Transit Priority Strategies for Multiple Routes Under Headway-Based Operations

Transcription

1 Transi Prioriy Sraegies for Muliple Roues Under Headway-Based Operaions Yongjie Lin, Xianfeng Yang, Gang-Len Chang, and Nan Zou This paper presens a ransi signal prioriy (TSP) model designed o consider he benefis boh o bus riders and o inersecion passenger car users. The proposed sraegy, which is mainly for headway-based bus operaions, offers he responsible agency a reliable way o deermine he opimal green exension or red runcaion duraion in response o muliple bus prioriy requess from differen roues. The conrol objecive is o minimize bus passenger waiing ime a he downsream bus sop while ensuring ha he delays for all passengers are no increased. In ess ha used field daa from Jinan, China, he proposed sraegy showed promise in reducing bus passenger waiing ime and oal inersecion delay. Furher exploraion wih simulaion experimens for sensiiviy analysis found ha TSP is mos effecive if he raio beween bus and passenger volumes exceeds a hreshold of %. Hounsell and Shresha repored ha in response o differen levels of passenger demand, ransi agencies ofen divide heir operaing sraegies ino wo groups: schedule-based service normally used for low-demand roues, and headway-based operaions appropriae for high-demand corridors (1). Wih eiher sraegy, ransi signal prioriy (TSP) has long been recognized as a promising mehod for improving ransi service reliabiliy (). Depending on he informaion available on he in-roue bus and he funcions of signal conrollers, a variey of TSP conrols can be implemened in pracice. However, maximizing TSP effeciveness remains a challenging issue. Wilbur Smih and Associaes e al. were among he firs o conduc bus preempion experimens o reduce bus ravel ime (3). Yagar and Han proposed some uncondiional prioriy sraegies for buses (). Researchers laer developed condiional prioriy sraegies o improve bus puncualiy ha were based on prioriy rules and he arge bus s performance wih respec o is schedule; hese sraegies assumed ha bus-associaed informaion was available from an auomaic vehicle locaion sysem or real-ime bus operaion managemen (5 7). Depending on he TSP focus, operaing agencies may selec differen conrol objecives o improve heir service reliabiliy. For example, Head e al. (8) and Ma e al. (9) proposed a conrol objecive of minimizing he oal delay for all deeced buses. Mirchandani e al. (1), Chrisofa and Skabardonis (11), and Li e al. (1) exended he objecives o reduce he oal vehicle delay of buses Y. Lin, School of Conrol Science and Engineering, Shandong Universiy, No Jingshi Road, Jinan, 561 Shandong, China. N. Zou, School of Conrol Science and Engineering, Shandong Universiy, C33, Mingde Building, 7 Shanda Nanlu, 51 Jinan, China. X. Yang and G.-L. Chang, Deparmen of Civil and Environmenal Engineering, Universiy of Maryland, 1173 Glenn L. Marin Hall, College Park, MD 7. Corresponding auhor: Y. Lin, yjlin@mail.sdu.edu.cn. Transporaion Research Record: Journal of he Transporaion Research Board, No. 356, Transporaion Research Board of he Naional Academies, Washingon, D.C., 13, pp DOI: 1.311/356-5 and passenger cars. Chang e al. (13), Vasudevan (1), and Wu e al. (15) seleced he oal person delay of buses and passenger cars as he conrol objecive. Chang e al. (16) and Kleoniki e al. (17) have conduced exensive simulaion experimens o compare he performance of various TSP models. Seward and Taube (18) and Abdy and Hellinga (19) also presened several mahemaical mehods o evaluae he performance of TSP conrol sraegies. Unlike schedule-based TSP research, very lile research on headway-based mehods has been repored in he lieraure. Hounsell e al. inroduced a mehod o gran bus prioriy according o he headway beween he curren bus and he las preceding bus (5). Ling and Shalaby used reinforcemen learning ha was based on he bus headway deviaion from is schedule o deermine he bes duraion of an exended signal phase; hey used Paramics sofware for simulaion and evaluaion (6). Hounsell e al. repored he operaions of bus signal prioriy wihin ibus in London and explored he effecs of global posiioning sysem locaional errors on bus prioriy benefis (7). Alun and Furh presened a combinaion mehod, including bus holding a a sop and condiional signal prioriy o lae buses, o make buses operae under a uniform headway (). Hounsell and Shresha recenly presened a new approach o gran bus prioriy for a headway-based service (1). The key logic of heir mehod is o gran a bus prioriy if is forward headway is longer han he backward headway. Despie he poenial effeciveness of Hounsell and Shresha s mehod, is poenial applicaion o a congesed inersecion ha may receive muliple ransi prioriy requess during he same cycle needs some enhancemens. For example, Figure 1 displays he disribuion of headways of bus Roue 35 in Jinan, China, colleced on March 6, 1. As shown in Figure 1a, he scheduled headway remained unchanged wihin he iniial ime period (e.g., from 1: o 16:3). However, as a resul of raffic congesion and inersecion delays, he deeced acual headways began o vary wih disance and ime. Figure 1b, which shows he absolue headway deviaion a he hird, sevenh, and 1h sops of Roue 35 a differen imes of he same day, reveals an increasing deviaion of headways along he roue, especially during he peak hour periods (i.e., 6: o 1: and 18: o :). Because differen buses experience differen levels of headway deviaion, graning signal prioriy o muliple bus requess while considering he poenial impacs on boh bus riders and passenger car drivers is a complex issue. To conribue o headway-based TSP research, his sudy addressed a scenario in which a signalized inersecion conroller needs o deermine how o gran ransi prioriy when various buses from differen roues are ahead or behind schedule. The convenional firscome, firs-served sraegy may improve he schedule reliabiliy of some buses, bu i does so a he cos of ohers; ha is, such a sraegy may reduce he headway beween buses ha are eiher on 3

2 Lin, Yang, Chang, and Zou 35 Headway (min) : 6:16 6:3 6: 7: 7:16 7:3 7:5 8:1 8:3 8:8 9: 9: 9:36 9:5 1:1 1:3 1:8 11: 11: 11: 1: 1: 1: 13: 13:16 13:35 13:55 1:15 1:3 1:8 15: 15: 15:36 15:5 16:8 16: 16:38 16:5 17: 17:18 17:3 17:8 18:5 18:5 18:9 19: : (a) Time HD a 3rd sop HD a 7h sop HD a1h sop Headway deviaion (min) 3 1 6:-7: 7:-8: 8:-9: 9:-1: 1:-11: 11:-1: 1:-13: 13:-1: 1:-15: 15:-16: 16:-17: 17:-18: 18:-19: 19:-: (b) Time FIGURE 1 Disribuion of (a) scheduled headway and (b) absolue headway deviaion on bus Roue 35 in Jinan. heir scheduled headways or even ahead of he required arrival ime a he nex sop. Depending on he sequence of buses from differen roues and heir deviaions from scheduled headways, he inersecion conroller needs a rigorous logic o deermine he lengh of green exension or red runcaion for muliple prioriy requess in order o minimize he waiing ime of passengers a he nex sop over he conrol period. More specifically, he objecives of his sudy were o Design a conrol sysem based on various measures of effeciveness o handle muliple prioriy requess from buses on differen roues and Idenify criical facors or relaionships ha may affec TSP efficiency under differen raffic condiions. This paper is organized as follows: he nex secion describes he basic problem, and he hird secion develops a model of headwaybased TSP conrol o improve bus reliabiliy service. The case sudy in he fourh secion demonsraes he model applicaion wih field daa from he ciy of Jinan. Sensiiviy analysis and conclusions are presened in he fifh and sixh secions, respecively. Descripion of Problem Assuming a small scheduled headway and randomly arriving passengers along a bus roue, Kulash indicaed ha he average passenger waiing ime can be esimaed wih Equaion 1 (1): EH ( ) var( H) Ew ( ) = + EH ( ) E(w) = expeced waiing ime per passenger, E(H) = mean headway, and var(h) = variance of he headway disribuion. Hence, under a fixed-headway operaing sysem, one poenially effecive way o reduce he average passenger waiing ime is o conrol or minimize he headway variance of all buses on he same roue. To do so, Hounsell and Shresha proposed a headway adjusmen rule for a roue operaion ha concurrenly considers hree adjacen buses (he curren bus, he forward bus, and he backward bus) (1). (1)

3 36 Transporaion Research Record 356 Roue 3 Roue 1 Roue Bus: Roue i Passenger : FIGURE Impacs of bus sequences over differen roues a a TSP-conrolled inersecion. Their proposed rule grans a prioriy o he bus behind is schedule on he basis of he headway beween he curren bus and he las preceding bus. In heir model, he approaching bus will be given a prioriy if is forward headway is larger han he backward headway. However, for a muliroue scenario, he decision o gran a prioriy involves more complex issues. Figure illusraes a scenario in which muliple buses from differen roues are approaching a TSP-conrolled inersecion. Their arrival sequence a he arge inersecion may creae a dilemma for he TSP conrol sysem. For example, he Roue 3 bus is behind schedule, bu he Roue 1 and Roue buses are ahead of schedule. According o he exiing conrol principle, a prioriy should be provided o he Roue 3 bus, bu no o he Roue 1 and Roue buses. However, a prioriy o Roue 3 bus will ineviably force he Roue 1 and Roue buses, called prioriy-driven buses, o pass hrough he inersecion, which may degrade he service reliabiliy of hese wo bus roues. Noe ha a prioriy provided o he major road will cerainly increase he delay of vehicles on he cross sree. Thus, how o properly make a prioriy decision on he basis of he overall sysem benefis becomes an imporan issue for TSP operaions. The model presened was developed o address his issue. Model Developmen The goal of he proposed conrol sysem is o use he TSP conrol o reduce bus headway variance and consequenly minimize he oal passenger waiing ime a he nex bus sops. Mos convenional TSP conrols provide a fixed bus-prioriy ime (i.e., 15 s) for green exension or red runcaion. Recen echnological advances, however, enable TSPs o provide varying prioriy imes, which promises o alleviae he conroller s dilemma wih he muliple-roue prioriy conrol scenario. Figure 3 illusraes he conrol srucure of he proposed sysem, in which he conrol module will be acivaed o process a prioriy decision a he end of a green phase according o he locaion and sequence of all deeced buses. In Figure 3, he variable R represens he communicaion ime among bus vehicles, signal conrollers, and he conrol cener; C is he reacion ime of signal conrollers. The decision oucome will be he number of buses graned prioriy and he required duraion for green exension or red runcaion. The conrol module is designed o make he prioriy decision on he basis of he available daa. The model assumes ha he locaions of all buses are available via he Global Posiioning Sysem or auomaic vehicle locaion sysems and ha he signal conroller is able o provide varying prioriy imes. The enire decision-making process for he TSP conrol module in response o muliple requess includes he following seps: Sep 1 Collec bus locaion daa and curren signal seings from he available communicaion sysem. Sep Esimae he maximal allowable duraion for green exension or red runcaion in erms of raffic condiions. To limi he impac of he prioriy on nonprioriy raffic volumes, he maximum allowed prioriy ime is deermined by he curren volume-o-capaciy (v/c) raio on he cross sree, as shown by Equaion : ( vc) i g g pq, gr pq, pq, β g p,q = green duraion of nonprioriy phase p in cycle q wihou prioriy, gr p,q = green reducion in nonprioriy inersecion approach caused by prioriy exension, and β = maximum allowed v/c raio on he cross sree afer prioriy. The minimum green ime is se as shown by Equaion 3 o ensure pedesrian safey: g gr min > p, q (3) pq, pq, min is he minimal green duraion of he nonprioriy phase. ()

4 Lin, Yang, Chang, and Zou 37 GPS Daa Conrol Module Prioriy Decision P: No prioriy P1: Only Bus 1 receives prioriy P: Bus 1, receive prioriy P3: Bus1,, 3 receive prioriy G R Signal Conroller R + C Variable Prioriy Time P3 P P1 P Bus 3 Bus 1 Bus Daa Updae FIGURE 3 Signal conrol logic of proposed TSP sysem. Sep 3 Deec he approaching buses and heir curren locaions a few seconds (he sum of communicaion ime C and reacion ime R plus he maximal allowable duraion) before he end of a green phase. Sep Esimae he poenial benefis of graning a prioriy o a differen number of deeced buses. The purpose of his sep is o esimae he resuling benefis if a prioriy of green exension or red runcaion for a specified lengh is graned o he major roue. Depending on he seleced crierion, one can esimae he delay from he perspecive of he ransi users, passenger car users, or he oal social benefis of roadway users. As he focus of TSP conrol is o minimize he headway variance of each bus roue, he firs sep o develop he conrol logic is o compue he resuling headway of each bus, given he curren bus locaions, if graned a prioriy. Sep.1 Calculae he headway of each deeced bus under an inended green exension or red runcaion. Assuming ha boh he forward and backward buses will keep heir curren driving condiions during he prioriy period, one can calculae he esimaed headway for each bus afer TSP conrol as shown in Equaions and 5: f f h ( k) = h ( k) + f ( k) SB ri, ri, ripq,,, ripq,,, () { } b b SB h ( k) = max h ( k) f ( k), (5) ri, ri, ripq,,, ripq,,, hr,i(k) f and hr,i(k) b = acual forward and backward headways, respecively, of bus i on roue r a sop k before receiving signal prioriy; r,i,p,q S B = ime savings of bus receiving prioriy a phase p of cycle q; and f r,i,p,q (k) = se of binary variables represening prioriy saus. Equaion is formulaed o reflec he fac ha if he subjec bus is sopped by a red signal, he acual headway o is forward bus will be increased (i.e., i will be longer han he arge headway); oherwise, he acual headway will remain unchanged. In oher words, when a subjec bus ges he prioriy and does no sop a he inersecion, he headway will be unchanged. Equaion 5 is consruced on he same noion. Given a deeced bus arrival sequence, he prioriy saus of each bus can be expressed as shown by Equaion 6: f ripq,,, eg pq, e,,, ( k)= 1 oherwise ripq e r,i,p,q is he required exra green ime for bus i o pass he inersecion a he end of a green phase and eg p,q denoes he addiional green duraions for all deeced buses, which need o be opimized. If f r,i,p,q (k) is equal o zero, hen bus i ges he prioriy. Single-bus prioriy and muliple-bus prioriy are disinguished by e r,i,p,q and eg p,q, respecively. (6)

5 38 Transporaion Research Record 356 The ime savings of each bus receiving a prioriy saus can be compued by Equaion 7: SB ripq,,, r pq, eripq,,, if prioriy sraegy isgreen exension = eripq,,, if prioriy sraegy is red runcaion r p,q is he red ime of phase p. The ime savings by a green exension is generally much larger han wih a red runcaion when he bus volume exceeds 6 vehicles/h (). Sep. Esimae he average passenger waiing ime a bus sops. The second ask a his decision sep is o compue he average waiing ime of passengers for each roue wih and wihou receiving signal prioriy, which can be calculaed wih Equaion 8: f b ( hri, ( k) ) + ( hri, ( k) ) f b ( hri,( k) + hri,( k) ) f b if hri,( k) >θ r,and hri,( k) >θr, ( ) N + h b k ri f b if hri,( k) θ r,and hri,( k) >θr α ri, ( k) =, ( ) N + h f k ri f b if hri,( k) >θr,and hri,( k) θr f b N if hri,( k) θr,and hri,( k) θr α r,i (k) = average waiing ime of passengers for each roue, θ r = hreshold o deermine if bus bunching for each roue exiss, and N = posiive consan for he resuling penaly. The oal passenger waiing ime for differen roues a he nex sop can be expressed by Equaion 9: ck ( ) = β c α ( k) r Rpq, r rik,, ri, i Irpq,, R p,q = se of deeced bus roue, I r,p,q = se of deeced bus vehicles, β r = weighed facor of each roue, and c r,i,k = number of passengers from bus i when bus arrives a sop k. Sep.3 ( 7) (8) (9) Compue he delay reducion for bus passengers and passenger car drivers in he arge arerial segmen. Assuming ha he arrival rae of passenger cars o he TSP inersecion is uniformly disribued when hese buses are graned a prioriy, he oal person delay reducion in he arerial can be approximaed by Equaion 1: SPC ripq,,, = r eg pq, pq, eg pq, if prioriy sraegy is green exension if prioriy sraegy isred runcaion ( 1) Thus, he oal person delay reducion for passenger cars on he arerial when receiving prioriy wih ransi vehicles can be shown as by Equaion 11: PC PC PC SPC PC d = TV n q (11) R ripq,,, pq, TV PC = ime value of passenger car drivers, n PC = average number of persons per passenger car, and q PC p,q = esimaed queue of passenger cars. q PC p,q can be esimaed wih he model proposed by Chang e al. (13). The person delay reducion of bus passengers wih a prioriy signal is calculaed wih Equaion 1: B B B dr = TV nri, ( k ) SB ripq,,, fripq,,, ( k) (1) r Rpq, TV B is he uni ime value of bus passengers and n B r,i(k) is he average number of on-board bus passengers. Sep. Esimae he increased delay for passenger car riders on he cross sree. Graning a prioriy o buses in he arerial will ineviably reduce he green ime on he cross sree, which will consequenly cause exra delay for cross-sree vehicles. The compuaion of he exra delay is based on wo separae pars: one is he increased delay of hose iniial queuing vehicles as a resul of he reducion of green ime; he oher is he exra delay of hese vehicles approaching he inersecion during he TSP execuion period. The average delay per queuing vehicle can be expressed by Equaion 13a: WPC1 ripq,,, = eg pq, if prioriy sraegy is greenexension eg + if prioriy sraegy is red runcaion r pq, pq, ( 13a) Wih he assumpions ha vehicles arriving a he cross sree during he TSP execuion period follow a uniform disribuion and each cycle can clear he queue a he cross sree, he average delay per approaching vehicle can be calculaed by using Equaion 13b: WPC ripq,,, eg pq, if prioriy sraegy is green exension = r eg pq, + pq, if prioriy sraegy isred runcaion ( 13b)

6 Lin, Yang, Chang, and Zou 39 Hence, one can approximae he increased person delay for passenger cars on he cross sree wih Equaion 1: ( ) PC PC PC d TV n q PC1 WPC1 q PC WPC = + (1) I pq, ripq,,, pq, ripq,,, q PC1 p,q and q PC p,q denoe he queue esimaion of queuing or approaching vehicles, respecively, which can be esimaed wih he model proposed by Chang e al. (13). By using Equaions 9, 11, 1, and 1, one can calculae he oal person delay reducion for on-board bus riders, hose waiing a he downsream bus sop, and hose passenger vehicle users a he arge inersecion during he TSP execuion period if given a prioriy green exension or red runcaion for p,q eg seconds, as shown by Equaion 15: PC PC B NON D = d d + d + ck ( ) c ( k) R I R (15) c NON (k) is he oal passenger waiing ime of all bus roues wihou prioriy. Bus passenger waiing ime saving could be one of he major conribuors o he oal person delay reducion. Therefore, Equaion 15 includes he passenger waiing ime savings. Sep 5 Deermine he prioriy sraegies and he opimized green duraion for he prioriy requess. This sysem will gran a bus prioriy on he major road for an exended p,q eg green seconds, caused by green exension or red runcaion, if he following crieria are saisfied: 1. To limi raffic disrupions on he cross sree, a red runcaion and green exension canno be aken simulaneously in one signal cycle;. The oal bus passenger waiing ime will be reduced; and 3. The oal person delay will no be increased by a TSP execuion. Sep 6 Execue he TSP conrol sraegy. The final opimal decision would be sen o he local signal conroller or conrol cener o execue he TSP conrol, including he exended green duraion for he prioriy phase and he green ime reducion for he nonprioriy approach. Case Sudy Experimenal Design To illusrae he applicabiliy and efficiency of he proposed sysem, his sudy used VISSIM as an unbiased ool for performance evaluaion. The auhors used he VISSIM-COM inerface o develop a program o simulae bus operaions and signal conrol logic wih VB.NET and he MYSQL daabase. During he simulaion, he program deecs and records he real-ime bus locaions, auomaically compues he ime-varying headway of each bus for each roue, and adjuss he signal imings according o he bus arrival sequence. Figure shows he flow char of he enire simulaor and decision process for he proposed TSP operaions. To search he opimal feasible soluion efficienly, each candidae soluion organized in he ascending order would be esed sequenially. Wei er Road in Jinan was seleced as a es case o evaluae he effeciveness of he proposed decision process for bus signal prioriy (Figure 5). The secion of ineres is abou 3 km long; however, o improve he accuracy of he simulaion, abou.5 km of Wei er Road and is conneced arerials were included in he simulaion model. The key raffic paern and geomeric feaures in he simulaion model are lised below: The oal ravel disance of bus roues is abou 6. o 6.8 km; The 3-km sudy secion of Wei er Road has six wo-way lanes; The v/c is abou.7; Sar VISSIM wih COM inerface Save bus locaion ino MYSQL daabase from VISSIM Green phase ends? Yes Soluion se wih waiing ime delay saving and oal person delay reducion (Ascending order by Eq. (9) and (15)) Soluion se is empy? No Delee he soluions wih negaive oal person delay reducion No Esimae he sequences and headway of deeced buses based on hisorical daa Calculae he passenger waiing ime by Eq. (9), v/c raio on he crossing sree Esimae oal person delay by Eq. (15) Decide maximal allowed prioriy ime Coninue wih he simulaion Yes Preserve feasible soluion se Selec he opimum from he feasible soluion se Updae he signal iming plan using VISSIM-COM No prioriy and no acion FIGURE Flowchar of simulaion evaluaion.

7 Transporaion Research Record 356 FIGURE 5 View of Wei er Road in Jinan. The mean headway is abou min, and he variance observed on he arge arerial ranges from o 6 min; There are eigh bus roues in wo direcions; No bus exclusive lane is available on he arerial; There are six inersecions along he arerial, only wo of which can offer bus prioriy; The duraion of simulaion ime is abou 3,6 s; The equivalen passenger number for buses and passenger cars B (k) = and npc = /vehicle, respecively; is n r,i The hreshold of bus bunching for each roue is θr = 1.5 min; The ime value of bus passengers and passenger car users is TVB =.6 and TVPC = 1., respecively; The penaly for occurrence of bus bunching is N = 1 min; and The sum of communicaion ime and reacion ime ( C + R) is 3 s. The hreshold of bus bunching, he weighing facor of each bus, and values of ime were obained from he field survey; he penaly for occurrence of bus bunching was deermined by increased waiing ime according o hisorical daa. The communicaion ime and reacion ime are discussed in he lieraure (3). Experimenal Resuls For conrol efficiency and convenience of case illusraion, his sudy only considered he TSP of green exension in he experimenal analysis. The proposed sraegy was evaluaed wih he following hree scenarios: Scenario 1. No prioriy conrol, Scenario. Prioriy o all requesed buses (15 s for green exension), and Scenario 3. The proposed conrol wih variable green exension. Several measures of effeciveness were seleced for model evaluaion: headway variance, passenger waiing ime, oal bus passenger delay (including waiing ime and ravel delay), and oal person delay of he enire nework. Figure 6 compares he resuls among differen scenarios. Some key findings are summarized below: 1. The proposed conrol in his sudy can ouperform he oher wo mehods in erms of reducion in bus headway variance (1.9%), passenger waiing ime (.8%), oal bus passenger delay (abou 6.7%), and oal person delay of all vehicles (abou 9.9%) (Figure 6).. Despie he lack of difference in average headways among he hree mehods, he variance of headways wih he proposed sraegy is far less han ha under he oher wo mehods (Figure 6a). The reducions in variance for Roues, 1, and 11 are up o 1.7%, 31.8%, and.9%, respecively, which is consisen wih he reducion in he oal passenger waiing ime (Figure 6b). Furhermore, he probabiliy of having bus bunching under he scenario of graning prioriy o all buses is 5% more han wih he proposed sraegy. 3. Because he proposed conrol mehod concurrenly considers he impacs of signal prioriy on buses and passenger cars, i can also achieve a beer performance han he oher wo mehods wih regard o reducion in bus passenger delay (Figure 6c). Noe ha bus passenger delay is he sum of increased passenger waiing ime and ravel ime. The proposed TSP model can significanly reduce he average waiing ime because in he prioriy-o-all-buses cases some on-ime or early buses are forced o obain prioriy, which ineviably increases he variance of bus headways and hus he average waiing ime for passengers a he sops in he downsream link.. Figure 6d reveals ha he proposed TSP sraegy produces less oal person delay for he enire arerial during he operaional period compared wih he prioriy-o-all-buses TSP. The laer mehod may cause significan impacs on cross-sree raffic flows ha could lead o a significan increase in he oal vehicle delay. Sensiiviy Analysis To evaluae he reliabiliy and effeciveness of he proposed sraegy, he model s sensiiviy was esed wih respec o he following hree key facors: The raio beween bus volume and oal passenger car volume, Traffic volume a he arerial, and Traffic volume on he cross sree. A summary of key variables for each scenario is lised in Table 1. As shown in Figure 7, regardless of he raio beween bus and raffic volumes, he proposed TSP sraegy can always reduce he bus passenger delay (he sum of he waiing ime and ravel ime delay).

8 he proposed model 1 prioriy o all buses wihou prioriy variance (min) he index of roues (a) he proposed model 1 prioriy o all buses 13 1 wihou prioriy waiing ime (min per person) he index of roues (b) delay (h) proposed model prioriy o all buses (c) wihou prioriy proposed model prioriy o all buses (d) wihou prioriy delay (h) FIGURE 6 Comparisons of hree TSP mehods for (a) disribuion of headway variance, (b) bus passenger waiing ime, (c) oal bus passenger delay, and (d) oal person delay of he enire arerial.

9 Transporaion Research Record 356 TABLE 1 Deailed Descripions of Scenarios A1 A8 Conclusion Scenario Traffic Volume a Prioriy Approach (vph) Bus Raio (%) Traffic Volume on Crossing Sree Number of Bus Roues in Two Direcions A1 1, 1 6 A, A3 1, 1 A, 7 1 A5 1, 3 16 A6, A7 1, 16 A8, 7 16 Noe: vph = vehicles per hour. However, he proposed conrol sraegy yields a more significan reducion in he oal nework person delay if he raio beween bus and oal raffic volumes exceeds %; such benefis will increase wih he oal inersecion raffic volume. The comparison beween differen raffic volumes in he prioriy approach reveals ha a larger delay reducion can be achieved wih he proposed sraegy under he scenario of having high raffic volume on he primary arerial and a high percenage of buses. This paper presens a headway-based TSP conrol sysem for muliple bus requess from differen roues. The proposed model aims o minimize he passenger waiing ime a bus sops wihou causing excessive impacs o he cross sree. The overlaps of muliple bus roues means ha he convenional firs-come, firs-served sraegy ofen fails o offer an efficien conrol because no every bus in he arge link is behind schedule. The proposed model uses he variable prioriy-ime echnique, which is capable of performing a more precise conrol and can give parial prioriy o deeced buses. To minimize he negaive impac o he enire inersecion, he proposed TSP sraegy also compues he oal person delay o ensure is efficiency. The performance evaluaion, which used field daa from Jinan under a simulaed plaform, clearly shows ha he proposed TSP conrol can significanly reduce he passenger waiing ime in he scenario of having muliple prioriy requess from muliple ransi roues. An exensive sensiiviy analysis revealed ha he proposed TSP can yield significan benefis o boh bus passengers and all users in he sysem if he raio beween bus and raffic volumes exceeds %. Such benefis are generally expeced o increase wih oal inersecion volume. Fuure research will address he following hree issues: (a) how o gran signal prioriy while reducing he impacs on he downsream inersecion (i.e., graning prioriy o a lae bus will also release more passenger cars, which may lead o congesion a he downsream Reducion (h) v=1 v= 1% % 3% % raio beween bus and oal passenger cars volume (a) v=1 v= Reducion (h) % % 3% % raio beween bus and oal passenger cars volume (b) FIGURE 7 Comparisons of performance wih and wihou prioriy: reducion in (a) bus passenger delay and (b) oal person delay.

10 Lin, Yang, Chang, and Zou 3 inersecion, especially on coordinaed arerials); (b) validaion of he reliabiliy and effeciveness of he TSP sysem under various geomeric configuraions and raffic demand paerns hrough more exensive experimens or field ess; and (c) design of a bus progression conrol sysem on urban arerials ha is based on bus dwelling ime a sops and global posiioning sysem bus locaion daa. Acknowledgmens The auhors express heir appreciaion for daa suppor from Jinan Public Transporaion Company and funding suppor from he China Scholarship Council. References 1. Hounsell, N. B., and B. P. Shresha. A New Approach for Co-Operaive Bus Prioriy a Traffic Signals. IEEE Transacions on Inelligen Transporaion Sysems, Vol. 13, No. 1, 1, pp Abkowiz, M., H. Slavin, R. Waksman, L. Englisher, and N. Wilson. Transi Service Reliabiliy. 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