when it arrives at the station the number of customers waiting to board is 20 percent larger than expected by the schedule, so it will need a bit more time for boarding and will be a bit more delayed. The next vehicle arriving at the same station (also on the schedule) will have 20 percent fewer boarding customers and will leave a bit sooner. The vehicle in front will increase the number of alighting customers per station as well. As the two vehicles continue down the route, the vehicle in front will fall farther and farther behind until the two vehicles are running together. If frequency is higher than 30 vehicles an hour (2-minute headway), the chances that one vehicle will arrive at its destination crowded and late, and the vehicle directly behind it will arrive nearly empty rises sharply. This irregularity leads to vehicle queue delays at stations (see Eq. 6.22).\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 173-184: code points 1-10

Therefore, if there are more than 30 vehicles an hour, there will be time savings from splitting the demand into more than one service, a local and a limited-stop service, just as a way of reducing the station queueing delay associated with this irregularity. Empirical evidence indicates that 22 vehicles an hour is optimal from the perspective of improving service regularity.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 186-189: code points 1-72

As a baseline, then, routes with frequencies of 20 or more per hour are candidates for the introduction of limited-stop services. If it is assumed that a standard 12-meter vehicle is at a reasonable design capacity at 60 customers per vehicle, 20 vehicles per hour translates roughly into a maximum load of 1,200 customers per hour. Limited-stop services can therefore be considered for services that have maximum load above 1,200 customers per hour, as follows:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 191-195: code points 1-48

\begin{enumerate}
\item \emphasis{At loads of 1,200–1,800:} It may make sense to introduce a service that only stops at the more popular stops when most boarding and alighting demand is concentrated at only a few stops along the corridor, but where the simple elimination of the stop is difficult for political reasons.% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 197-200: code points 1-0
\item \emphasis{At loads greater than 1,800}: If demand is relatively evenly distributed along a corridor, it is desirable to split this demand up into more specialized services, as it will not add much waiting time (due to high frequencies related to the demand), and will increase speed for many customers, while also improving comfort and regularity of service.% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 200-204: code points 1-0
\item If trip lengths are long, or the renovation rate is low, these may indicate the need for limited-stop or express services.% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 204-205: code points 1-20
\end{enumerate}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 197-205: code points 1-20

Beyond these basic principles, more detailed analysis should be done to determine whether limited-stop services are needed and where they should stop. To make a more detailed determination, something needs to be known of the trip origins and destinations of the customers using each bus route. Normally this is done by gathering enough information to put a corridor-specific OD matrix into a simulation model, and then running alternative scenarios to see how they perform. The following sections provide some basic guidance as to the sorts of local and limited-stop service patterns that one might test and why. Once he demand patterns of the alternaive services are output from the model, the following provides some tools to make a determination on the best pattern using cost-benefit analysis.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 207-214: code points 1-78

\subsubsection{1}{The Costs of Implementing Limited-Stop Services}
\label{volume:operations:chapter:service-planning:section:deciding-on-stop-elimination-and-express-services:subSection:implementing-limited-stop-services:subSubSection:the-costs-of-implementing-limited-stop-services}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 216-344: code points 1-82

The primary downside of implementing a limited-stop service is that it divides the ridership between the two services, cutting the frequency of the original local service, and hence increasing waiting times for the local service. Therefore, in order to determine whether it makes sense to add a limited-stop service, one must begin by calculating the total cost associated with waiting for a bus on a local route, as this will be the main cost of adding a limited route. In the sections that follow, the benefits will be calculated.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 218-223: code points 1-14

The cost of implementing an express route results in:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 225-225: code points 1-53

Eq. 6.50\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 227-227: code points 1-8

$ \text{ExpressCost} = \text{WaitCost}_\text{express} + \text{WaitCost}_\text{local} - \text{WaitCost}_\text{original service} $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 229-229: code points 1-130

Where:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 231-231: code points 1-6

\begin{itemize}
\item $ \text{ExpressCost} $: Additional cost of waiting during the peak hour with express service implementation;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 233-234: code points 1-0
\item $ \text{WaitCost}_\text{original service} $:Total waiting cost of the original service;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 234-235: code points 1-0
\item $ \text{WaitCost}_\text{express} $: Total waiting cost of the included express service;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 235-236: code points 1-0
\item $ \text{WaitCost}_\text{local} $: Total waiting cost of the new local service.% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 236-236: code points 1-86
\end{itemize}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 233-236: code points 1-86

The cost of waiting for a route (original, new express, or new local) service (WaitCostrouteexpress) is calculated using the previously explained formula from Section 6.4.3 Equation 6.12:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 238-239: code points 1-86

$ \text{WaitCost}_\text{route} =  \text{Ren}_\text{route} * \text{Cost}_\text{wait} * 0.5 * (1+ Irr_\text{route}) *\text{LoadFactor} * \text{VSize} $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 241-241: code points 1-151

Where:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 243-244: code points 1-0

\begin{itemize}
\item $\text{WaitCostRoute}$: Total waiting time cost generated to the route users (in \$);% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 244-245: code points 1-0
\item $\text{Ren}_\text{route}$: Renovation factor of the route;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 245-246: code points 1-0
\item $ \text{Costwait}$: Average user waiting cost (\$\slash{}time);% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 246-247: code points 1-0
\item $ \text{Irr}\text{route}$: Irregularity index of the route; measure of the variance between the actual headways and the scheduled headways (usually near 0.3, see Section 6.3.9);% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 247-249: code points 1-0
\item $ \text{V}_\text{Size}$: Vehicle capacity;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 249-250: code points 1-0
\item $ \text{LoadFactor}$: Design load factor (usually 0.85).% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 250-250: code points 1-64
\end{itemize}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 244-250: code points 1-64

Note that frequency itself does not factor into this equation as the cost of waiting does not change based on how long customers must wait. The more demand, the greater number of people waiting, but the higher the frequency, the shorter wait per person; as a result, the total cost of the wait is the same either way. For low demand, each person faces a longer wait but the wait affects fewer people, so in the end, total demand is not related to total waiting cost.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 252-256: code points 1-59

If a BRT service is unlikely to have a functional operational control system, or if a regular bus service cannot easily be measured, it is often sufficient to simply use a standard operational irregularity index, which is usually around 0.3 based on empirical observation, or:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 258-260: code points 1-63

$ \text{WaitCost}_\text{route} =  \text{Ren}_\text{route} * \text{Cost}_\text{wait} * 0.5 * (1+0.3) *\text{LoadFactor} * \text{VSize} $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 262-262: code points 1-137

However, the level of irregularity usually varies with the frequency, and that will have a significant impact on irregularity. In order to evaluate irregularity varying with frequency (Freqroute), the formula needs to be modified to the following:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 264-266: code points 1-38

Eq. 6.51\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 268-268: code points 1-8

$ \text{WaitCost}_\text{route} =  \text{Ren}_\text{route} * \text{Cost}_\text{wait} * 0.5 * (1+ ({\text{Freq}_\text{route}  \over \text{Freq}_\text{optimum}  }) ^2) *\text{LoadFactor} * \text{VSize} $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 270-270: code points 1-202

Where:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 272-273: code points 1-0

\begin{itemize}
\item $\text{WaitCostRoute}$: Total waiting time cost generated to the route users (in \$);% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 273-274: code points 1-0
\item $\text{Ren}_\text{route}$: Renovation factor of the route;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 274-275: code points 1-0
\item $ \text{Costwait}$: Average user waiting cost (\$\slash{}time);% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 275-276: code points 1-0
\item $ \text{Irr}\text{route}$: Irregularity index of the route; measure of the variance between the actual headways and the scheduled headways (usually near 0.3, see Section 6.3.9);% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 276-278: code points 1-0
\item $ \text{Freq}_{route}$: Frequency of the route (vehicles\slash{}time)% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 278-279: code points 1-0
\item $ \text{V}_\text{Size}$: Vehicle capacity;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 279-280: code points 1-0
\item $ \text{LoadFactor}$: Design load factor (usually 0.85);% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 280-281: code points 1-0
\item $ \text{Freq}_{optimum}$: Optimum frequency to avoid irregularity of boarding and alighting;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 281-281: code points 1-100
\end{itemize}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 273-281: code points 1-100

Therefore, the formula can simply be rewritten as:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 283-283: code points 1-50

$ \text{WaitCost}_\text{route} =  \text{Ren}_\text{route} * \text{Cost}_\text{wait} * 0.5 * (1+ ({\text{Freq}_\text{route}  \over 22 }) ^2) *\text{LoadFactor} * \text{VSize} $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 285-285: code points 1-177

For example, if a route is split in two, one local and the other limited, and if half of the original frequency is assigned to each new route, the results for each route become:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 287-288: code points 1-75

$ \text{WaitCost}_\text{express} = \text{WaitCost}_\text{local} $ $  = Re_\text{original service} *\text{Cost}_\text{wait} * 0.5 * (1+ ({\text{Freq}_\text{original service}  \over 22 }) ^2) *\text{LoadFactor} * \text{VSize} $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 290-291: code points 1-161

If we call $ K = Ren_\text{original service}*\text{Cost}_\text{wait} * 0.5 * \text{LoadFactor} * \text{VSize} $ , Eq. 6.42 can be rewritten as:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 293-294: code points 1-31

$ \text{ExpressCost} = \text{WaitCost}_\text{express} + \text{WaitCost}_\text{local} - \text{WaitCost}_\text{originalservice} $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 296-296: code points 1-129

$ \text{ExpressCost} = 2 * \text{WaitCost}_\text{local} - \text{WaitCost}_\text{originalservice} $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 298-298: code points 1-100

$ \text{ExpressCost} = 2 * K *(1+ ({0.5 * \text{Freq}_\text{original service}  \over 22 }) ^2) - K * (1+ ({0.5 * \text{Freq}_\text{original service}  \over 22 }) ^2) $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 300-300: code points 1-169

$ \text{ExpressCost} =  K *(2+2*({0.5 * \text{Freq}_\text{original service}  \over 22 }) ^2 - 1 -  ({\text{Freq}_\text{original service}  \over 22 }) ^2) $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 302-302: code points 1-157

$ \text{ExpressCost} =  K *(1+2*0.25*({ \text{Freq}_\text{original service}  \over 22 }) ^2 - ({\text{Freq}_\text{original service}  \over 22 }) ^2) $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 304-304: code points 1-152

$ \text{ExpressCost} =  K *(1+0.5*({ \text{Freq}_\text{original service}  \over 22 }) ^2 - ({\text{Freq}_\text{original service}  \over 22 }) ^2) $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 306-306: code points 1-149

$ \text{ExpressCost} =  K *(1-0.5*({ \text{Freq}_\text{original service}  \over 22 }) ^2 ) ^2) $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 308-308: code points 1-98

The express cost multiplier $ (1-0.5*({ \text{Freq}_\text{original service}  \over 22 }) ^2 ) ^2) $ is shown on the graph in Figure 6.60 as is K shown in function of $ {\text{Freq}_\text{original service} \over 22} (22 = \text{Freq}_\text{optimum}) $:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 311-312: code points 1-153

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/d0e8fcfafb850afd44bc35c6cab91a2e4c0a43c1.jpeg}
		\fignote{60}{The cost factor of splitting a route into a local route and a new limited-stop route when the relation of frequency to optimal frequency ($Fr \over Fot$) is considered: When the frequency rises above 31 ($ 31 \over 22 = 1.4 $) the benefit from reduced service irregularity is greater than the time lost waiting for a lower frequency service.\label{chapter:service-planning:figure:the-cost-factor-of-splitting-a-route-into-a-local-route-and-a-new-limited-stop-route-when-the-relation-of-frequency-to-optimal-frequency-froverfot-is-considered-when-the-frequency-rises-above-31-31over2214-the-benefit-from-reduced-service-irregularity-is-greater-than-the-time-lost-waiting-for-a-lower-frequency-service}}{Arthur Szász.}
	}
\fi

In the graph on Figure 6.60, the “1” on the x axis represents 22 buses per hour ($22 \over 22$). The 1.4 represents roughly 31 buses per hour ($31 \over 22 = 1.4$). At greater than 31 buses per hour, the additional waiting caused by the reduced frequency from the splitting of the original route for the creation of a new express service is outweighed by the benefit of reducing the irregularity in bus arrivals to the point where CostWait always becomes a negative cost, or in other words, a benefit. Therefore, if a BRT route has more than thirty-one vehicles an hour, it generally makes sense to split it into a new limited-stop service just to reduce irregularity, even if boarding and alighting volumes are nearly uniform between stops.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 319-325: code points 1-96

If multiple ($n$) routes are created, then the total wait cost for each new route needs to be calculated:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 327-327: code points 1-107

Eq. 6.52\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 329-329: code points 1-8

$ \text{ExpressCost} = \text{WaitCost}_\text{express(1)} + \ldots +  \text{WaitCost}_\text{express(n)} +  \text{WaitCost}_\text{local} - \text{WaitCost}_\text{original service}$\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 331-331: code points 1-179

Where:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 334-334: code points 1-6

$ \text{ExpressCost} $: Additional cost of implementing limited-stop services;\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 336-336: code points 1-80

$ WaitCost_\text{express(1)} $: Total waiting cost of the first added express service;\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 338-338: code points 1-88

$ WaitCost_\text{express(n)} $: Total waiting cost of n-th additional added express service;\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 340-340: code points 1-94

$ WaitCost_\text{local} $: Total waiting cost of adding one local service;\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 342-342: code points 1-76

$ WaitCost_\text{original service}$: Total waiting cost of the original service.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 344-344: code points 1-82

\subsubsection{2}{Benefits of Implementing Limited-Stop Services}
\label{volume:operations:chapter:service-planning:section:deciding-on-stop-elimination-and-express-services:subSection:implementing-limited-stop-services:subSubSection:benefits-of-implementing-limited-stop-services}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 346-395: code points 1-26

The main advantage of removing stations from a given service is that these vehicles will travel faster. For the most part, the total ridership on the route will simply be divided between the original service and the new limited-stop service, so there will be no significant impact on overall boarding (Tb) and alighting (Ta) time.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 348-351: code points 1-20

\emphasis{Hence, the benefit is a function of the reduction of fixed dwell time ($T_0$) for each station removed.}\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 353-353: code points 1-107

The value of this benefit comes from two things:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 355-355: code points 1-48

\begin{itemize}
\item \emphasis{A} The reduction in the travel time for all the customers that are using the limited-stop route ($\text{Load}_\text{limited-stop at 
k}$) on each link where a station k is skipped. This should be multiplied by the value of customers’ time ($C_\text{travel}$), which is usually treated as half their cost of waiting, or $ C_\text{travel} = Cw/2$. In the above examples, a constant value of waiting of US\$12 per hour has been used so that in the examples in this section a constant value of travel time will be \$6 per hour. It is usually set at one-third of the average wage.% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 357-361: code points 1-104
\end{itemize}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 357-361: code points 1-104

\begin{itemize}
\item \emphasis{B} The reduction in the travel time for the BRT vehicles, which would need less time to deliver the same service. The value of the operational cost reduction per bus resulting from the faster bus speeds is equal to the bus operational cost per hour ($\text{Cost}_\text{bus}$) multiplied by the number of buses that benefit from the stop reduction ($F_\text{limited-stop-at-k}$).% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 363-366: code points 1-57
\end{itemize}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 363-366: code points 1-57

So the benefit of creating a limited-stop service is expressed as follows:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 368-368: code points 1-74

Eq. 6.53\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 370-370: code points 1-8

$ ExpressBenefit=T_0* \sum_{k=\text{k=skipped station}} \text{Load}_\text{limited-stop-at-k}*\text{Cost}_\text{travel}+\text{Freq}_\text{limited-stop-at-k}*\text{Cost}_\text{bus} $ Where:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 372-373: code points 1-6

\begin{itemize}
\item $ \text{ExpressBenefit} $: Benefit of implementing limited-stop services;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 375-376: code points 1-0
\item $ T_0$: Fixed dwell time (or “dead time”);% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 376-377: code points 1-0
\item $ \text{Load}_\text{limited stop at k}$: Passenger load that uses the new limited-stop route on each link where a station k is skipped;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 377-379: code points 1-0
\item $ \text{Cost}_\text{travel}$: Passenger value of time when travelling;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 379-380: code points 1-0
\item $ \text{Freq}_\text{limited-stop-at-k}$: Number of buses that benefit from the removal of station, k;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 380-381: code points 1-0
\item $ \text{Cost}_\text{bus}$: Bus operational cost per hour (see Section 6.3.12).% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 381-381: code points 1-86
\end{itemize}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 375-381: code points 1-86

An express route should be created when there is a net benefit, or when $\text{Benefit}_\text{express} $ is greater than the total waiting cost of adding that route, as calculated in the previous subsection item.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 383-384: code points 1-91

Eq. 6.54\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 386-386: code points 1-8

$ \text{ExpressBenefit}>\text{ExpressCost} $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 388-388: code points 1-46

Where:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 390-391: code points 1-0

\begin{itemize}
\item $ \text{ExpressBenefit}: $ Benefit of implementing limited-stop services;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 391-392: code points 1-0
\item $ \text{ExpressCost}: $ Total waiting cost of adding route.% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 392-392: code points 1-67
\end{itemize}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 391-392: code points 1-67

For more complex scenarios, the total benefits of each route added need to be weighed against the total costs of each route added.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 394-395: code points 1-26

\subsubsection{3}{Examples of Typical Service Patterns}
\label{volume:operations:chapter:service-planning:section:deciding-on-stop-elimination-and-express-services:subSection:implementing-limited-stop-services:subSubSection:examples-of-typical-service-patterns}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 397-456: code points 1-9

In the examples that follow, the standard data set in Table 6.31 will not vary by scenario. This data can easily be collected for a planned BRT corridor.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 399-400: code points 1-51

It is assumed that it has already been decided that the optimum number of BRT stations is twenty-five, based on the formula provided in Section 6.7.1, showing an optimal distance between stations. We also assume that the vehicle design capacity has already been decided as a 150-passenger (i.e., VSize * LoadFactor) articulated bus due to the high demand. Then, based on the BRT design and vehicle type, each station is assumed to have a fixed dwell time of thirty seconds, based on data collected from bus operators. The operational cost of this vehicle is US\$105 per hour (this is the total bus operating costs needed for the calculation, rather than just the fixed costs). Based on the prevailing wage rate and willingness-to-pay studies, the cost of travel time is US\$6 per hour, and waiting is US\$12 per hour.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 402-410: code points 1-0

\tabletitle{31}{Data Set for Examples of Limited-Stop Services Inclusion}
\label{chapter:service-planning:table:data-set-for-examples-of-limited-stop-services-inclusion}
\halign to 30\tablemodule{%
	\vtop{\sffamily\footnotesize\noindent\hsize=12\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\cr
	\color{gray75}\bfseries Description& \color{gray75}\bfseries Variable& \color{gray75}\bfseries Value& \color{gray75}\bfseries Unit \cr
	\noalign{\vskip 1mm} \hline \noalign{\vskip 2mm} 
	\color{gray50}Number of stations&
	\color{gray50}Nstations&
	\color{gray50}25&
	\color{gray50}stations\cr
	\noalign{\vskip 2mm 
}	\color{gray50}Renovation rate&
	\color{gray50}Ren&
	\color{gray50}1.461&
	\color{gray50}—\cr
	\noalign{\vskip 2mm 
}	\color{gray50}Optimal frequency&
	\color{gray50}Freqoptimum&
	\color{gray50}22&
	\color{gray50}BRT-vehicles\slash{}hour\cr
	\noalign{\vskip 2mm 
}	\color{gray50}BRT vehicle design capacity&
	\color{gray50}Vsize * LoadFactor&
	\color{gray50}150&
	\color{gray50}pax\cr
	\noalign{\vskip 2mm 
}	\color{gray50}Fixed dwell time&
	\color{gray50}T 0&
	\color{gray50}30&
	\color{gray50}seconds\cr
	\noalign{\vskip 2mm 
}	\color{gray50}BRT vehicle operational cost&
	\color{gray50}Costbus&
	\color{gray50}105&
	\color{gray50}US\$\slash{}hour\cr
	\noalign{\vskip 2mm 
}	\color{gray50}Customer travel cost&
	\color{gray50}Costtravel&
	\color{gray50}6&
	\color{gray50}US\$\slash{}hour\cr
	\noalign{\vskip 2mm 
}	\color{gray50}Customer wait cost&
	\color{gray50}Costwait&
	\color{gray50}12&
	\color{gray50}US\$\slash{}hour\cr
	\noalign{\vskip 2mm 
}}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 410-456: code points 1-9

\subsection{3}{Limited-Stop Services When Demand Is Uniform}
\label{volume:operations:chapter:service-planning:section:deciding-on-stop-elimination-and-express-services:subSection:limited-stop-services-when-demand-is-uniform}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 458-780: code points 1-25

Some BRT services have fairly uniform demand, with customers getting on and off a route in more or less even numbers consistently throughout the corridor. Limited-stop services are the least likely to be attractive in the context of homogenous demand, but they are still sometimes attractive, particularly if there is a lot of irregularity resulting from high frequencies. In many instances, limited-stop services are attractive only during peak periods.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 460-464: code points 1-40

When demand is uniform, certain patterns of limited-stop service prove to be mathematically optimal—namely those that skip a cluster of stations.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 466-467: code points 1-38

In this example, it is assumed that there is a one-way local bus route, and demand is shaped in a perfect curve throughout the route, as per Table 6.32. In other words, it is assumed that each of the twenty-five station stops is a trip origin (O) and a trip destination (D) in a local origin-destination matrix, and that fifty-eight customers are travelling between each zone.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 469-472: code points 1-60

In a real-world situation, this data should have already been collected and put into a spreadsheet. Most demand modeling software can estimate the OD matrix from boarding and alighting counts, but it is better to have real station-to-station OD data.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 474-476: code points 1-47


			\ifxetex
				% disabled for now
			\else
				{  % group required to avoid fignote settings escaping
					\tabletitle{32}{Uniform Origin-Destination (OD) Matrix Example}
\label{chapter:service-planning:table:uniform-origin-destination-od-matrix-example}

					\img{\hsize}{operations/assets/9e99431cf9f8f3bdd3612d0e220835ba7d678342.png}
				}
			\fi

The OD matrix of Table 6.32 would result in the boarding and alighting per station and loads after leaving the station as shown on Table 6.33 and Figure 6.61 where the dots near the x axis show the number of customers boarding (blue) and alighting (red) at each station; the green line indicates the load at each station.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 482-485: code points 1-46

Note that other OD patterns could yield the boarding and alighting results observed in the table, and a different OD matrix will require another optimal service pattern; that is why it is best to have the real OD matrix for the whole operating time or day.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 487-489: code points 1-51


			\ifxetex
				% disabled for now
			\else
				{  % group required to avoid fignote settings escaping
					\tabletitle{33}{Boarding, Alighting, and Loads per Station}
\label{chapter:service-planning:table:boarding-alighting-and-loads-per-station}

					\img{\hsize}{operations/assets/77c54d8b10d41833b86ced825ab541b12ee2219a.png}
				}
			\fi

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/cc0d97712d0db56773d030410f917bd0507f2cc1.jpeg}
		\fignote{61}{Demand profile on a route where a uniform number of customers (fifty-eight) are travelling between each possible stop. Blue dots represent the number of boardings at each stop, red dots represent the alightings at each stop, and the green line represents the number of customers on board buses between each stop during the peak hour.\label{chapter:service-planning:figure:demand-profile-on-a-route-where-a-uniform-number-of-customers-fifty-eight-are-travelling-between-each-possible-stop-blue-dots-represent-the-number-of-boardings-at-each-stop-red-dots-represent-the-alightings-at-each-stop-and-the-green-line-represents-the-number-of-customers-on-board-buses-between-each-stop-during-the-peak-hour}}{Pedro Szász.}
	}
\fi

The maximum hourly load on the critical link is 9,048 (MaxLoad). It occurs between the twelfth and thirteenth stations. As the design bus capacity (VSize * LoadFactor) is 150, the frequency (F) should be set at around 61 per hour, or\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 500-502: code points 1-32

$ F = {9048 \over 150} = 61.32 $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 504-504: code points 1-34

The determination to be made is whether there would be benefits in splitting this demand into a limited-stop service and a local service, and if so, which stations should be skipped by the limited-stop service. There are multiple service patterns that might be tested, but certain standard approaches tend to optimize results. In the case of homogenous demand, a limited-stop service that bypasses the middle stations in the corridor, where the relation of loads to boarding and alighting are higher, proves mathematically to always be superior to other stopping patterns such as skipping stations or clusters of stations at the beginning, middle, and end of a route. As such, no other alternatives are tested under homogenous demand.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 506-513: code points 1-7

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/e2372bcd774f55c82056a6681f70457c93f8eb35.jpeg}
		\fignote{62}{Stop sequence for an express service with uniform demand profile (fifty-eight customers between each stop) where both the local and the express stop at all Zone “A” stations and Zone “C” stations but where the express does not stop in Zone “B” stations. Image\label{chapter:service-planning:figure:stop-sequence-for-an-express-service-with-uniform-demand-profile-fifty-eight-customers-between-each-stop-where-both-the-local-and-the-express-stop-at-all-zone-a-stations-and-zone-c-stations-but-where-the-express-does-not-stop-in-zone-b-stations-image}}{Pedro Szász.}
	}
\fi

When demand is relatively uniform in a manner similar to this example, it often makes sense to have a limited service run local at the beginning and at the end of its route, and run express in the middle of the route. Figure 6.62 demonstrates this by dividing the route into three zones—A, B, and C. In this case, the limited skips all seven stations in the middle Zone B (stations ten to seventeen).\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 519-522: code points 1-92

For a limited service to yield benefits, a sufficient number of customers need to gain enough time from the removal of stations to make up for the loss of frequency that results from splitting the route. To make it worthwhile for customers, the service needs to pass at least a cluster of stations where the total fixed dwell time saved is greater than the new waiting time imposed by the loss of frequency.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 524-527: code points 1-99

From looking at the curve, it may appear that the limited-stop service bypasses the majority of the demand, but keep in mind that the curve says that the majority of the demand is actually \emphasis{on the bus }in the middle of the corridor and that boardings and alightings combined are uniform throughout.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 529-531: code points 1-98

Based on the proposed split of the service in two:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 533-534: code points 1-0

\begin{itemize}
\item Customers travelling between points within Zone A or between points within Zone C will be indifferent to the two services, and will just take whichever vehicle comes first; there is no cost and no benefit derived from the creation of the new service for those customers;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 534-537: code points 1-0
\item Customers travelling between Zone A and Zone B, or between Zone B and Zone C will have to take the local bus, and they will perceive time losses due to the lower frequency on the local service;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 537-539: code points 1-0
\item While customers travelling between Zone A and Zone C could take either service, all would take the limited-stop service because, in this example, the time saved from skipping the intermediate stops is greater than the time lost due to waiting for another vehicle. Those who cannot figure out how to read the service maps or confused tourists might be exceptions.% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 539-542: code points 1-63
\end{itemize}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 534-542: code points 1-63

Those taking the limited-stop service gain significant time savings through bypassing stops in Section B from their route.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 544-545: code points 1-19


			\ifxetex
				% disabled for now
			\else
				{  % group required to avoid fignote settings escaping
					\tabletitle{34}{Demand Division by Zone}
\label{chapter:service-planning:table:demand-division-by-zone}

					\img{\hsize}{operations/assets/a86fe62953d7dbdf0a30fe8523cf2fb8f009e00b.jpg}
				}
			\fi

In Table 6.34, the areas highlighted in yellow are trips within Zone A and within Zone C that will be split evenly between the local and express service. The area in pink will be served entirely by the local service, and the area in blue will be served entirely by the express service.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 556-558: code points 1-83


			\ifxetex
				% disabled for now
			\else
				{  % group required to avoid fignote settings escaping
					\tabletitle{35}{Origin Destination Matrix for Uniform Demand on a Bus Route}
\label{chapter:service-planning:table:origin-destination-matrix-for-uniform-demand-on-a-bus-route}

					\img{\hsize}{operations/assets/2bc8493950b6480406ad70b2952a73952f9ecb79.png}
				}
			\fi

Given the demand profile presented here, the load for each service would divide as shown in Figure 6.63.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 564-565: code points 1-98

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/42c1666e3486503af785a7a7feafff03384b9afe.jpeg}
		\fignote{63}{Service Load divided between the local and the limited service in a uniform demand example scenario. Image\label{chapter:service-planning:figure:service-load-divided-between-the-local-and-the-limited-service-in-a-uniform-demand-example-scenario-image}}{Pedro Szász.}
	}
\fi

If this division of the demand is assigned on a station-by-station basis to each service, the boarding and alighting numbers for the limited route are given in Table 6.35. The difference between the boarding and alighting numbers on the limited-stop service and on the original route would be the boarding and alighting remaining on the local service (not shown).\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 570-573: code points 1-53


			\ifxetex
				% disabled for now
			\else
				{  % group required to avoid fignote settings escaping
					\tabletitle{36}{Example Division of Customers between Limited-Stop and Local Services}
\label{chapter:service-planning:table:example-division-of-customers-between-limited-stop-and-local-services}

					\img{\hsize}{operations/assets/1bc8c1f4ff86d5eef76b8c78f5802d5e245d1b19.png}
				}
			\fi

In this case, the benefit is quite simple to estimate, by formula (Equation 6.53):\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 579-580: code points 1-6

$ ExpressBenefit=T_0* \sum_{k=\text{skiped station}} \text{Load}_\text{limited-stop-at-k}*\text{Cost}_\text{travel}+\text{Freq}_\text{limited-stop-at-k}*\text{Cost}_\text{bus} $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 582-582: code points 1-179

Sum for all stations “k” where the limited does not stop.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 584-584: code points 1-57

The $ \text{Load}_\text{limited stop at k} $ is the number of customers on board the express bus that are passing any station “k” that is jumped by the limited-stop service. In this example, all trips from Zone A to Zone C, which is the area shaded in blue on Table 6.35, or demand from stations (one to nine) to stations (seventeen to twenty-five):\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 586-589: code points 1-27

$ \sum_{k= \text{skipped station}} \text{Load}_\text{limited-stop-at-k} = 9 * 9 * 58 = 4698 \text{pass/h} $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 591-591: code points 1-109

This is because there are nine by nine zones where there are only express customers and each interzonal demand is 58, so 4,698 customers.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 593-594: code points 1-33

The frequency of the limited and the local route will vary depending on the demand the limited route captures. In this case,\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 596-597: code points 1-23

$ F_\text{express} = {4698 \over 150} = 31.32\text{bus/hour} $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 599-599: code points 1-64

$ F_\text{local} = {4350 \over 150} = 28.68\text{bus/hour} $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 601-601: code points 1-62

Therefore\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 603-603: code points 1-9

$ ExpressBenefit= 30 / 3600 * 7 * (4698 * 6 + 31.32 *105 ) = 1826\text{US\$/hour} $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 605-605: code points 1-85

Where $ 30 / 3600 * 7 = 30 $ seconds of fixed dwell time per stop removed\slash{}3600 seconds in an hour times 7 stops removed; 4,698 is the number of customers; 6 is their value of an hour; 31.32 is the frequency; and 105 is the operating cost per bus per hour.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 607-609: code points 1-39

Recalling that the cost of adding the limited-stop service will be as follows (Equation 6.52):\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 611-611: code points 1-94

$ \text{ExpressCost} = \text{WaitCost}_\text{express(1)} + \ldots +  \text{WaitCost}_\text{express(n)} +  \text{WaitCost}_\text{local} - \text{WaitCost}_\text{original service}$\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 614-614: code points 1-179

And that (Equation 6.51):\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 616-616: code points 1-25

$ \text{WaitCost}_\text{route} =  \text{Ren}_\text{route} * \text{Cost}_\text{wait} * 0.5 * (1+ ({\text{Freq}_\text{route}  \over \text{Freq}_\text{optimum}  }) ^2) *\text{LoadFactor} * \text{VSize} $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 618-618: code points 1-202

Given the data set for all examples:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 620-620: code points 1-36

\begin{itemize}
\item $ \text{LoadFactor} * \text{VSize} = 150 $% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 622-623: code points 1-0
\item $ \text{Ren} = 1.46 $% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 623-624: code points 1-0
\item $ \text{Cost}_\text{wait} = 12 $% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 624-625: code points 1-0
\item $ \text{Freq}_\text{originalservice} = 60 $% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 625-626: code points 1-0
\item $ \text{Freq}_\text{local} = 28.68 $% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 626-627: code points 1-0
\item $ \text{Freq}_\text{express} = 31.32 $% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 627-627: code points 1-46
\end{itemize}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 622-627: code points 1-46

$ \text{WaitCost}_\text{original service}=0.5*1.461*150*12*(1+(0.5* 60/22)^2 = 3760 $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 629-629: code points 1-87

$ \text{WaitCost}_\text{local} = 0.5 * 1.461 * 150 *12 * 1+ (0.5*31.32/22)^2 = 1874 $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 631-631: code points 1-87

$ \text{WaitCost}_\text{express} =  0.5 * 1.461 * 150 * 12 * 1 + ( 0.5*31.32/22)^2=1981 $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 633-633: code points 1-91

$ \text{ExpressCost} = 1981 + 1874 - 3760 =  95 \text{US\$/hour} $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 635-635: code points 1-68

So, in this case, $ \text{ExpressBenefit} = 1826 \text{US\$/hour} $ and $ C_{w \text{total}} = 95 \text{US\$/hour}$. In this case, the waiting cost associated with adding another service is very low, because the original service was so frequent that there was a lot of needless waiting due to the irregularity of service, and much of this delay is mitigated by the reduction in frequencies. (Note that the effect of irregularity reduction is a bit exaggerated here, as the portion of users that can take both services will contribute to irregularity of both services in Zones A and C as if it was only one service with a frequency of sixty BRT vehicles per hour.)\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 638-643: code points 1-96

Therefore, as $ \text{ExpressBenefit} > \text{ExpressCost} $ it can be said that adding a limited-stop service is a very good idea in this case.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 645-646: code points 1-23

The optimal number of stations to be skipped on the proposed express service is the next determination to make. A rough calculation can be used as a basic guide. In short, the service should make sure that the time saved by the people able to skip stations is greater than the additional time added by the loss of frequency for the people that have to remain on the local service. For example, cutting the frequency from sixty to thirty-one buses per hour implies only an additional minute of waiting. While the average wait is half a minute, one minute is used because the actual average wait time is multiplied by two to factor in people’s perception of the wait time. Thus, the reduction in frequency adds about 1.3 minutes in new delay to customers, if a standard irregularity of 0.3 is used.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 648-655: code points 1-69

With a fixed dwell time at the station stops at thirty seconds, at least three or four stations need to be removed to attract any customers, and probably more. If too many stations are taken away, there will not be enough customers on the new limited to justify a high-frequency limited service, so the range of stations to be removed shall be limited as well.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 657-660: code points 1-51

The following method provides a way of testing whether more or fewer stations should be removed. In essence, the same process run for the specific scenario (seven stations removed) needs to be tested for all other reasonable alternatives.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 662-664: code points 1-34


			\ifxetex
				% disabled for now
			\else
				{  % group required to avoid fignote settings escaping
					\tabletitle{37}{Total Benefits with Varying Numbers of Stops Removed from the Example}
\label{chapter:service-planning:table:total-benefits-with-varying-numbers-of-stops-removed-from-the-example}

					\img{\hsize}{operations/assets/0a540a456eaf64d8fa757d7f436ab0105c6b5a2f.png}
				}
			\fi

In Table 6.37, the first three columns represent the stopping pattern of various alternative limited services (divided into Segments A, B, and C). The first row represents a scenario where the first eleven stations are both local and limited, the next three stations are local only, and the last eleven stations are both local and limited. The second row represents a scenario in which the first ten stations are shared, then the express service skips five stations, then the last ten stations are again shared, and so on.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 670-675: code points 1-41

The second set of columns (four columns) shows the division of customers between the limited only, the local only, and the customers shared by the two services based on the previously stated assumptions. It is broken out in this way because only the riders interested in taking the express service (going from Zone A to Zone C) enjoy benefits from the removal of stations. The remainder of the limited bus customers (those who take the express and use it as a local within Zone A and Zone C) do not benefit from the removal of stations.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 677-682: code points 1-29

In the third row of the table the initial example is tested. An express service is implemented with seven stops skipped and there are 4,698 customers who benefit from the removal of stations, or those customers moving between Zone A and Zone C.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 684-686: code points 1-43

In addition to showing the required frequency for the limited-stop service, the table also includes calculations of time savings per bus, which is equal to the number of stations skipped by the limited service in Zone B, multiplied by thirty seconds of fixed dwell time saved per station. So for the first row, Zone B stations are equal to three in scenario I, so 1.5 minutes are saved per bus; if five stations are removed, 2.5 minutes are saved per bus, and so forth.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 688-692: code points 1-57

The next column shows the number of customer hours of benefit from the express service. It multiplies the number of express customers that bypass the seven stations (total load of customers passing stations in Zone B) by the savings per bus.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 694-696: code points 1-34

The next column shows the benefits in terms of bus travel time, so it multiplies the frequency of the limited-stop service (46.8 for the first row) by the time savings per bus (1.5 minutes for the first row), then divides the total by 60 to give an hour figure (yields 1.17 hours of bus operating time saved in the scenario of the first row).\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 698-701: code points 1-34

Finally, times saved for customers and vehicles are respectively multiplied by the value of time (in the first row: customers’ 175.45 hours saved multiplied by US\$6\slash{}hour results in US\$1,053 and operating cost per bus of US\$105\slash{}hour times saved 1.17 hours save results in US\$123, so the total benefit of the express service [for 3 stops removed] is US\$1,176).\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 703-706: code points 1-57

These benefits then need to be compared to the net cost of replacing the original service with two new services, one local and one express, as is shown on Table 6.38. These net costs can be deducted from the benefit to indicate total net benefits (last column).\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 708-710: code points 1-57


			\ifxetex
				% disabled for now
			\else
				{  % group required to avoid fignote settings escaping
					\tabletitle{38}{Benefits Net of Costs for Varying Numbers of Eliminated Stops}
\label{chapter:service-planning:table:benefits-net-of-costs-for-varying-numbers-of-eliminated-stops}

					\img{\hsize}{operations/assets/2049e7d5755feef52e65314c284a029529277a23.jpg}
				}
			\fi

These net benefits are then calculated for all situations proposed, following the method of the original scenario used in this example. The result turns out to favor the initially tested situation: skipping seven stations. The net benefit of skipping seven stations—US\$1,741—exceeds the net benefit of every other scenario.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 716-719: code points 1-40

The following table shows the degree of sensitivity of the total benefit to total demand. In Table 6.39, the same attributes are assigned, except the demand is cut by 40 percent across the board. In that situation, instead of the frequency dropping from 60 to 30, with a considerable improvement of irregularity (with 22 being optimal) it drops from 30 to 15 and the irregularity benefit is smaller. Once the time penalty for adding the service is relatively greater and the number of beneficiaries of the new limited service is relatively lower, skipping nine stations becomes slightly more beneficial than skipping seven stations. Hence, in uniform demand, the benefits of the limited service are highly sensitive to demand levels.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 721-728: code points 1-7


			\ifxetex
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			\else
				{  % group required to avoid fignote settings escaping
					\tabletitle{39}{Net Benefits of Costs with Varying Numbers of Eliminated Stops under Lower Demand Scenario}
\label{chapter:service-planning:table:net-benefits-of-costs-with-varying-numbers-of-eliminated-stops-under-lower-demand-scenario}

					\img{\hsize}{operations/assets/2049e7d5755feef52e65314c284a029529277a23.jpg}
				}
			\fi

\subsubsection{1}{Demand Patterns Typical of Trunk-and-Feeder Systems}
\label{volume:operations:chapter:service-planning:section:deciding-on-stop-elimination-and-express-services:subSection:limited-stop-services-when-demand-is-uniform:subSubSection:demand-patterns-typical-of-trunk-and-feeder-systems}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 734-780: code points 1-25

In some systems, such as a trunk-and-feeder system, it is likely that demand will be concentrated at the beginning and\slash{}or end of the BRT trunk corridor—for instance, at the transfer station on one end and the downtown on the other. Demand will tend to concentrate in this way because the feeder routes on one end would tend to discharge large numbers of customers at the transfer terminal, and there would be a similar concentration of boardings and alightings at the central business district (CBD).\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 736-740: code points 1-89

In this example, a total of 17,276 boardings and alightings are assumed, the same number as in the uniform demand example, but in this case, 50 percent of them occur at the first and last stations (25 percent at each) instead of only 8.3 percent.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 742-744: code points 1-45

The boarding and alighting and OD matrix of the corridor, if all other stations have uniform demand, would look like Table 6.40 and, if only one service operated with this OD pattern, the load would look like the load diagram in Figure 6.64.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 746-748: code points 1-37


			\ifxetex
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				{  % group required to avoid fignote settings escaping
					\tabletitle{40}{Origin Destination Matrix for Demand Concentrated at Terminals}
\label{chapter:service-planning:table:origin-destination-matrix-for-demand-concentrated-at-terminals}

					\img{\hsize}{operations/assets/d91d7a2923615d6a6926bea0cc357c868659c4a6.png}
				}
			\fi

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/cb6763cb1658e6d159f2eac474e3219d46bf2e07.jpeg}
		\fignote{64}{Demand profile for a corridor where most demand is travelling between the two end terminals.\label{chapter:service-planning:figure:demand-profile-for-a-corridor-where-most-demand-is-travelling-between-the-two-end-terminals}}{Pedro Szász.}
	}
\fi

In this case, it is worth considering adding a service that runs directly between the first station (the transfer terminal) and the last terminal (downtown). If such a service were added, the ridership would split between the limited and local service as per Table 6.41.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 757-759: code points 1-68


			\ifxetex
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				{  % group required to avoid fignote settings escaping
					\tabletitle{41}{Loads on the Local and Limited}
\label{chapter:service-planning:table:loads-on-the-local-and-limited}

					\img{\hsize}{operations/assets/d1998c625137183b07f1291fc968e2ac67aaa70a.png}
				}
			\fi

On Table 6.42, the same stopping pattern is tested for their ridership and comparative costs and benefits, but in each one, an additional station is removed at the beginning and ending of the limited-stop service; the formulas and method from the previous example are used to calculate the net benefit.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 765-768: code points 1-26


			\ifxetex
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				{  % group required to avoid fignote settings escaping
					\tabletitle{42}{Costs and Benefits of Varying Stopping Patterns}
\label{chapter:service-planning:table:costs-and-benefits-of-varying-stopping-patterns}

					\img{\hsize}{operations/assets/84021fa46cbb03367483bd22b8dc16e74ca1e495.png}
				}
			\fi

In this case, a limited-stop service that stops only at the first and last stations brings more benefits to customers. These benefits significantly outweigh the costs. With a maximum load on the critical link of the limited route at 4,327, and a related frequency of 29 trips per hour (4,327\slash{}150), the maximum load remaining on the local service of 6,568 passengers per hour yields a frequency of 44. This is still high enough to cause an elevated level of irregularity in the boarding and alighting process, so another express route might be added. Based on the previous example, this new service would skip the middle stations.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 774-780: code points 1-25

\subsection{4}{Demand Concentrated at a Few Stops}
\label{volume:operations:chapter:service-planning:section:deciding-on-stop-elimination-and-express-services:subSection:demand-concentrated-at-a-few-stops}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 782-864: code points 1-103

It is also common for demand to be concentrated at a few stops along a corridor because there are some large trip generators or attractors in those locations, like hospitals, schools, high-density housing developments, or shopping malls. Such a corridor might result in a boarding and alighting pattern like Figure 6.65.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 784-787: code points 1-12

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/1cd1187f2a894e2de010aa35ffdcdd4f7581136c.png}
		\fignote{65}{Demand profile for a corridor with demand heavily concentrated between a few important stops.\label{chapter:service-planning:figure:demand-profile-for-a-corridor-with-demand-heavily-concentrated-between-a-few-important-stops}}{Pedro Szász.}
	}
\fi

The trip origin and destination matrix would look something like that shown in Table 6.43, where the total number of trips is similar to the previous examples.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 792-793: code points 1-58


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					\tabletitle{43}{Origin Destination Matrix Example for Clustered Demand on a Corridor}
\label{chapter:service-planning:table:origin-destination-matrix-example-for-clustered-demand-on-a-corridor}

					\img{\hsize}{operations/assets/667d926b1f677d2910484aa22e0c33f9afb84b03.png}
				}
			\fi

Two options are tested to illustrate some general principles, correspondent boarding, alighting, and loads are shown in Table 6.44 where the stations highlighted in red would be both limited and local stops, while the stations in gray would be served only by the local service.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 799-802: code points 1-0

\begin{itemize}
\item One limited-stop service that stops only at the high volume stations, \#1, \#7, \#13, \#19, and \#25.% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 802-803: code points 1-0
\item One limited-stop service that stops at \#1–7, then \#13, then \#19–25.% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 803-803: code points 1-76
\end{itemize}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 802-803: code points 1-76


			\ifxetex
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					\tabletitle{44}{Boardings, Alightings, and Load Comparison between Varying Service Patterns for Clustered Demand Example}
\label{chapter:service-planning:table:boardings-alightings-and-load-comparison-between-varying-service-patterns-for-clustered-demand-example}

					\img{\hsize}{operations/assets/78c526b3c3ffc5732b707c0d1ee6f1e923cbaa90.png}
				}
			\fi

The loads assumes that the time savings from the number of stations skipped is greater than the loss of time waiting for the next express bus for all possible express bus trips, so customers between the stations served by the express service (red cells) use that service.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 810-812: code points 1-93


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					\tabletitle{45}{Loads Passing Stations and Benefits for Two Alternative Express Services under Clustered Demand Example}
\label{chapter:service-planning:table:loads-passing-stations-and-benefits-for-two-alternative-express-services-under-clustered-demand-example}

					\img{\hsize}{operations/assets/5a3757413afe78595b9f234fdea86645340cd559.png}
				}
			\fi

The loads aboard an express service passing the stations skipped for each alternative are listed under the column “Load (k)” in Table 6.45, and the value of the time savings associated with this benefit are calculated in the “Total” column.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 819-821: code points 1-55


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					\tabletitle{46}{Frequency and Operational Vehicle Benefits for Two Alternative Express Services under Clustered Demand Example}
\label{chapter:service-planning:table:frequency-and-operational-vehicle-benefits-for-two-alternative-express-services-under-clustered-demand-example}

					\img{\hsize}{operations/assets/4a3923cdf7c89d405a56b2af6c82cbb042b8932e.png}
				}
			\fi

In Table 6.46, the required frequency for the new express route is calculated from the maximum load on the express route divided by 150, the designed bus capacity. This is multiplied by the number of stations removed in each scenario and by the operational cost savings per hour to yield the total bus cost savings for each alternative.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 828-831: code points 1-48

Table 6.47 shows the (waiting) costs associated with the lower frequency to be subtracted from the benefits.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 833-834: code points 1-9


			\ifxetex
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					\tabletitle{47}{Costs of the Two Alternative Express Services under Clustered Demand Example}
\label{chapter:service-planning:table:costs-of-the-two-alternative-express-services-under-clustered-demand-example}

					\img{\hsize}{operations/assets/2bfe01526e3e1bc4a7092d772940ca7848afe05d.png}
				}
			\fi

In the second option of express service, the new express service captures a lot more demand, bringing the frequency of both the express and the local service into a more optimal range, significantly reducing the irregularity of service. The benefit from reduced irregularity is greater than the cost in waiting caused by the reduction in frequency, so in this case the “cost” is negative, or a “benefit.”\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 840-844: code points 1-15

As a result, the net benefit of the alternative with express service attending a cluster of stations at the beginning and ending of the route, rather than only stopping at the high-demand stations, performs much better, as shown in Table 6.48.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 846-848: code points 1-36


			\ifxetex
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					\tabletitle{48}{Net Benefits of the Two Alternative Express Services under Clustered Demand Example}
\label{chapter:service-planning:table:net-benefits-of-the-two-alternative-express-services-under-clustered-demand-example}

					\img{\hsize}{operations/assets/b9555b1aeeda3a3543164664f3bbf8e6575839f0.png}
				}
			\fi

At these high levels of demand, additional express routes can be tried following similarly clustered patterns focusing on higher demand clusters of stations, and their relative costs and benefits tested.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 854-856: code points 1-26

Several clusters of stopping stations should be tested, adding more types of services until the frequency of each route is near the optimal range of twenty-two. The diagram in Figure 6.66 is the original service concept that was developed for TransMilenio in Bogotá loosely based on these principles.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 858-860: code points 1-88

\ifxetex
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\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/64358f3386aa41fc865865e2dfce09d73f143777.jpeg}
		\fignote{66}{Diagram of original service concept for TransMilenio, based on the concept of clustering stations served by express services (each dot is a served station). It included three express services in order to place each service frequency in the range of optimal frequencies. Diagram\label{chapter:service-planning:figure:diagram-of-original-service-concept-for-transmilenio-based-on-the-concept-of-clustering-stations-served-by-express-services-each-dot-is-a-served-station-it-included-three-express-services-in-order-to-place-each-service-frequency-in-the-range-of-optimal-frequencies-diagram}}{ITDP.}
	}
\fi

\subsection{5}{Demand Concentrated at One End of a Corridor}
\label{volume:operations:chapter:service-planning:section:deciding-on-stop-elimination-and-express-services:subSection:demand-concentrated-at-one-end-of-a-corridor}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 866-935: code points 1-33

There are occasions when there is a very high demand at the beginning of a route and this demand gradually diminishes throughout the route. This situation normally results in the afternoon peak, when there is a monocentric CBD, or when there is a large transfer terminal.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 868-870: code points 1-62

The demand in this case is always decreasing as in Figure 6.67, and the internal O\slash{}D matrix with total similar to the previous examples is shown in Table 6.48.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 872-873: code points 1-56


			\ifxetex
				% disabled for now
			\else
				{  % group required to avoid fignote settings escaping
					\tabletitle{49}{Origin Destination Matrix Example for Declining Demand on a Bus Corridor}
\label{chapter:service-planning:table:origin-destination-matrix-example-for-declining-demand-on-a-bus-corridor}

					\img{\hsize}{operations/assets/2e3f80ceb8070eefd9b64b46a606d939961ef371.png}
				}
			\fi

This yields the following boarding, alighting, and load pattern on the original service. This example is taken from the real case of the Santo Amaro—Nove de Julho corridor, project implemented in 1986 in São Paulo.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 879-880: code points 1-103

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/ca175dee2c1fc1c628bb379db30359afd02ff643.jpeg}
		\fignote{67}{Demand profile for a corridor with all trips boarding at a single terminal but alighting in even numbers at station stops along the corridor.\label{chapter:service-planning:figure:demand-profile-for-a-corridor-with-all-trips-boarding-at-a-single-terminal-but-alighting-in-even-numbers-at-station-stops-along-the-corridor}}{Pedro Szász.}
	}
\fi

In this example there are 15,000 customers boarding at the first station, a transfer terminal, and just 2,395 customers boarding at the remaining 33 stations. In this situation, a service plan similar to the one shown in Figure 6.68 turns out to be optimal.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 885-887: code points 1-56

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/0e95d69d9970dbb86a556ff4dc49c1d2946b9b70.jpeg}
		\fignote{68}{Optimal service pattern for a corridor with most demand boarding at a single terminal but alighting in even numbers at station stops along the corridor. Image\label{chapter:service-planning:figure:optimal-service-pattern-for-a-corridor-with-most-demand-boarding-at-a-single-terminal-but-alighting-in-even-numbers-at-station-stops-along-the-corridor-image}}{Arthur Szász.}
	}
\fi

Each route serves a specific stretch of the corridor. The route goes express from the terminal (or CBD) to the beginning of the stretch it services, then it makes all the stops in its service area, and then returns (usually express) to the terminal. The return is express, because the demand in the opposite direction is generally much lower.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 892-895: code points 1-34

The big difference between this scenario and earlier scenarios is that, as the express routes do not reach the end of the corridor, there is a significant reduction in total cycle time (TC) and consequently a sizable fleet reduction. Each express service is designed to meet the direct demand from the terminal (or CBD) to a specific service zone.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 897-900: code points 1-36


			\ifxetex
				% disabled for now
			\else
				{  % group required to avoid fignote settings escaping
					\tabletitle{50}{Boarding, Alighting, and Load per Designed Service on Declining Demand Example Corridor}
\label{chapter:service-planning:table:boarding-alighting-and-load-per-designed-service-on-declining-demand-example-corridor}

					\img{\hsize}{operations/assets/c210f3c6acda0b701cb76fe677cd0e1b5fc9ca13.png}
				}
			\fi

One local service can attend to all the trips not destined for the terminal (2,395 passengers per hour that board and alight along the corridor). This service has a maximum load of around 986 passengers per hour.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 906-908: code points 1-34

In this case, the benefits to passengers of the new services are as shown in Table 6.51 and the benefits to operations of the new services are as shown in Table 6.52.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 910-911: code points 1-61


			\ifxetex
				% disabled for now
			\else
				{  % group required to avoid fignote settings escaping
					\tabletitle{51}{Benefits of New Services to Passengers}
\label{chapter:service-planning:table:benefits-of-new-services-to-passengers}

					\img{\hsize}{operations/assets/36090a1787495d03512737a1da35741330657913.png}
				}
			\fi


			\ifxetex
				% disabled for now
			\else
				{  % group required to avoid fignote settings escaping
					\tabletitle{52}{Benefits of New Services to Operations}
\label{chapter:service-planning:table:benefits-of-new-services-to-operations}

					\img{\hsize}{operations/assets/88cf35660149a3976480eb9a28407662b29d5bc0.png}
				}
			\fi

In this case, because of the early return of some of the vehicles, there are savings in running time for vehicles, not only from the removal of stations. To include this benefit, the operational time savings for not running till the end of the corridor are also calculated.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 921-923: code points 1-94

Benefits add operational savings (US\$3,538) and passenger savings (US\$1,500) to the total of US\$5,038.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 925-925: code points 1-102


			\ifxetex
				% disabled for now
			\else
				{  % group required to avoid fignote settings escaping
					\tabletitle{53}{Costs}
\label{chapter:service-planning:table:costs}

					\img{\hsize}{operations/assets/320acb7d26cdcf97d6b23c79288108e4fe566f6d.png}
				}
			\fi

Following the formula for calculating the costs of implementing the new express routes (the net balance of wait cost per route), the additional cost is US\$524, as summarized in Table 6.53. Resulting in a net benefit of (US\$5,038–US\$524) US\$4,515. In this example, the fact that many services allowed early return led to a dramatic reduction in operating costs, as buses were able to reduce their cycle times.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 931-935: code points 1-33

\subsection{6}{Shortened Routes}
\label{volume:operations:chapter:service-planning:section:deciding-on-stop-elimination-and-express-services:subSection:shortened-routes}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 937-1032: code points 1-0

Even within simple BRT systems that only allow for local stations, it is possible to adjust the service to better meet the demand by having some bus routes turn around before reaching the terminal. The same corridor can host several routes of varying lengths. A single corridor may be split into two or more routes covering a different portion of the corridor.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 939-942: code points 1-52

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/9e4e683858c600540845623e76c50a8bdb08368e.png}
		\fignote{69}{Adding a second local service that covers only the highest demand segment of a corridor can reduce operating costs while limiting additional delay for customers. Image\label{chapter:service-planning:figure:adding-a-second-local-service-that-covers-only-the-highest-demand-segment-of-a-corridor-can-reduce-operating-costs-while-limiting-additional-delay-for-customers-image}}{Pedro Szász.}
	}
\fi

In Figure 6.69, a diagram shows the loads along an existing bus corridor. If the demand on a given part of the corridor is high, a second service can be added that operates only on that part of the route. All customers travelling between any OD pair on the shorter service will be indifferent to the two bus routes, so there is no lost travel time for any customer. There are, however, significant operational cost savings, as in the previous example, and the BRT vehicles operating on the shortened service avoid a large number of stations.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 948-953: code points 1-27

Shortened routes focusing on higher-demand central areas will contribute to high operating efficiencies. These efficiency gains will help reduce the number of vehicles required to serve the corridor.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 955-956: code points 1-94

Looking at Figure 6.69, where most of the corridor’s demand occurs in the central area, if there is only one service operating the entire length of the corridor, all vehicles would depart from point T and operate with low load factors at the beginning and the end of the corridor. However, if vehicles were to operate a shortened route beginning from point R, then the number of vehicles required to serve the corridor will be reduced and the load factor per bus will increase. This fleet reduction is calculated as:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 958-963: code points 1-3

Eq. 6.55\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 965-965: code points 1-8

$ \text{Fleet reduction} = {{2*|R-T| \over V_\text{corridor} } * A - B) \over \text{VSize} * \text{LoadFactor}} $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 967-967: code points 1-115

Where:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 969-970: code points 1-0

\begin{itemize}
\item $ T $: Terminal position;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 970-971: code points 1-0
\item $ R $: Early return position;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 971-972: code points 1-0
\item $ V_\text{corridor} $: Corridor commercial speed;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 972-973: code points 1-0
\item $ |R-T| $: Distance between early return position and terminal;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 973-974: code points 1-0
\item $ |R-T|/V_\text{corridor} $: Travel time between early return position and terminal;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 974-975: code points 1-0
\item $ A $: Maximum Demand on the Critical Link (MaxLoad);% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 975-976: code points 1-0
\item $ B $: Load on point \$.% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 976-976: code points 1-31
\end{itemize}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 970-976: code points 1-31

Example:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 978-978: code points 1-8

$ A = 15,000 \text{passengers/hour} $;\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 980-980: code points 1-40

$ B = 10,000 \text{passengers/hour} $;\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 982-982: code points 1-40

$ V = 25 \text{km/hour} $;\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 984-984: code points 1-28

$ T = 0 $;\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 986-986: code points 1-12

$ R = 5 \text{km}$;\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 988-988: code points 1-21

$ {(R-T)/V} = 12\text{minutes(uni-directional time)} = (5/25) \text{hours} $;\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 990-990: code points 1-79

$ \text{VSize} * \text{LoadFactor} = 150 pax/bus (vehicle capacity) $.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 992-992: code points 1-72

$ \text{Fleet reduction}= {2* {|5-0| /over 25} * 15,000 – 10,000 \over 150 } =6 \text{vehicles} $\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 994-994: code points 1-99

In this case, as might be typical of a downtown, most of the demand may be headed downtown from two different directions. For instance, in Yichang, China, along the new BRT corridor, bus routes previously operated all the way through the CBD from north to south and south to north.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 996-998: code points 1-76

In this situation, the vehicles frequently run with low occupancy on either end. Severing one long route in the middle of the city center would force a transfer on a large number of customers with destinations on the far side of the city center. However, having each route pass through to the far edge of the CBD, overlapping through the highest demand section of the city, avoids the transfer and also allows for a higher frequency of service for all customers operating in the zone where the routes from both sides overlap.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 1000-1005: code points 1-8

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/4c1858533afc6480509482ecc877bd4838b2881d.jpeg}
		\fignote{70}{Yichang overlapping services can be maintained only in the CBD doubling frequency in the high demand part of the corridor, while limiting total route length to minimize irregularity.\label{chapter:service-planning:figure:yichang-overlapping-services-can-be-maintained-only-in-the-cbd-doubling-frequency-in-the-high-demand-part-of-the-corridor-while-limiting-total-route-length-to-minimize-irregularity}}{ITDP.}
	}
\fi

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/254659a06348e30225d997db8154ac101aae2b33.jpeg}
		\fignote{71}{The need for transfers is also reduced when local routes are overlapping in the CBD, zoom of proposed design in Yichang CBD.\label{chapter:service-planning:figure:the-need-for-transfers-is-also-reduced-when-local-routes-are-overlapping-in-the-cbd-zoom-of-proposed-design-in-yichang-cbd}}{ITDP.}
	}
\fi

The specific costs and benefits of these general approaches should be tested with the actual OD matrix for each corridor.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 1014-1015: code points 1-18

These early turn-around services can significantly improve the system’s financial performance, but they must be linked with clear customer information about which vehicle is approaching the station and its destination. Otherwise, customers can become confused and frustrated.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 1017-1019: code points 1-73

In general, the shortened routes are not terminated at the station with the highest boarding and alighting volumes in the system. These stations are already stressed by the quantity of customers and the intensity of customer movements. Further, since these stations tend to be located in the densest portion of the urban area, there are fewer opportunities to efficiently turn the vehicles around. Normally these shortened services terminate just beyond such high-volume stations.\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 1021-1025: code points 1-57

This type of service programming will typically reduce overall operational costs by as much as 10 percent. In order to accommodate a shortened route option, the planning process should provide sufficient flexibility with regard to:\par
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 1027-1030: code points 1-0

\begin{itemize}
\item Providing places where vehicles can make U-turns within the BRT system;% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 1030-1031: code points 1-0
\item Designing the station areas with sufficient extra capacity to allow for service adjustments.% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 1031-1032: code points 1-0
\end{itemize}
% @ guide/06-service_planning/67-deciding-on-stop-elimination-and-express-services.src: lines 1030-1032: code points 1-0

\section{8}{Creating New Routes and Combining Old Routes}
\label{volume:operations:chapter:service-planning:section:creating-new-routes-and-combining-old-routes}
% @ guide/06-service_planning/68-creating-new-routes-and-combining-old-routes.src: lines 3-162: code points 1-0

\quotation{The path is the goal.}{Mahatma Gandhi, political and spiritual leader, 1847–1948}
% @ guide/06-service_planning/68-creating-new-routes-and-combining-old-routes.src: lines 5-6: code points 1-59

There are two fairly typical problems of existing public transport routing that emerge for historical reasons. One problem is that a traditional public transport market may have routes that run along a major road and then terminate at a terminal in the middle of the city, where at some time in the past, a terminal was built, or a minibus taxi rank was created. Often, however, there are many customers who are not going anywhere near the downtown terminal, but to some point beyond it. As such, these traditional routes may force a majority of customers to have to transfer and leave a lot of buses needlessly idling downtown. In such conditions, routes that continue through the CBD for some distance should be considered. In other words, this is the opposite problem of the one addressed in subsection \emphasis{Shortened Routes }of Section 6.7.2 above where a route needlessly continued too far, and an early return would have been more efficient. In this case, the route was artificially severed midway for historical reasons. In both cases, the approach to a solution should be similar.\par
% @ guide/06-service_planning/68-creating-new-routes-and-combining-old-routes.src: lines 8-18: code points 1-32

Another typical situation that emerges is that bus routes in cities are organized along a fixed grid pattern. These service patterns also emerged historically for ease of customer network legibility. These grid network patterns also have the advantage of allowing for a lot of directional flexibility with only one transfer. This sort of service plan is common in cities in the United States, where for decades each bus service will tend to ply up and down one specific street in a grid. This is a reasonable service pattern if little else is known about the pattern of trip origins and destinations, or if trip patterns are randomly distributed across the grid. In most cases, where there is a grid, many people are transferring at least once and possibly twice to reach their destination. As there is delay involved in the transfer, if a majority of people are all headed in a single direction that requires a transfer (say, toward downtown), it may make more sense to offer a service that turns the corner rather than just running straight up and down a single arterial and forcing a majority of customers to transfer.\par
% @ guide/06-service_planning/68-creating-new-routes-and-combining-old-routes.src: lines 20-30: code points 1-75

When a BRT corridor is introduced into a grid, one service on a particular street is suddenly much faster than services on alternative streets. If the speed improvement is significant, it may well pull a lot of demand off of bus services on parallel streets, particularly for longer distance trips, capturing demand that otherwise would have been distributed to several stops. In this case, offering some services between popular trip origins and destinations that turn onto the BRT corridor and off the BRT corridor could prove to be advantageous by avoiding the transfer penalty on as many customers as possible.\par
% @ guide/06-service_planning/68-creating-new-routes-and-combining-old-routes.src: lines 32-37: code points 1-97

An example of this can be seen from the BRT service planning for Ashland Avenue in Chicago. The bus routes in Chicago mainly run north and south up the major arterials, or east and west on crosstown streets. The city plans to build Gold or Silver-standard BRT infrastructure through both the Central Loop downtown (Washington and Madison Streets) and along Ashland Avenue. One existing non-BRT bus route (\#20) runs east-west connecting Ashland and points west to the Central Loop. Another bus route (\#9) runs north-south on Ashland Avenue. The demand on Ashland from Route \#9 alone came nowhere near to saturating the planned BRT corridor, so tests were run to see if there would be any benefit in pulling additional demand onto Ashland.\par
% @ guide/06-service_planning/68-creating-new-routes-and-combining-old-routes.src: lines 39-46: code points 1-8

In this case, the service planning team had boarding and alighting data on all the relevant bus routes that interacted with the two corridors, and transfer survey data from all the relevant transfer points. The team mapped the transfer volumes to give a first indication of where customers might be transferring, and did further transfer surveys in those locations. Using simple probability to predict how many customers are likely to transfer from one bus route to the next, the team constructed a corridor-specific origin destination (OD) matrix to test the likely demand and time savings of a few alternative additional services.\par
% @ guide/06-service_planning/68-creating-new-routes-and-combining-old-routes.src: lines 48-53: code points 1-108

They ended up testing the demand levels, and costs and benefits of several alternative routes:\par
% @ guide/06-service_planning/68-creating-new-routes-and-combining-old-routes.src: lines 55-55: code points 1-94

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/135ad713693b432e06249a2b9ae8ccdd8c5a70b0.jpeg}
		\fignote{72}{For the Ashland and Central Loop BRT projects in Chicago, original typical grid-pattern bus services will not optimally serve the demand when converted to BRT. Image\label{chapter:service-planning:figure:for-the-ashland-and-central-loop-brt-projects-in-chicago-original-typical-grid-pattern-bus-services-will-not-optimally-serve-the-demand-when-converted-to-brt-image}}{Pedro Szász.}
	}
\fi

\ifxetex
	% disabled for now
\else
	{  % group required to avoid fignote settings escaping
		\img{\hsize}{operations/assets/f447d4bfbdc446fdd0bd53a9026ed71bbe12057c.jpeg}
		\fignote{73}{For the Ashland and Central Loop BRT projects in Chicago, BRT service planning revealed that two L-shaped (top) and two S-shaped services (bottom) providing direct connections between Ashland and the Central Loop could provide the optimal service improvement. Image\label{chapter:service-planning:figure:for-the-ashland-and-central-loop-brt-projects-in-chicago-brt-service-planning-revealed-that-two-l-shaped-top-and-two-s-shaped-services-bottom-providing-direct-connections-between-ashland-and-the-central-loop-could-provide-the-optimal-service-improvement-image}}{Pedro Szász.}
	}
\fi

In addition to recommending a BRT service to replace Route \#9 up and down Ashland, a southern “L” shaped route was recommended connecting to the Central Loop BRT link, a northern “L” shaped route connecting to the Central Loop BRT, and two “S” shaped routes, coming from the west, turning onto Ashland for a stretch, and then turning again into the Central Loop, as shown above.\par
% @ guide/06-service_planning/68-creating-new-routes-and-combining-old-routes.src: lines 64-68: code points 1-0

\tabletitle{54}{Recommended Frequency per Route}
\label{chapter:service-planning:table:recommended-frequency-per-route}
\halign to 30\tablemodule{%
	\vtop{\sffamily\footnotesize\noindent\hsize=6\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\hbox to 0.5\tablemodule{}&
	\hbox to 0.5\tablemodule{}\vtop{\sffamily\footnotesize\noindent\hsize=5\tablemodule#}\cr
	\color{gray75}\bfseries Scenario& \color{gray75}\bfseries Baseline& \color{gray75}\bfseries Standard BRT Route& \color{gray75}\bfseries L Shaped Routes& \color{gray75}\bfseries L and S Shaped Routes \cr
	\noalign{\vskip 1mm} \hline \noalign{\vskip 2mm} 
	\color{gray50}Local Route&
	\color{gray50}6.5&
	\color{gray50}2&
	\color{gray50}1&
	\color{gray50}1\cr
	\noalign{\vskip 2mm 
}	\color{gray50}BRT 1&
	\color{gray50}0&
	\color{gray50}10&
	\color{gray50}4&
	\color{gray50}4\cr
	\noalign{\vskip 2mm 
}	\color{gray50}LN&
	\color{gray50}0&
	\color{gray50}0&
	\color{gray50}6&
	\color{gray50}5\cr
	\noalign{\vskip 2mm 
}	\color{gray50}NS&
	\color{gray50}0&
	\color{gray50}0&
	\color{gray50}5&
	\color{gray50}4\cr
	\noalign{\vskip 2mm 
}	\color{gray50}SN&
	\color{gray50}0&
	\color{gray50}0&
	\color{gray50}0&
	\color{gray50}4\cr
	\noalign{\vskip 2mm 
}	\color{gray50}SS&
	\color{gray50}0&
	\color{gray50}0&
	\color{gray50}0&
	\color{gray50}4\cr
	\noalign{\vskip 2mm 
}	\color{gray50}SE&
	\color{gray50}0&
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In this case, with the construction of the BRT corridor, the introduction of L- and S- shaped routes that better corresponded to the travel patterns of most people would bring significant user benefits. Total travel time would be reduced for some customers because of increased speeds along the BRT corridor. Some customers would benefit because they would avoid the time previously consumed by transferring either to a bus or a rail line. While the frequency per route drops, because most customers can choose either the direct route or the L-shaped route, the customers who benefit from the inclusion of the new routes outweigh the additional waiting times for a few customers.\par
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		\fignote{74}{Total estimated benefits for four alternative service plans based on modeled results on Chicago’s Ashland corridor: Existing services (baseline), the initial proposal for eliminated stops along Ashland, a service scenario where two additional routes with direct services to the CBD have been added, and a final service scenario where “S” shaped routes have been added. Image\label{chapter:service-planning:figure:total-estimated-benefits-for-four-alternative-service-plans-based-on-modeled-results-on-chicagos-ashland-corridor-existing-services-baseline-the-initial-proposal-for-eliminated-stops-along-ashland-a-service-scenario-where-two-additional-routes-with-direct-services-to-the-cbd-have-been-added-and-a-final-service-scenario-where-s-shaped-routes-have-been-added-image}}{Pedro Szász.}
	}
\fi

These benefits are significantly greater in high-demand scenarios, where reducing the frequency per route is generally beneficial, and they are marginal in lower demand scenarios. Another service-planning problem that has emerged in some of the larger BRT networks is the lack of inter-corridor routes. This problem tends to manifest itself most acutely in trunk-only or trunk-and-feeder systems. Mexico City, Teheran, and Jakarta all initially developed trunk-only services. These systems all had BRT corridors with very simple services that operated only one local service up and down each BRT trunk corridor. This resulted in crush transfer loads at critical transit points in the BRT network. The worst example of this, which persists, is the overcrowding at the Harmony station in Jakarta. Similar crush loads are observed at the key transfer points in Teheran. Much of this overcrowding has already been mitigated in Mexico City and Jakarta by simply adding a route that travels between one corridor and the next, avoiding the need for a substantial portion of the customers to transfer.\par
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		\fignote{75}{Jakarta’s BRT Harmoni (a central transfer) station during the peak hour. Image\label{chapter:service-planning:figure:jakartas-brt-harmoni-a-central-transfer-station-during-the-peak-hour-image}}{Karl Fjellstrom, Far East BRT.}
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If the original BRT system was developed with “direct” BRT services with a reasonably optimal service plan, this problem would be unlikely.\par
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If the corridor selection process outlined in Chapter 5: Corridor and Network Development is followed, the first BRT corridor is the corridor with the highest vehicle demand and the slowest speeds. If this corridor is given services that operate on and off the BRT trunk corridor, then chances are that the second corridor will simply be an infrastructure upgrade along one or more of these services that already use the first BRT corridor. Even if the original BRT system is a trunk-and-feeder system, it is usually no problem to introduce inter-corridor routes within the trunk system.\par
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		\fignote{76}{BRT and the synergies of route permutations. Image\label{chapter:service-planning:figure:brt-and-the-synergies-of-route-permutations-image}}{ITDP.}
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Bogotá’s TransMilenio system, despite being a trunk-and-feeder system, has an extensive variety of inter-corridor routes. Customers at a single station may have as many as ten different routes from which to choose, including local and limited-stop services.\par
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\section{9}{Pulling Services onto a BRT Trunk Corridor from a Parallel Corridor}
\label{volume:operations:chapter:service-planning:section:pulling-services-onto-a-brt-trunk-corridor-from-a-parallel-corridor}
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\quotation{Eventually, all things merge into one, and a river runs through it.}{Norman Maclean, author, 1902–1990}
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If the BRT trunk corridor is not saturated after adding all the existing routes onto the corridor by the BRT service plan, it may be advantageous to take a bus route that currently does not use the BRT corridor, and pull it onto the BRT corridor. The result will likely be a travel time savings for some customers, as their trip will be sped up on the BRT portion of the route. However, it could also mean a travel time loss for other customers, if the rerouting results in a longer trip for them or longer walks. These costs and benefits need to be weighed in order to make the decision.\par
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		\fignote{77}{Three options for planning routes near a BRT corridor. Image\label{chapter:service-planning:figure:three-options-for-planning-routes-near-a-brt-corridor-image}}{ITDP.}
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Above are three simplified scenarios that show the basic options for handling an existing route that travels \emphasis{near }the BRT corridor.\par
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\begin{itemize}
\item Option I represents the way bus routes are currently configured—the green line is the BRT corridor with a BRT route on top of it, and the blue line is an existing bus route that travels near the BRT corridor and ends in the same place;% @ guide/06-service_planning/69-pulling-services-onto-a-brt-trunk-corridor-from-a-parallel-corridor.src: lines 19-22: code points 1-0
\item Option II represents a decision to “route on” the blue service to use the BRT infrastructure, but retain it as a “direct service”;% @ guide/06-service_planning/69-pulling-services-onto-a-brt-trunk-corridor-from-a-parallel-corridor.src: lines 22-24: code points 1-0
\item Option III represents a route that has been “routed on” to a BRT corridor, but split into a trunk feeder service.% @ guide/06-service_planning/69-pulling-services-onto-a-brt-trunk-corridor-from-a-parallel-corridor.src: lines 24-25: code points 1-15
\end{itemize}
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If there is sufficient demand to justify it, a fourth option would be to retain the current route and add a new route that uses the BRT trunk corridor for part of the route. Option I is preferable when pulling a bus service onto a new, faster BRT corridor introduces more delay due to the indirectness of the route than it saves due to the superior BRT infrastructure. Option II is preferred when the travel-time savings of pulling the route onto the BRT corridor for part of its journey saves more time and serves as many customers as the current route operating in mixed traffic conditions. Option II introduces some indirectness of route but avoids any transfer penalty. Option III would be preferred mainly when there are significant time savings benefits to rerouting onto the BRT trunk corridor, yet the addition of a fully direct service in the optimal vehicle size for that service would saturate the BRT corridor, slowing down the speeds for the busway. The indirectness of route and transfer penalty would need to be compensated by both the higher speeds of using the BRT trunk corridor and the higher frequencies in the new feeder route.\par
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In some cases, it is best to create a hybrid of Options I and II, where the blue route is routed onto the BRT corridor, while the original blue route service is retained. Frequency would need to be split between the two, and this would allow customers who benefit more from one or the other scenario to have the option of which route to take. Many of the issues described in the limited-services section apply here since you are again splitting frequencies. However, this might also be a more politically feasible solution—even when there are greater benefits to routing a service onto the BRT corridor—because it can often be politically challenging to eliminate a route altogether.\par
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