ESTIMATING CAPACITY OF HIGH VOLUME BUS RAPID TRANSIT STATIONS

ESTIMATING CAPACITY OF HIGH VOLUME BUS RAPID TRANSIT STATIONS Jack M. Reilly, Ph.D. Professor of Practice, Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute 110 8th Street, Room JEC 4032, Troy, NY 12180 USA Felipe Aros-Vera, M.S. Ph.D. Candidate, Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute 110 8th Street, Room JEC 4037, Troy, NY 12180 USA Keywords: bus rapid transit, simulation, transit capacity A paper submitted to the Transportation Research Board 2013 Annual Meeting Washington, DC. January, 2013 Text word count: 4,032 Figures and tables: 8 Total word count: 6,032 1

ESTIMATING CAPACITY OF HIGH VOLUME BUS RAPID TRANSIT STATIONS Jack M. Reilly, Professor of Practice, Rensselaer Polytechnic Institute Felipe Aros-Vera, Graduate Student, Rensselaer Polytechnic Institute Abstract A critical element in estimating the capacity of a bus rapid transit (BRT) line is the flow capacity of the running way measured in buses per hour. In this paper, we estimate capacity in high volume bus services by using a simulation model. The inputs to the model include the mean dwell time of arriving buses, the dwell time variability, the headway variation of arriving buses, the configuration of the boarding locations and the presence or absence of a traffic signal. The output of the model is an estimate of the number of buses which can serve the stop per hour with a tolerable failure rate. The failure rate is the probability that arriving buses will not be able to access a boarding berth due to its being occupied by a previously arriving bus. The capacity of various stop configurations such as number of berths and queuing areas is also examined. The model does not require extensive data collection to yield reasonable results. The paper includes tables showing the capacity for a range of input options. The procedure was applied to the operation of Transmilenio in Bogota, Colombia. 1. Introduction The widespread introduction of Bus Rapid Transit systems, particularly in the developing world, has demonstrated that in certain circumstances, well-designed bus systems can provide capacity that rivals the volume on most rail rapid transit systems. Determining the system capacity is useful for both assessing the capability of existing systems for future growth and for designing new systems. To date, there have been few analysis tools to assess the capacity of such systems as a function of attributes such as vehicle size and configuration, station and vehicle geometry and traffic control devices. While the (US) Transit Capacity and Quality of Service Manual (Kittelson & Associates, 2003) provides some guidance in this area, it does not provide satisfactory results where the passenger or vehicle volume far exceeds the range of normal US practice. In this paper, we assess the throughput capacity of a bus station as a function of dwell time distribution, headway distribution, stop design attributes and traffic control devices in the vicinity of the bus station by developing a fairly simple simulation model in ARENA (Rockwell Automation, 2010). The model also incorporates as an input the minimum acceptable probability that an arriving bus will not be able to dock at a station without delay. With even limited field data, the tables developed in the model can provide a good planning level estimate of capacity. 2

2. Background and existing literature The two essential determinants of bus transit corridor passenger capacity are the vehicle capacity (measured in persons per vehicle) and the running way capacity (measured in vehicles per hour). The running way capacity on exclusive bus lanes is almost always determined by the bus operations through the critical stop (Fernandez and Planzer, 2002, Kittelson & Associates, 2003, Fernandez, 2010). The critical stop acts as a bottleneck which impedes the flow of buses along the route. The critical stop is normally the busiest stop along the route. All other things being equal, a stop with more variability in dwell time will have a lower capacity than one with lower dispersion owing to vehicle queuing at the stop. A convenient, practical decision rule is that the stop with the highest sum of the mean plus two standard deviations of the dwell time is the critical stop. There are several variations in the design of high capacity bus stations. A typical high capacity station includes more than one boarding locations and a first in-first out queue discipline. That is, buses cannot bypass other buses waiting in the station. In some cases, routes are pre-assigned to specific boarding locations within stations. There is relatively little published material on transit station capacity at multiple berth facilities. The US Transit Capacity and Quality of Service Manual (TCQSM), by Kittelson & Associates (2003), provides some guidance on how to compute capacity at multiple berth stops. This procedure applies only where the bus stop contains multiple berths, there is no passing capability and buses are not-preassigned to specific berths. Essentially, the manual provides an estimate of the capacity (relative to the capacity of the first boarding berth) of each successive berth at a bus stop. The source data for this assessment was observations of bus operations at the Port Authority Bus Terminal on New York, the main attributes of which were non-level boarding trough a single door and on-board fare collection. A different approach includes the utilization of simulation models to estimate bus stop capacity. Two simulation models for bus stop operations can be found in the literature IRENE (Gibson et al., 1989) and PASSION (Fernandez, 2001, Fernandez and Planzer, 2002). PASSION represents the enhancement of IRENE in terms of passenger considerations and flexibility. PASSION capabilities include passenger, exit and bus modules being able to represent a big variety of scenarios. However, the necessary data for calibration and input make these models unsuitable for preliminary evaluation and testing. In fact, microsimulation implies having data that, in most cases in the developing world, has not been collected or even conceived to be necessary for making decisions. A difficulty in determining the capacity of a multiple boarding area bus stop is that models cannot be easily validated in practice. Typically, a transit operator designs a service to operate below capacity and it is difficult to design an experiment to determine capacity. Accordingly, we developed this model as planning level model not an operations analysis model. Its utility is more in the early design phases of high capacity bus service to enable a rough estimate of how capacity changes with physical design characteristics and patterns of bus arrival and dwell time. 3

3. Methodology description Bus stop capacity calculations are conceptually straightforward. The first step is to determine the required service time for arriving vehicles. The service time is comprised of four components. The first is the dwell time, the time that the bus is stopped at the station. The second component is the clearance time, the time for a bus to exit the station and re-enter the traffic stream. The third time is the safe separation time between successive buses serving the station. This is the time between door closing of a bus and the door opening of the following bus in the station. The fourth component is an operating margin. This factor can be interpreted as a buffer time to allow for random variation in the dwell time and in the arrival pattern of buses (headway variation). In a perfect world of constant dwell times and uniform headways, this factor reduces to zero. The amount of time for the operating margin depends on the allowable failure rate the probability that an arriving bus is unable to reach an unoccupied berth due to its occupancy by another bus. To achieve low failure rates, a high operating margin is required. The formula below shows the traditional computational procedure which includes the effect of boarding time and clearance time, randomness in dwell and interarrival times, and the effective capacity of multiple berth bus stops. B s = N el B l =N el * (3600*(g/C))/(t c + t d (g/c) +Zc v t d ) Where, B s = bus stop capacity (bus/h) B l = individual loading area bus capacity (bus/h) N el = number of effective loading areas 3,600 = seconds per hour (Eq.1) g/c = green time ratio (effective green time to total signal cycle time) t c = clearance time (s) t d = mean dwell time (s) Z = standard normal variable corresponding to a desired failure rate (one-tailed test) c v = coefficient of variation of dwell times Essentially the busway capacity computation procedure is to find the product of the effective number of loading areas (N el ) and the capacity per loading area (B l ). Equation 1 is generalized for a near side bus stop at a signalized intersection. For a midblock, far side or unsignalized intersection where the bus lane is in the major travel direction, g/c would be equal to one. The number of effective loading areas (N el ) is the ratio of total bus capacity of a multiple berth stop to the capacity of a single berth stop. The TCQSM contains a set of tables for estimating the number of effective loading areas as a function of the number of actual loading areas. These tables were developed from observations at the Port Authority Bus Terminal in New York City, one of the largest in the US. In several circumstances outside of the US, the service operating scheme at stations is more complex. This is the case of Transmilenio in Bogota, Colombia. The Transmilenio running way consists of a single lane in each direction with off-line stations. Buses are able to pass each other in most circumstances. Not 4

all buses serve all stops. During the peak hour, on some corridors, the bus volume is about 300 buses per hour for an average headway of about 12 seconds. Other service attributes are level boarding between the bus and the station platform, off-board fare collection, multiple, wide boarding doors and a fleet comprised primarily of articulated buses with some bi-articulated buses. As a result, dwell times are relatively short and observed corridor passenger volumes can exceed 40,000 persons per hour. The latter estimates are out the ranges present at the Port Authority making the TCQSM unsuitable for the case of Transmilenio. Our formulation of the problem was to determine through simulation the failure rate associated with varying levels of mean dwell time, dwell time variability and headway and headway variability. A number of alternate stop configurations were incorporated as was the presence or absence of a traffic signal at the stop for near-side stops. From this, we were able to determine the maximum frequency in buses per hour at which the target failure rate was achieved. This formulation incorporated all of the inputs of the model articulated in Eq. 1 but was tailored for high capacity BRT operation, such as Transmilenio in Bogota, Colombia. We assume that a station has either one or two loading berths. The station may include a queuing space for buses to enter the loading berths. Once in the boarding lane, buses may not pass each other. The set of routes assigned to berth 1 is distinct from the routes assigned to berth 2. A plan view of such a station, typical in Transmilenio, is shown in Figure 1. Note that in the Transmilenio system, some high volume stations have two or three such modules. Figure 1: Plan View of Transmilenio Bus Station In order to present a set of tools to analyze this and other situations, the following four configurations were modeled: 1. Single loading berth no queuing space 2. Single loading berth queuing space for one bus 3. Dual loading berth no queuing space 4. Dual loading berth queuing space for one bus Station capacity, measured in buses per hour, was defined for several acceptable failure rates including 5%, 10% and 25%, with the failure rate being defined as the probability that an arriving bus will not be able to enter either a vacant berth or a queuing space. Another variable in each of these assessments included mean service time with values of 20, 30, 40, 50, 60 and 75 seconds 1. These values reflected a range of service times observed in the literature and in practice. The final two input variables were service time variability and arrival rate variability. We reviewed field and published data to make an assessment of the appropriate ranges of these variables. Estimates of service time variability were obtained from Transmilenio. In Transmilenio, typical peak hour headways 1 The term service time is used in these calculations. Service time includes the dwell time (time the bus is stopped) as well as the safe separation time between successive vehicles and the delay time to re-enter the traffic stream. The mean safe separation time is on the order of 12 seconds and the mean re-entry time is about 3 seconds. 5

are very short. However, the variability in headways, measured as the coefficient of variation, was very high, on the order of 0.8, owing to things such as dwell time variability at upstream stops, the presence of upstream traffic signals and most importantly, significant bus to bus interference at stations due to the system operating at near capacity. Other observed data on headway variability were reported by Huang (2010) for the BRT system in Jinan, China which has an exclusive median right of way. The observed headway coefficient of variation was on the order of 0.3 to 0.4. The BRT route reported by Huang paper had a 3 to 5 minute headway along a single route and little bus to bus interference as there is in Bogota. To simplify the model formulation, these two variables (headway variability and service time variability) were staged as either high or low. Definitions are shown in the table below. Table 1 - Service Variability Levels Input Level Definition Service time variability Low 0.4 times mean service time High 0.8 time mean service time Headway variability Low 0.4 times mean headway High 0.8 time mean headway Based on field data, the interarrival time and stop service time were determined to follow a normal distribution. 2 This analysis resulted in the development of 8 capacity tables two for each of the four service domains described above and the presence or absence of a traffic signal at the station. Table 3 presents a summary of the results at 10% failure rate and low values of headway and dwell time variability. Table 4 is the detailed table associated with the case of two boarding locations, followed by a queuing space without a traffic signal. This would be the highest capacity of the 8 cases tested. Table 3 Approximate Bus Station Capacity for Various Station Configurations in Vehicles per Hour Service Time (sec.) Loading Berths Queuing Space Traffic Signal 30 40 50 60 75 1 Yes Yes 58 46 35 30 25 1 Yes No 64 47 44 33 26 1 No Yes 37 32 26 20 17 1 No No 47 37 30 23 18 2 Yes Yes 75 61 48 43 33 2 Yes No 90 67 51 45 33 2 No Yes 64 50 41 37 30 2 No No 79 57 50 40 31 Assumptions: low dwell time variability and low headway variability. 10% failure rate 2 A Kolmogorov-Smirnoff test was used to determine that the normal distribution was a good approximation of the actual distribution. 6

Table 4 - Approximate Capacity of Double Berth, With Queuing Area, No Traffic Signal (vehicles per hour) Failure Rate Service Time (sec.) Service Time CV Headway CV 5% 10% 25% 30 40% 40% 74 90 105 40% 80% 56 80 94 80% 40% 56 63 84 80% 80% 54 64 82 40 40% 40% 55 67 78 40% 80% 48 62 76 80% 40% 46 51 61 80% 80% 39 44 66 50 40% 40% 48 51 68 40% 80% 36 46 60 80% 40% 37 41 52 80% 80% 32 35 50 60 40% 40% 41 45 52 40% 80% 35 42 54 80% 40% 25 33 43 80% 80% 26 32 42 75 40% 40% 30 33 41 40% 80% 27 31 45 80% 40% 24 27 34 80% 80% 20 26 36 * CV coefficient of variation = standard deviation/mean These tables require relatively little data collection effort to estimate station capacity. On high volume BRT services, mean dwell times can be obtained with about an hour s worth of observations. A similar length of time would enable a determination of low or high values of service time and headway variability. These data are for articulated (18m) buses which require a safe separation time of about 12 seconds. The use of non-articulated (13 m) buses are likely to increase capacity slightly since the time for the bus to clear the station is about 10 seconds less. Conversely, a bi-articulated bus takes 15 seconds to clear the station. The determination of an acceptable failure rate is more complex. In cases where some buses bypass certain stops, the inability of buses serving the stop to access either the berth or the queuing area may result in blocking through buses. In such cases a low failure rate of about 10% is suggested. In high volume cases, a high failure rate may result in a queue which may not dissipate for a long time, perhaps as 7

much as several minutes. The photograph in Figure 2 below shows a long queue at a Transmilenio station with many buses bypassing the next station. Fortunately, queues such as this normally dissipate within 2 minutes. Figure 2 Transmilenio Station (Bogota) With Long Queue 4. Application of the methodology The model was applied to the operation of the Transmilenio system in Bogota, which, by observation is operating near capacity during peak hours. The first step of the procedure used was to determine the levels of the input variables - peak hour service times (including dwell, separation and clearance times), and headway and service time variability. The two stops observed was Calle 100 (a stop near a large employment area with a large number of morning discharges and Calle 72 ( stop in the downtown area with a large number of afternoon boardings.) Mean Dwell Time Transmilenio has a very sophisticated vehicle location system which assists in service control. One of the data elements collected by the system is the time between door opening and door closing of arriving buses. This data provides the basis for estimating the mean and distribution of dwell times. Once a bus comes to a stop at the boarding location, it takes about 1.5 seconds for the door to open and accept 8

passengers. A similar delay occurred between the time the door starts to close and the bus started departure from the stop. Accordingly, 3 seconds were added to the electronic data recording to estimate dwell time distribution. Separation Time Stop Table 4 Door Open and Close Time Time Period Dwell Time Mean (sec.) 9 Standard Deviation Coefficient of Variation Calle 100 AM Peak 24 17 0.71 PM Peak 22 14 0.64 Calle 72 AM Peak 19 15 0.79 PM Peak 20 10 0.50 Separation time reflects the fact that there must be a time gap between departing and entering buses to account for driver reaction time and the ability for a following bus to safely stop in the event of a sudden deceleration of a preceding bus. If an arriving bus is queued behind a bus at the loading berth, there is a time between the movement of the departing bus and the stopping of the entering bus. This allows for the departing bus to clear the platform and allow for a safe stopping distance for the entering bus. Based on several observations this time is about 12-13 seconds. This is consistent with the mechanics of bus operations. Clearance Time Buses at stops must re-enter the traffic stream. Insofar as the adjacent lane is exclusively for buses, there are likely to be frequent headway gaps of sufficient duration to allow bus reentry without interference. The vehicle volume in the bypass lane includes buses which are bypassing the station and buses stopped at the station upstream from the re-entering bus. The maximum volume of such buses is about 300 vehicles per hour. Using data from the TCQSM, the re-entry time would be about 3 seconds. The total mean service time for the combination of dwell, separation and clearance time for each of the critical stops is shown in Table 5 below. Table 5 - Dwell Time Assessment Stops at Calle 76 and 100 Headway Component Data Source Stop 100 Time (sec.) Stop 76 Time (sec.) Station dwell time door opening and closing time Based on field observation 3.0 3.0 time doors are open (mean) Based on data from Transmilenio 19.0 18.0 Safe separation time Based on field observation 12.0 12.0 Clearance (re-entry) time Use TCQSM for volume = 300 3.0 3.0 buses per hour Minimum time between buses Sum of all elements 36.0 47.0

Dwell and Headway Variability Dwell time variability was estimated from the Transmilenio AVL system. Headway variability was based on actual field observation. The dwell time coefficient of variation was estimated from the AVL data at 0.4 and the headway coefficient of variation was estimated from field observation at 0.8 5. Concluding remarks The table below illustrates the capacity of the Transmilenio system at various failure rates. The ability of the system to carry over 40,000 persons per hour per direction is due to the fact that most buses bypass each station and that in some stations, there are two bus boarding areas, each operating independently which doubles the effective capacity. Note that observed volumes exceed these levels owing to the fact that a large number of passengers are on buses which bypass the critical stop. Table 6- Running Way Capacity Stop Failure Rate 5% 10% 25% vehicle capacity Calle 100 71 97 130 160 Calle 76 119 154 201 160 Line Capacity at 25% Failure Rate 20,800 32,160 This work represents an initial attempt to estimate running way capacity in a more complex environment than generally encountered in the US. It has been demonstrated that it is easy to use and develops reasonable results. It is more useful for the purpose of system planning than for operations analysis. That is, it can serve as a tool to assess a number of alternate station design schemes during preliminary design. It provides limited insight into diagnosis of a facility operating at near capacity. More detailed simulation models, some of which are described previously in this paper are better suited to this task. While, in general, BRT frequencies in the US are much lower than those in the developing world, there is some application of this paper to some specific US situations. In many cities, particularly those laid out in radial pattern, a number of bus routes converge along a single street resulting in corridor bus volumes which may exceed 100 buses per hour. Under such circumstances, the tables in this paper may give insights into improving the throughput capacity of the critical stop. In such circumstances, transit operators may choose to pre-assign routes to specific, separated bus boarding areas at busy stops. Some enhancements could be considered in this analysis. First, the model does not well capture the case where specific buses are assigned to specific berths in two berth stops, where the berths must be accessed in a sequential fashion. We estimate that this constraint reduces the effective capacity by about 10%. 10

Acknowledgements This report was financed by the Transport Research Support Program, TRS of the World Bank. The authors acknowledge the assistance of Dr. Ajay Kumar, World Bank project manager, Sam Zimmerman, consultant to the World Bank, Dario Hidalgo of EMBARQ, the staff of Transmilenio, S.A. in Bogota, especially Sandra Angel and Constanza Garci. References FERNANDEZ, R. 2001. A new approach to bus stop modelling. Traffic engineering & control, 42, 240-246. FERNANDEZ, R. 2010. Modelling public transport stops by microscopic simulation. Transportation Research Part C: Emerging Technologies, 18, 856-868. FERNANDEZ, R. & PLANZER, R. 2002. On the capacity of bus transit systems. Transport Reviews, 22, 267-293. GIBSON, J., BAELA, I. & WILLUMSEN, L. 1989. Bus-stops, congestion and congested busstops. Traffic engineering & control, 30, 291-302. KITTELSON & ASSOCIATES 2003. Transit Capacity and Quality of Service Manual, Washington, D.C., Transportation Research Board. ROCKWELL AUTOMATION. 2010. Rockwell Automation [Online]. Available: http://www.arenasimulation.com [Accessed May 2 2011]. 11