1 1 1 1 1 1 1 1 0 1 0 1 0 1 Hve they bunched yet? An explortory study of the impcts of bus bunching on dwell nd running times Dvid Verbich School of Urbn Plnning Fculty of Engineering McGill University Suite 00, 1 Sherbrooke St. W. Montrél, Québec, HA 0C Cnd E-mil: dvid.verbich@mil.mcgill.c Ehb Dib Deprtment of Civil Engineering - Trnsporttion Engineering University of Toronto St. George Street, Room: SF001M Toronto, Ontrio, MS 1A Cnd Tel.: 1--00 Fx: 1-- e-mil: ehb.dib@utoronto.c Ahmed El-Geneidy* School of Urbn Plnning Fculty of Engineering McGill University Suite 00, 1 Sherbrooke St. W. Montrél, Québec, HA 0C Cnd Tel.: 1--1 Fx: 1-- E-mil: hmed.elgeneidy@mcgill.c *Corresponding uthor April 01 Word Count 0, 1 Figures, nd Tbles For cittion plese use: Verbich, D., Dib, E., & El-Geneidy, A. (ccepted). Hve they bunched yet? An explortory study of the impcts of bus bunching on dwell nd running time. Public Trnsport: Plnning nd Opertions. 1
1 1 1 1 1 1 1 1 0 1 ABSTRACT If trnsit gencies wish to retin nd ttrct riders, they need to provide relible nd efficient services. Trnsit gencies tend to run high-frequency bus routes during pek hours, nd in mny cities, different routes cn lso overlp long mjor corridors. In some instnces, consecutive buses cn rrive t shred stop simultneously or one bus my rrive while nother bus is currently servicing the stop. This phenomenon, known s bus bunching, cn dely buses nd pssengers, nd is usully inefficient. In this study, we ttempt to understnd how bus bunching from the sme or different routes cn impct bus opertions, specificlly dwell nd running times. This reserch uses stop-level records obtined from utomtic vehicle loction (AVL) nd utomtic pssenger counter (APC) systems from TriMet, Portlnd, OR. Using liner modeling, we find tht bus bunching increses both dwell nd running times. Specificlly, when different routes bunch or re scheduled to rrive t bus stop within short time frme, or when buses from the sme route rrive with short time frme, dwell times increse by ~ s. Similrly, bus bunching from the sme route or different route prolongs running times by ~0 s. Our findings suggest tht bus schedulers nd opertors should consider dding more time between consecutive buses from different routes t shred stops to minimize the negtive impcts tht we observed from bus bunching. KEYWORDS: Running time, Dwell time, High-frequency, Bunching, Dely, Overlp
1 1 1 1 1 1 1 1 0 1 0 1 INTRODUCTION In n effort to ttrct nd retin bus riders, trnsit gencies continuously djust bus schedules nd routes. These djustments im to improve bus running times s well s to increse the trnsit coverge within cities. Customers view both s crucil components of ny trnsit system nd these fetures re importnt to compete with other modes, specificlly privte vehicles. Nevertheless, some bus opertions cn hve unintended consequences. In prticulr, while providing frequent service nd wht some customers deem s highly relible since they cn expect buses to rrive with regulr hedwys, high-frequency bus routes (with hedwys of minutes or less) cn become victims of bus bunching (Dgnzo, 00). Bus bunching hs frequently surfced in public converstions, nd its impct on user s perception frequently domintes the hedlines (Merevick, 01; Provost, 01; Simcoe, 01). Generlly, bus bunching results in consecutive buses rriving t bus stop within short mount of time, typiclly cused by hedwy devitions due to trffic or other rod condition. For trnsit opertors, bunching my result in inefficient cpcity utiliztion, while frustrting customers who my need to wit longer for subsequent buses (TCRP, 01). In ddition to high-frequency services, trnsit gencies lso tend to run severl routes into centrl business districts through shred corridors. In effect, buses strting from different points will converge onto corridor nd shre series of stops. This service pttern, known s service overlp, cn lso result in bus bunching nd increse running time for both routes. Here we ttempt to nswer the following reserch question: how does bus bunching from buses on the sme or different route ffect dwell times nd thus running time? If trnsit plnners hve clerer understnding of the nunces of bunching t bus stops with overlpping service, then pproprite mesures could be tken to mitigte the cuses nd effects of bus bunching. Wht follows is cse study of the impct of bus bunching on bus opertions on corridor with overlpping bus routes in Portlnd, OR. This pper strts with literture review on running nd dwell time models, s well s n overview of bus bunching. Next, we describe the bus route studied in this pper nd our methodology. Third, we present our results nd findings from the models. Finlly, we discuss our findings nd propose potentil policies bsed on our results. LITERATURE REVIEW
1 1 1 1 1 1 1 1 0 1 0 1 For customers, quick nd relible bus service is essentil; importntly, trvel time rnks consistently high on stisfction surveys, long with witing time (Dib, Bdmi, & El-Geneidy, 01; Hensher, Stopher, & Bullock, 00; Yoh, Iseki, Smrt, & Tylor, 0). Therefore, from n opertor s perspective, both running nd witing times re importnt fctors to mesure nd mintin within cceptble bounds. For exmple, reserch hs consistently found tht reduced running times cn ttrct nd mintin riders (Boyle, 00; Hollnder, 00). Moreover, riders lso vlue frequent service (Strthmn et l., 1). Nonetheless, compromise between frequent service nd relibility, in terms of service vribility, cn influence customer stisfction since some studies show tht customers prefer consistent bus rrivls over frequent service (Dsklkis & Strthopoulos, 00; Pulley et l., 00). Mny importnt chrcteristics cn influence running time, which is the time tken for bus to run its customer-serving route. Rider ctivities like bordings nd lightings, lift ctivity, time of dy, s well s unforeseen circumstnces due to trffic or wether, impct running time (Abkowitz & Engelstein, 1; Levinson, 1; Strthmn et l., 000). Trnsit gencies ttempt to control severl fctors to optimize running time. Newer work revels tht dditionl strtegies, such s reserved lnes, trnsit signl priority nd bus stop consolidtion cn reduce running times, while smrtcrd fre collection systems nd rticulted buses cn prolong running times (Dib & El-Geneidy, 01; El-Geneidy, Strthmn, Kimpel, & Crout, 00; El-Geneidy & Vijykumr, 0; Suprennt-Legult & El-Geneidy, 0). An importnt contributor to running times is the dwell time, defined typiclly s the length of time bus stops to serve pssengers t stop; both door nd pssenger ctivities re considered in dwell time models (Dueker, Kimpel, Strthmn, & Clls, 00; El-Geneidy & Vijykumr, 0). Dwell time contributes nywhere between 0% to running time (Brr, Beton, Chirmonte, & Orosz, 0; Levinson, 1); understnding the fctors underlying dwell time cn id trnsit gencies to minimize dwells nd speed up bus opertions (Abkowitz & Engelstein, 1; Levine & Torng, 1). Pssenger ctivity nd bus lod (number of pssengers on bord) ply lrge role in determining dwells, nd low-floor buses nd rticulted buses cn reduce dwell times (Dib & El-Geneidy, 01; Dueker et l., 00; El-Geneidy & Vijykumr, 0; Levine & Torng, 1). Fre collection procedures t the first door, lift opertions, stop shelters nd signlized intersections cn prolong dwell times (Dib & El-Geneidy, 01; Dueker et l., 00).
1 1 1 1 1 1 1 1 0 1 0 1 Despite extensive work on dwell nd running times, less work hs been conducted on bus bunching nd its impct on opertions. Bunching occurs when buses rrive t stop nerly simultneously, or when bus rrives t stop recently served by preceding bus. Bunching results from disrupted scheduled hedwys between buses, represents wsted cpcity for opertors, nd prolongs wit times for customers becuse of overcrowded led buses (TCRP, 01b). Bus bunching hs previously been reserched in order to better understnd its cuses or its overll impct on service levels. For instnce, the occurrence of bus bunching increses with route length (Feng & Figliozzi, 01). Moreover, using simultions, holding points were found to reduce the levels of bunching on high-frequency circulr bus route (Holroyd & Scrggs, 1). Most reserch on bus bunching hs used mthemticl pproches to generte theoreticl holding techniques to eliminte or reduce bunching (Dgnzo, 00; Dgnzo & Pilchowski, 0; Eberlein, Wilson, & Bernstein, 001; Hickmn, 001), or to model cuses of or to predict bus bunching (Moreir-Mtis, Ferreir, Gm, Mendes-Moreir, & de Sous, 01; Moreir- Mtis, Gm, Mendes-Moreir, & de Sous, 01). Nevertheless, how bus bunching cn impct dwell nd running times is unknown, especilly with regrd to overlpping services. Previous work on shred locl nd express service corridor in Montrel found tht fter implementing rticulted buses for the express service, running time ws incresed for both the express nd locl services (Dib & El-Geneidy, 01). This finding demonstrtes the importnce of elucidting the impcts of overlpping services long shred corridor. Though scheduled bunching between different routes my enble trnsfers, it remins unknown how bunching from the sme or different routes my differentilly ffect running nd dwell times. METHODOLOGY The min gol of this pper is determine how the dwell nd running times of bus service re impcted by the fct tht it shres corridor with other overlpping bus services. We study two situtions: (1) how n rriving bus s dwell nd running times is impcted by bunching with bus from the sme route long specific segment of bus route tht is shred with mny bus services, nd () how n rriving bus s dwell nd running times is impcted by bunching with bus from different route long specific segment of bus route tht is shred with mny bus services. By studying these situtions, we cn provide plnners with pproprite wys to understnd the impcts of bunching within shred corridor.
Cse study We used stop-level AVL/APC from TriMet, Portlnd, Oregon for Route 1 long the Brbur Blvd. corridor (Figure 1). We chose this route primrily becuse it experienced no chnges in terms of route structure nd schedule, hs vriety long its route, nd hs overlpping service routes long some segments. Route 1 runs est-west crossing through downtown Portlnd nd overlps with severl routes, including Routes 1,,,,,, nd. The verge hedwy of Route 1 is 1 min, with minimum hedwy of min during pek hours nd mximum of min during off-pek hours. The verge stop spcing of the corridor is bout 0 meters. A totl of signlized intersections re functioning long the nlyzed segment (Figure 1, nlyzed segment). 1 1 1 1 1 1 1 1 0 1 Figure 1. TriMet's Route 1 nd nlyzed segment of SW Brbur Blvd. The AVL/APC rchived dt originte from 1 st of September 01 until th of November 01 for Route 1 s well s for other overlpping routes (listed bove). Given the reltively short time frme inspected, sesonl vritions my be unccounted for. Since ll TriMet buses re equipped with AVL coupled with APC technology, we were ble to ccurtely clculte bus dwell times nd running times, s well s bunching s we describe below. Moreover, detiled trip informtion, like scheduled deprture time, rrivl time nd ctul
1 1 1 1 1 1 1 1 0 1 0 1 deprture times, long with pssenger ctivity is vilble for every stop. It should be noted tht ll buses nd signls long the studied corridor re equipped with n opertionl trnsit signl priority (TSP) system tht ws ctive during the dt collection period. Dt preprtion for dwell time model For the dwell time model, over 00,000 records for ll bus stops served by ll the forementioned routes were first exmined. We clened the source dt by removing system recording errors, duplicted records, nd holidy nd weekend trips. Using this AVL/APC dt, we first clculted dwell time, defined s bus deprture minus bus rrivl t individul stops. In previous work investigting bunching, such s for holding strtegies imed t correcting bunching (e.g., (Berrebi, Wtkins, & Lvl, 01; Cts et l., 01; Dgnzo, 00; Hmmerle, Hynes, & McNeil, 00)), bunching ws visulized using time-spce digrms, or defined using hedwy vritions or hedwy differences between consecutive buses (e.g., subtrcting deprture times for consecutive buses (Figliozzi, Feng, & Lfferriere, 01)). To determine bus bunching here, we took similr pproch to previous work using TriMet AVL/APC dt (Figliozzi et l., 01) by investigting hedwys between consecutive buses. We creted dummy vribles imed to cpture bus bunching, so if hedwys between consecutive buses fell within predefined rnge, we defined this hedwy or bus rrngement s bus bunching. This bus bunching hedwy ws clculted s: (rrivl time of bus of interest, i,) (deprture time of previous bus, i-1). Therefore, bus bunching refers to bus rriving when previous bus is still servicing or stnding t the bus stop, or when bus rrives nd the leder bus hs left the stop within predefined temporl rnge. A negtive vlue for this vrible indictes tht leder bus, i-1, is still servicing stop when bus of interest, i, rrives, or in other words, tht the bus of interest, i, rrives before the leder bus, i-1, deprts. A vlue of 0 indictes tht leder bus, i-1, is deprting when bus of interest, i, rrives. Finlly, positive vlue indictes tht leder bus, i-1, hs left the stop when bus of interest, i, rrives; note tht this is the typicl scheme for rrivls nd deprtures. Previous reserch used three-minute hedwys between consecutive bus deprtures s threshold for bus bunching, cknowledging tht this rbitrry threshold my be modified for given reserch question (Figliozzi et l., 01). Here, to determine the hedwy threshold tht could qulify s bus bunching, we defined different rnges of hedwys between consecutive buses s bus bunching (for exmple, bus of interest rriving between 0 0 s of previous bus
1 1 1 1 1 1 1 1 0 1 0 1 deprture) nd used the generted dummy vribles in dwell time models; this procedure ws used to vlidte chosen hedwy rnge bsed on the model output nd how vribles in dwell time model should preform given previous work. The time intervls we specified re: bus of interest, i, rriving within 0 0 s nd 0-0 s of previous bus, i-1, still t the stop (negtive vlues for rrivl deprture), bus, i, rriving s previous bus, i-1, hs just deprted (0 s), nd bus, i, rriving within 0 0 s nd 0 0 s of the previous bus, i-l, deprting (positive vlues for rrivl deprture). Plese see Tble 1 for detiled vribles. These time intervls re expressly short in order to cpture the effects of bunching within smll time window; these vlues re more conservtive thn previous study tht used three-minute time window (Figliozzi et l., 01). Moreover, we determined whether this previous leder bus, i-l, ws from the sme or different route s n rriving bus of interest, i. When bus i-1 ws from different route, we lso specified whether deprture of the bus of interest, i, ws scheduled to occur before the deprture of the previous bus, i-1; we clled this scheduled overlp. To determine scheduled overlp, we first determined whether the scheduled deprture time of bus i ws scheduled to occur before the scheduled deprture time of bus i-1. If this sitution occurred, we generted dummy vrible equl to 1. This dummy vrible ws then multiplied by nother dummy vrible tht coded for our definition of bus bunching, tht is, when this rrngement occurred nd the hedwys (bus i rrivl time bus i-1 ctul deprture time) were within our defined rnges. When these two conditions were met, this is wht we clled scheduled overlp. If bus, i, deprted from stop when previous bus, i-1 (from different route), ws present nd this ws unscheduled, we clled this occurrence unscheduled deprture or bunching from different route. In this wy, we cptured how bus bunching/overlp tht occurs from the sme service or different service my impct dwell nd running times. We nlyzed dwell times of Route 1 stops over ~. km (. mi) between SW Brbur nd Cpitol Hwy intersection south west of the downtown nd the intersection t SW Min nd Pcific Hwy in the south west becuse of the vilbility of AVL/APC dt for ll routes tht shre this segment (Routes 1,,,,,, nd ), which mkes it possible to investigte the impct of overlpping services on Route 1 (Figure 1). After clculting dwell times nd hedwys between buses, we removed dt from stops from other routes, leving over 0,000 stop-level records for Route 1. Since bus bunching cn involve two buses t one stop
1 1 1 simultneously nd the triling bus my not experience pssenger ctivity, essentilly resulting in dwell times equl to 0, we kept stops with dwell times equl to 0 in our dtset specificlly becuse of our interest in bus bunching. We then removed the 1 st nd th percentiles of dwells, s well s first stops, lyovers, nd stops without dt pertining to physicl chrcteristics of the bus stop, leving 1, records. We lso removed questionble dt entries, for exmple, records with lrge numbers of bordings nd lightings, or lift ctivities, but with dwell times too short to be plusible (two such records). Finlly, we removed stops where bus of interest, bus i, rrived nd previous bus, bus i-1, ws t the stop for more thn 0 s becuse these rre occurrences (0 records) my represent typicl situtions cused by rod incidents or trffic conditions, for instnce; moreover, dummy vribles for this rrngement yielded difficult to interpret coefficients in the dwell time model output. The finl dtset used to model dwell time included 1, records. Descriptions of ll vribles used in the models re shown in Tble 1. Tble 1. Description of vribles used in both models. Vrible nme Description Dwell time (s) Dwell time mesured in seconds between the rrivl nd deprture of bus (dependent vrible) Running time (s) Totl trvel time mesured in seconds long specified segment of Brbur Blvd. (dependent vrible) AM pek Dummy vrible equl to 1 if the dwell (or trip) occurred between.m. PM pek Dummy vrible equl to 1 if the dwell (or trip) occurred between p.m. Evening nd night Dummy vrible equl to 1 if the dwell (or trip) occurred between p.m. nd midnight Overnight Dummy vrible equl to 1 if the dwell (or trip) occurred between midnight nd.m. Ons Totl number of bording pssengers t stop (or trip) Offs Totl number of lighting pssengers t stop (or trip) Direction Dummy vrible equl to one for inbound trips Totl pssenger ctivity Totl number of pssengers bording nd lighting t stop (or trip) Totl pssenger ctivity^ The squre of the totl number of pssengers bording nd lighting t stop (or trip) Lift Totl lift ctivity t stop (or long trip segment) Pssenger lod The totl number of pssengers on bus t stop (or mximum for trip) Pssenger lod^ The squre of the totl number of pssengers on bus t stop (or mximum for trip) Dely t the strt (s) The dely t the strt of trip in seconds (difference between ctul deprture time nd scheduled time t the first stop of route) Stop mde Dummy vrible equl to 1 if n ctul stop ws mde (or sum of ll stops mde for trip for running time) Unscheduled stop Dummy vrible equl to 1 if stop is n unscheduled stop long trip Stop t time point Dummy vrible equl to 1 if bus stop is holding point (or totl
Vrible nme Description number of time points for trip for running time) Signlized intersection Dummy vrible equl to 1 if the bus stop is t trffic light tht is equipped with n opertionl trnsit signl priority (TSP) system Shelter Dummy vrible equl to 1 if stop hs bus shelter Dwell time Previous -0-0 sme Dummy vrible equl to 1 if bus, i, rrives t stop between 0 0 s BEFORE the deprture of previous bus, i-1, of the SAME route Previous -0-0 different Dummy vrible equl to 1 if bus, i, rrives t stop between 0 0 scheduled overlp s BEFORE the deprture of previous bus, i-1, of DIFFERENT Previous -0-0 different unscheduled Previous -0 0 sme Previous -0 0 different scheduled overlp Previous -0 0 different unscheduled Previous 0 sme Previous 0 different scheduled overlp Previous 0 different unscheduled Previous 0 0 sme Previous 0 0 different Previous 0 0 sme Previous 0 0 different No bunching (0+) sme No bunching (0+) different route nd this is scheduled overlp Dummy vrible equl to 1 if bus, i, rrives t stop between 0 0 s BEFORE the deprture of previous bus, i-1, of DIFFERENT route nd this is unscheduled deprture (or bunching) Dummy vrible equl to 1 if bus, i, rrives t stop between 0 0 s BEFORE the deprture of previous bus, i-1, of the SAME route Dummy vrible equl to 1 if bus, i, rrives t stop between 0 0 s BEFORE the deprture of previous bus, i-1, of DIFFERENT route nd this is scheduled overlp Dummy vrible equl to 1 if bus rrives, i, t stop between 0 0 s BEFORE the deprture of previous bus, i-1, of DIFFERENT route nd this is unscheduled deprture (or bunching) Dummy vrible equl to 1 if bus, i, rrives t stop t the SAME TIME previous bus, i-1, is deprting nd is from the SAME route Dummy vrible equl to 1 if bus, i, rrives t stop t the SAME TIME previous bus, i-1, is deprting nd is from DIFFERENT route nd this is scheduled overlp Dummy vrible equl to 1 if bus, i, rrives t stop t the SAME TIME previous bus, i-1, is deprting nd is from DIFFERENT route nd this is unscheduled deprture (or bunching) Dummy vrible equl to 1 if bus, i, rrives t stop 0 0 s AFTER previous bus, i-1, hs left nd is from the SAME route Dummy vrible equl to 1 if bus, i, rrives t stop 0 0 s AFTER previous bus, i-1, hs left nd is from DIFFERENT route Dummy vrible equl to 1 if bus rrives, i, t stop 0 0 s AFTER previous bus, i-1, hs left nd is from the SAME route Dummy vrible equl to 1 if bus, i, rrives t stop 0 0 s AFTER previous bus, i-1, hs left nd is from DIFFERENT route Dummy vrible equl to 1 if bus, i, rrives t stop 0 s AFTER previous bus, i-1, hs left (no bunching) from the SAME route (bse condition) Dummy vrible equl to 1 if bus, i, rrives t stop 0 s AFTER previous bus hs, i-1, left (no bunching) from DIFFERENT route Running time First trip Dummy vrible equl to 1 if the trip is the first trip of the dy Sum of previous -0 0 sme Occurrences long trip segment when bus, i, rrives t stop 0 0 s BEFORE the deprture of previous bus, i-1, of the SAME route Sum of previous -0 0 different scheduled overlp Occurrences long trip segment when bus, i, rrives t stop 0 0 s BEFORE the deprture of previous bus, i-1, of DIFFERENT route nd is scheduled overlp Sum of previous 0 0 different Occurrences long trip segment when bus, i, rrives t stop 0 0 Sum of no bunching (0+) different s AFTER the deprture of previous bus, i-1, of DIFFERENT route Occurrences long trip segment when no bunching occurred with bus, i-1, of DIFFERENT route previously servicing the stop
1 1 1 1 1 1 1 1 0 1 0 In this pper, we im to understnd how bus bunching, tht is, consecutive buses rriving within short (<0 s) time windows t stop by using the dummies we constructed for different temporl spects of bunching, cn impct dwell times. Tble 1 includes list nd detiled descriptions of dummy vribles used to explore bunching, s well s other vribles incorported in the sttisticl nlysis. For exmple, in our dwell time model, one dummy vrible previous 0 0 different is ment to cpture instnces where bus of interest, i, rrives t stop 0 to 0 s fter bus i-1 from different route hs left the stop. According to previous studies, the generl fctors ffecting dwell time include pssenger ctivity in terms of bording nd lighting, lift usge, time of the dy, nd delys t the beginning of trip (Dueker et l., 00). A positive coefficient vlue for vrible indictes tht this vrible will increse dwell time, while negtive vlue signifies tht this vrible will decrese dwell time of the bus of interest (bus i). Dt preprtion for running time model Using the sme dtset s bove, we nlyzed nerly,000 trips of Route 1 long the southwest Brbur Blvd. corridor. Segments nlyzed included westbound nd estbound trips, specified by dummy vrible for downtown-bound (estbound) trips tht strted t SW Brbur nd Cpitol Hwy (westbound) nd hd between stops, nd trips tht strted t SW Min nd Pcific Hwy (estbound/downtown-bound) nd hd between 0 stops. Upon nlyzing these trips, trips with pssenger ctivity below three were removed, nd the 1 st nd th percentiles of running times were lso removed. As bove, trips where bus bunching occurred with previous bus stnding for more thn 0 s fter the rrivl of the bus of interest were discrded. After this clening process, the running time model used, trips. The dependent vrible, running time, ws clculted s rrivl time t the first stop minus deprture time t the lst stop of the studied segment (without including the lyovers). To cpture bunching t the segment-level, we summed instnces of bunching s defined in our dwell time model to clculte the number of occurrences of different types of bus bunching. For exmple, sum of previous 0 0 different dummy cptures the number of times long trip segment tht bus of interest, i, rrives t stop 0 to 0 s fter bus from different route (i-1) hs serviced the sme stop. These dummy vribles will
1 1 llow us to understnd how different types of bunching, nmely with bus of the sme or of different route, cn influence running time. RESULTS Descriptive sttistics Tble presents summry sttistics for the vribles in the dwell time model, while Tble presents summry sttistics for the dt used in the running time model. Along the studied corridor, Route 1 hs verge dwell times of. s, with devition round the men of 1. s (Tble ). Moreover, the verge running time for Route 1 long the segment of interest is 1. s (or bout min) with stndrd devition of 1. s (or bout min) (Tble ). Below, we present the results of regression models. Tble. Dwell time model summry sttistics. Vrible nme Men Std. Dev. Minimum Mximum Dwell time (s). 1. 0 AM pek 0.1 0. 0 1 PM pek 0.1 0. 0 1 Evening nd night 0. 0. 0 1 Overnight 0.0 0. 0 1 Ons 0. 1.0 0 Offs 0. 0. 0 0 Totl pssenger ctivity^.. 0 1 Lift 0.00 0.0 0 Pssenger lod.0. 0 0 Pssenger lod^ 1.0 0.1 0 00 Dely t the strt (s).0 1.0-0 1 Stop mde 0. 0. 0 1 Unscheduled stop 0.01 0.1 0 1 Stop t time point 0.01 0. 0 1 Signlized intersection 0.1 0. 0 1 Shelter 0. 0. 0 1 Previous -0-0 sme 0.000 0.01 0 1 Previous -0-0 different scheduled overlp 0.000 0.01 0 1 Previous -0-0 different unscheduled 0.0001 0.00 0 1 Previous -0 0 sme 0.000 0.0 0 1 Previous -0 0 different scheduled overlp 0.000 0.01 0 1 Previous -0 0 different unscheduled 0.000 0.01 0 1 Previous 0 sme 0.0001 0.00 0 1 Previous 0 different scheduled overlp 0.0000 0.00 0 1 Previous 0 different unscheduled 0.0001 0.00 0 1 Previous 0 0 sme 0.00 0.0 0 1 Previous 0 0 different 0.00 0.0 0 1 Previous 0 0 sme 0.00 0.0 0 1 Previous 0 0 different 0.00 0.01 0 1 No bunching (0+) sme 0. 0. 0 1 No bunching (0+) different 0.0 0. 0 1 N = 1, stop-level observtions 1
1 1 1 1 1 1 1 1 0 1 Tble. Running time model summry sttistics. Vrible nme Men Std. Dev. Minimum Mximum Running time (s) 1. 1. 1 0 AM pek 0.1 0. 0 1 PM pek 0. 0.0 0 1 Evening nd night 0. 0. 0 1 Overnight 0.0 0. 0 1 Direction 0. 0.0 0 1 Totl pssenger ctivity..0 Lift 0.0 0.1 0 Mximum of pssenger lod 1.. 0 Mximum of pssenger lod^.. 0 Dely t the strt (s). 1. -1 1 Totl stops mde.1. 1 First trip 0.01 0.1 0 1 Sum of previous -0 0 sme 0.01 0.1 0 Sum of previous -0 0 different scheduled overlp 0.01 0.1 0 Sum of previous 0 0 different 0. 0. 0 Sum of no bunching (0+) different 1.0. 0 N =, trips Dwell time model We developed liner regression model using dwell time in seconds s the dependent vrible. Only vribles tht displyed significnce or re policy relevnt vribles were mintined in the model. The output of this model is reported in Tble, nd contins 1, records nd explins % of the vrition in dwell time. This proportion of explined vrition is consistent with previous models (Dib & El-Geneidy, 01; Dueker et l., 00; El-Geneidy & Vijykumr, 0). Regrding key policy vribles, we find generlly, tht compred to no bus bunching, bus bunching prolongs dwell time. If bus rrives t stop while previous bus hs not deprted for 0 0 s, then the dwell of this rriving bus is incresed by. s if it is bunched with bus from the sme route. If bus rrives t stop nd bus from different route (scheduled stop) hs not deprted for 0 0 s, then 1. s is dded to dwell time of the rriving bus. If unscheduled bunching occurs with bus of different route (bus rrives nd previous bus from different route hs been stnding for 0 0 s), then dwells re lengthened by. s. These findings suggests tht bunching prolongs dwell times, likely due to pssenger trnsfers between different bus routes, s well s mneuvering resulting from closely spced buses. If this time window (bus i rriving while previous bus i-1 is still stnding) is between 0 0 s t scheduled service overlp (different routes), then. s re dded to dwells, while 1
. s re dded to dwells if the stop from different route ws unscheduled. If bus i from the sme route rrives nd the previous bus hs been t the stop for 0 0 s nd is from the sme route, then 1. s re dded to the dwell time of bus i. This is likely becuse the preceding bus from the sme route will hve picked up most pssengers. Overll, the presence of stnding bus will prolong dwells of n rriving bus becuse of incresed mneuvering time nd pssenger ctivity relted to the previous bus. In ddition, the impct of bus bunching on dwell times does not depend on whether the previous bus servicing stop is from the sme or different route. In other words, the differences between bunching from different or the sme routes re minor. Tble. Dwell time model. % CI % CI Coefficient t-sttistic Vrible nme Lower bound Upper bound Constnt 0.1*** 0. 0. 1.00 AM pek -0.*** -.1-0. -0. PM pek 0.***. 0. 0.1 Evening nd night -0.*** -.0-0. -0.1 Overnight -1.0*** -1.01-1. -0. Ons.*** 1... Offs.***..0.0 Totl pssenger ctivity^ -0.1*** -. -0.1-0.1 Lift 1.***. 0..0 Pssenger lod -0.*** -. -0.1-0.0 Pssenger lod^ 0.00*** 1. 0.001 0.00 Dely t the strt (s) -0.000*** -. -0.000-0.000 Stop mde.*** 1.. 1.01 Unscheduled stop.*** 1.1.0. Stop t time point.01***.0..1 Signlized intersection.*** 1...0 Shelter 1.***. 1. 1.1 Previous -0-0 sme.***.0. 1. Previous -0-0 different scheduled overlp 1.***.. 1.1 Previous -0-0 different unscheduled.***.. 1. Previous -0 0 sme 1.**. 0.0.0 Previous -0 0 different scheduled overlp.**.1 1.. Previous -0 0 different unscheduled.***... Previous 0 sme 0. 0.1 -.0. Previous 0 different scheduled overlp -. -1. -1.. Previous 0 different unscheduled -1. -0.1 -.0. Previous 0 0 sme -1.*** -. -1. -0. Previous 0 0 different 0. 1.1-0. 1.0 Previous 0 0 sme -1.0*** -. -1.0-0.0 Previous 0 0 different.***. 1.. No bunching (0+) different 0.0***. 0. 0. N 1, Adjusted R 0. F sttistics (0, 1) 1. F significnce (Prob > F) 0.00 1
1 1 1 1 1 1 1 1 0 1 0 1 compred to No bunching (0+) fter stop ws serviced by the SAME route ***Significnt t %; **Significnt t % When bus i rrives t stop fter previous bus i-1 from the sme route hs been deprted for 0 0 s, then 1. s re sved on dwells, nd this svings is lso similr to buses rriving fter bus hs left for 0 0 s nd is from the sme route. These results suggest tht dwells of subsequent buses re shorter becuse the previous bus will hve picked up most pssengers. In contrst, if the rriving bus is from different route tht hs deprted for 0 0 s, then. s re dded to the dwell time compred to bus tht rrives fter 0 s from the sme route. This my be explined by users behvior t stops with overlpping routes, since fter the rrivl nd deprture of bus, riders witing for nother route my leve the proximity of the stop nd thus tke longer to bord the subsequent rriving bus they re witing for. Finlly, dwell time of n rriving bus is minimlly impcted (incresed by 0.0 s) by bus from different route tht hs been deprted for more thn 0 s, compred to the bse sitution of bus rriving more thn 0 s fter deprted bus is from the sme route. This my be explined by drivers behvior; drivers my slow down their deprture t stops with overlpping service to ensure tht they pick up pssengers witing for this trip. The control vribles in the dwell time model behve s lrgely expected bsed on previous literture (Dueker et l., 00; El-Geneidy & Vijykumr, 0; Stewrt & El- Geneidy, 01). Dwells will be shorter in the AM pek, likely becuse of regulr customers fmilirity with bus bording, but PM pek dwells re longer. Evening nd night dwells, s well s overnight dwells, re both shorter thn off-pek dwells. Every pssenger bording nd lighting dds. s nd. s, respectively, while the pssenger ctivity squred-term indictes tht every dditionl pssenger quickens dwells by bout 0.1 s. Lift ctivity increses dwell time, s does mking n unscheduled stop. Buses stopping t signlized intersection stop will increse dwells by nerly s becuse red lights cn prolong bus stnding, while stop mde t stop with shelter will increse dwells by nerly s becuse pssengers tke longer to bord the bus in these res. Running time model Next, we developed bus running time model to understnd how the bus bunching tht we found prolongs dwell times my impct running time. We tested how the frequency of bus bunching occurrences ffected running times; we tested different time intervls nd bus rrngements nd 1
1 1 1 1 1 1 1 1 0 1 dropped from the model those vribles, like occurrences of buses rriving s bus from the sme route is leving (sum of previous 0 sme), tht were not significnt. Moreover, only vribles tht disply significnce or re policy relevnt vribles were mintined in the model. Our model, which nlyzed, trips, explins 0% of the vrition in running time, comprble with similr models (Dib & El-Geneidy, 01; Kimpel, Strthmn, Bertini, & Clls, 00). Interestingly, our model (Tble ) revels tht ech time bus i rrives t stop nd the previous bus i-1 from the sme route hs been stnding for 0 0 s, then the running time of the rriving bus increses by. s. This vlue represents bout % of the segment verge running time (Tble ). If this sitution occurs with bus from different route nd is scheduled overlp (scheduled rrivls occurring within 0 s of ech other), then.1 s re dded to the rriving bus running time. Once bunched, running time will be dded to the following bus since it needs to wit for the preceding bus to deprt from stop or mneuver round it. Ech time bus from different route rrives t stop fter previous bus hs left for 0 0 s, the running time of the bus is. s longer, while. s is dded to running time if bus rrives nd no bunching occurs nd the previous bus ws from different route. These findings suggest tht service overlpping increses running times. As mentioned in the previous section (Dwell time model) this likely results from drivers behvior. It seems tht drivers slow down their deprture t stops with overlpping service to ensure tht they re not missing ny pssengers witing for this trip. Tble. Running time model. Vrible nme Coefficient t-sttistic % CI % CI Lower bound Upper bound Constnt 1.0*** 1. 1.. AM pek. 1. -1. 1. PM pek.***.. 1. Evening nd night -.*** -. -. -. Overnight -1.*** -. -1. -1. Direction 1.1***..0 0.0 Totl pssenger ctivity.*** 1..0.0 Lift.***. 0.. Mximum of pssenger lod -1.0*** -.1 -. -1.1 Mximum of pssenger lod^ 0.0***. 0.01 0.01 Hedwy dely t the strt (s) -0.0*** -. -0.0-0.0 Totl stops mde 1.1*** 1.. 1. First trip -.0** -. -. -. Sum of previous -0 0 sme.***.0.1 1.0 Sum of previous -0 0 different.1**.1 1.0 0. 1
Vrible nme Coefficient t-sttistic % CI Lower bound % CI Upper bound scheduled overlp Sum of previous 0 0 different.**.1.1 1. Sum of no bunching (0+) different.***.1.0. N, Adjusted R F sttistics F significnce (Prob > F) ***Significnt t %; **Significnt t % 0.0 (1, 0) 1. 0.00 The remining vribles show tht running times re longer during the fternoon pek, but substntilly shorter during evening nd overnight trips. Inbound trips re 1.1 s longer thn outbound trips, likely due to pek-hour trffic. Pssenger ctivity dds bout. s, nd lift ctivity dds. s to running time. Delys t the beginning of trip will shorten totl running time, likely becuse drivers ttempt to mke up this dely, which is consistent with previous reserch (Dib & El-Geneidy, 01). Finlly, the first trip of the dy hs short running times, mostly due to fewer stops mde (which dd 1.1 s per stop to running time) nd less pssenger ctivity. 1
1 1 1 1 1 1 1 1 0 1 0 CONCLUSIONS AND DISCUSSION The min objective of this rticle is to understnd the impct of bus bunching on bus dwell nd running times while ccounting for overlpping bus routes. Using two sttisticl models, we nlyzed rchived dt obtined from TriMet s AVL nd APC systems for corridor in Portlnd, OR served by high-frequency bus routes to determine how bunching impcts bus opertions. The first model is dwell time model nd investigted the impcts of bunching nd overlpping service stops on disggregted dwell times. The second model is running time model, exmining the impcts of bus bunching nd overlpping service stops on the segment route-level of nlysis. We found tht bus bunching increses both dwell nd running times. The mount of time dded by bunching does not depend on whether the previous bus servicing stop is from the sme or different route. Insted, the dded time depends to lrger extent on mount of time between rriving nd deprting buses. In other words, our study reveled tht bunching nd overlpping service from different routes impct bus opertions lmost similrly to bunching by the sme route. Thus, while scheduling ner-simultneous rrivls for different routes could fcilitte route trnsfer, trnsit gencies should overlp bus routes with cution in order to minimize delys on the system. One importnt contribution of this reserch is tht trnsit plnners nd schedulers should dd more time between trips, prticulrly from different routes in order to decrese dwell time nd running time delys tht result from overlpping services t stops. Specificlly, our work indictes tht scheduled overlps or bunched vehicles where different routes rrive nd deprt within 0 s of one nother will prolong both dwells (dding bout s) nd running times (dding bout s). These vlues decrese if the routes rrive nd deprt within 0 s, nd bunching dds only bout seconds to dwell time nd with no significnt impct on running time. Given this finding, to ensure miniml delys, schedulers nd opertors should ensure tht buses from different routes should hve ctul hedwys of more thn 0 seconds. We recognize tht this my not lwys be possible given trnsfer times or pssenger ctivity. However, considering bunching is importnt t the plnning stge in order to decrese service delys during ctul opertions. In ddition, our reserch indictes tht using holding or other control techniques to decrese bunching nd inserting more time between buses is useful (Moreir- Mtis, Mendes-Moreir, de Sous, & Gm, 01). 1
1 1 1 1 1 1 1 1 0 1 0 1 Previous work hs studied the generl cuses of bus bunching, nmely hedwy delys t the strt of the route (Hmmerle et l., 00), or focused on corrective ction by implementing holding points long route (Holroyd & Scrggs, 1) or by djusting bus cruising speeds (Dgnzo & Pilchowski, 0). As dwells directly ffect running time feture vlued by customers (Dib & El-Geneidy, 01; Vuchic, 00) our models predict tht both dwells nd running times will be incresed by bunching. As result, bunching cn dversely ffect customer stisfction (Merevick, 01; Provost, 01; Simcoe, 01). Importntly, not ll bunching ffects dwell or running times similrly, nd our novel findings revel some nunces of bunching depending on rrivls nd deprtures. Overll, we found tht impcts of bus bunching on dwell times vries bsed on the rrivls nd deprtures of the buses, so tht the longer bus hs been servicing stop, more time is dded to the dwell time of the subsequent bus. Given the previous finding tht bunching worsens long the length of the route (Feng & Figliozzi, 01) suggests tht these prolonged dwells will increse the running time of buses long the sme route nd therefore overll running time, which we confirmed in the running time model. One potentil strtegy to reduce bunching could be to introduce more holding points t the opertionl stge to void the penlties of bunching on dwell nd running times. Therefore, trnsit gencies will need trde-off between the dded mount of slck time for bus holding nd dely if bunching hppened. Thus, study tht focuses on this trde-off is recommended. Finlly, this study offers trnsit plnners nd policy mkers better understnding of the impcts of bunching long shred corridor on the service dwell time nd trvel time. These findings re not limited to TriMet, s other trnsit gencies, by using similr methodology, cn use our models to understnd how overlpping service nd bunching my influence the system performnce t different loctions nd stop setups. Minimizing bunching while providing relible nd frequent service remins chllenge for trnsit gencies. ACKNOWLEGMENTS We thnk TriMet for providing the dt for this study, nd prticulrly Steve Clls nd Miles Crumley. We thnk Chris Loong for collecting bus stop environment dt. This work ws funded by Nturl Sciences nd Engineering Reserch Council of Cnd (NSERC) Discovery 1
Grnt. We lso would like to thnk the three nonymous reviewers for their feedbck on the erlier version of the mnuscript. The ides nd findings presented in this pper represent the uthors views in n cdemic exercise. 0
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