Improving synchronized transfers in public transit networks using real-time tactics

Transcription

1 Improving synchronized trnsfers in public trnsit networks using rel-time tctics Zhongjun Wu 1,2,3, Grhm Currie 3, Wei Wng 1,2 1 Jingsu Key Lbortory of Urbn ITS, Si Pi Lou 2#, Nnjing, , Chin 2 School of Trnsporttion, Southest University, Si Pi Lou 2#, Nnjing, , Chin 3 Public Trnsport Reserch Group, Institute of Trnsport Studies, Deprtment of Civil Engineering, Monsh University, 23 College Wlk, Clyton Victori 3800 Austrli Emil for correspondence: grhm.currie@monsh.edu Abstrct This work presents n optimiztion procedure with rel-time opertionl tctics to decrese or eliminte bus opertionl devition from schedules, nd to increse the ctul occurrence of synchronized trnsfers t plnned network trnsfer points. An rrivl time devition-bsed dynmic speed djustment model is proposed for updting vehicle operting speed in rel time. Three opertionl tctics, including chnging speed, holding nd skip stopping strtegies re tested in the optimiztion using rel-time informtion. A cse study tests how close the vehicle s running sttus keeps up with the plnned schedule nd how much delys chnge fter deploying the tctics tested. Results show tht by pplying the proposed methodology, the length of devition intervl for direct trnsfer cn be significntly incresed on two routes tested by between 798% nd 353%. Buses cn rrive t trnsfer points s plnned while deprture time devition rnges from -600s/+417s nd from -600s/+839s for the two routes tested. Ares for future reserch re identified. Key word: public trnsport, trnsfer optimiztion, opertionl tctics, synchronized trnsfers 1 Introduction Public trnsit (PT) systems re plying importnt roles in improving urbn mobility, reducing rod trffic ccidents, decresing ir pollution nd fostering more livble cities. It is pprent tht dvnced, relible, convenient, nd comfortble PT systems cn ttrct more privte cr users. A mjor feture of successful PT systems is convenient nd well coordinted (or synchronised) trnsfers between public trnsport modes t sttions nd interchnge points. Bus systems operting in mixed trffic on rods dominte most public trnsport systems provided in cities. One of the most chllenging problems of providing PT in cities is how to operte buses relibly in mixed trffic (Ceder, 2007). The dynmic, stochstic, nd uncertin chrcters of trffic often mke bus schedules errtic nd the plnned synchronized PT trnsfers do not lwys mterilize in prctice. More thn 50 yers go Newell nd Potts (1964) hd lredy pointed out tht if no control strtegies re used, even very smll disturbnce

2 cn cuse serious off-schedule running. To cope with this sitution, they proposed rel time opertionl phse imed t improving the trnsfer relibility using opertionl tctics with reltime dt. With the recent development of informtion nd communiction technology obtining rel-time dt nd deploying online tctics is now fesible, however pproches to mke these tctics work in prctice re needed to enble deployment of these methods. This reserch pper presents n optimiztion procedure with rel-time opertionl tctics to decrese or eliminte bus opertionl devition from schedules, nd to increse the ctul occurrence of synchronized trnsfers t plnned network trnsfer points. The pper is structured s follows; firstly, previous reserch in the field is outlined, then some concepts of PT route performnce relevnt to the modelling re introduced. This is followed by n description of the opertionl time devition predictive model the dynmic speed djustment model. A cse study using routes on the Beijing PT network is then outlined nd is used to ssess the benefits of methodology. The pper ends with summry nd conclusions including identifiction of res for future reserch. 2 Reserch Context Two mjor phses hve been identified where plnning of public trnsport might be improved; the plnning phse nd the opertions phse (Ceder et l.,1986; Ceder,2007). The plnning phse consists of network design nd timetble creting two ctivities bsed on priori dt. Network design ims to reduce trnsfer wlking time (Ceder, 2015; Chowdhury et l., 2013, Zho, 2004) by mesuring of network integrtion, integrting the physicl connection of trnsfers nd optimizing the lyout of trnsfer centers. Timetble development is criticl prt of the plnning phse with focus on improving schedule relibility of PT routes by developing mximum synchronized fixed timetble (Domschke, 1989; Voss, 1992; Ceder et l.,2001) or timed trnsfer (Vuchic, 2005; Abkowitz et l.,1987, Mxwell, 1999), nd optimizing slck time (Lee,1991; Zho,2006) within the schedule. Becuse of the dynmic, stochstic, nd uncertin chrcteristics of trffic, plnned synchronized PT trnsfers do not lwys mterilize in prctice. Indeed, more thn 50 yers go, Newell nd Potts (1964) hd lredy pointed out tht if no control strtegies re used, even very smll disturbnce cn cuse serious off-schedule running. To cope with this sitution, n opertions phse ws proposed by reserchers iming t improving trnsfer relibility using opertionl tctics with rel-time dt. The more recent development of informtion nd communiction technology mkes obtining rel-time dt nd deploying online tctics more fesible in contemporry opertions plnning. However mjor chllenge remins in how to best go bout this. In the opertions phse, recent studies focus on using rel-time control strtegies with vilble informtion. Dessouky (1999) showed the potentil benefits of rel-time control of timed trnsfers by using intelligent trnsporttion systems 0, nd exmined simulted systems using holding nd disptching (2003). Reserch by Hds et l. (2010), Ceder et l. (2013), Liu et l.(2014;2015), nd Nesheli et l.(2014) lso showed tht by using selected opertionl tctics, the totl pssenger trvel time cn be considerbly reduced nd the frequency of direct trnsfers cn be significntly improved.

3 Though the opertions phse cn contribute gretly to the improved occurrence of synchronized trnsfers t trnsfer points, their remin two mjor gps in reserch in this field: firstly, existing studies forecst only vehicle rrivl times t trnsfer points s reference. In prctice relibility needs to be focussed on wider set of loctions nd for deprtures s well s rrivls. Secondly, existing reserch only considers the effects of improved opertions on the number of direct trnsfers or totl pssenger trvel time. The ctul schedule dherence performnce of the vehicle is not considered. Yet this ffects ll pssengers on the bus route who re not trnsferring (in mny cses in the rel world this cn represent mjority of users). This is clerly mjor omission in existing reserch. In this study, the bove issues re ddressed in n pproch to optimise synchronised trnsfers using rel time opertionl tctics. 3 Conceptul explntions This nlysis dopted timing points s the loctions most suitble to djust bus opertions in rel time. Other reserchers e.g. Liu et l (2014) hve used trnsfer points s the nodes to improve opertionl performnce. However, this method my reduce the prediction ccurcy, in the cse of long distnce between the ctul loction of vehicle nd trnsfer point. In ddition there re typiclly mny more timing points on bus routes thn trnsfer points hence more chnces to improve opertionl relibility in rel time. Timing points chosen on bus routes to be control points in order to prevent bunching nd to hold buses if they re running erly to schedule. With the use of the time-point, it is possible to obtin more ccurte prediction of opertionl devition. Time-points my be terminl, trnsfer points, key stop/sttion with lrger pssenger lighting nd/or bording, or other key plces on bus route. A public trnsit route cn be divided into severl sections by time-points, nd ech section is regrded s control unit in this reserch. Besides, in order to describe with convenience, the no-time-point is clled stop nd the prt between two consecutive stops or between stop nd time-point is clled segment. Therefore, the typicl structure of public trnsit route is shown in Figure 1. Figure 1 Structure of typicl public trnsit route Time-point Stop Segment 4 Model In this section, two different models re proposed, including: 1) the opertionl time devition predictive model, nd 2) the time devition-bsed dynmic speed djustment model. The first one is built to forecst opertionl time devition of vehicle rrivl t ech time-point with some rel-time informtion, such s pssenger demnd nd trffic condition. The second one is

4 designed for deciding which kind of speed chnge (speed up or down) will be chosen nd recommending wht trget speed to dopt for bus opertions. 4.1 Nottion Some nottions, which will be used lter in this pper, re shown s following: k = The code of time-point; T ( ) k = Plnned rrivl time t time-point k, which is given in timetble; T( k ) = Predictive rrivl time t time-point k; T ( ) k = Actul rrivl time t time-point k; d ( ) k = The rrivl devition t time-point k; tx ( ) = Dwell time t plce x, which could be stop or time-point; b = Ded time required for vehicle decelertion nd ccelertion; = B Mrginl dwell time per bording pssenger; = Mrginl dwell time per lighting pssenger; A Bx ( )= Estimted number of bording pssenger t plce x ; Ax ( ) = Estimted number of lighting pssenger t plce x ; ( k ) = The rnge of trvel time when vehicle running-lte between time-point k nd k+1; ( k ) = The rnge of trvel time when vehicle running-erly between time-point k nd k+1; b t i = The chnge of trvel time in segment i; L = i The distnce of segment i; V = The plnned verge trvelling speed in segment i; Pi V = The recommended verge trvelling speed in segment i; Ri V = The mximum verge trvelling speed in segment i; i mx V = The minimum verge trvelling speed in segment i; i min d ( ) b g x = The ctul rrivl time devition t trnsfer point x without tctics; d ( ) x g = The ctul rrivl time devition t trnsfer point x with tctics 4.2 Assumptions Without loss of generlity, the following ssumptions re mde: A1:A mximum synchronized timetble is creted for PT network, which mens ll the rrivl time of ech trip t every time-point is known. A2:It is ssumed tht the rel-time estimtion of pssenger origin-destintion mtrix, vehicle rel-time loction nd trffic condition long PT route re vilble. A3:Some opertionl fctors, such s the mximum/minimum verge trvelling speed, nd verge plnned trvelling speed, re vilble.

5 A4:PT opertors cn deliver timely suggested opertionl tctics informtion to drivers without very long dely. A5: Driver will comply with the recommended opertionl tctics provided by PT opertors, nd the rection time cn be ignored. A6: Pssengers who rrive fter the deprture time will wit for the next vehicle of this route. 4.3 The opertionl time devition predictive model Understnding the opertionl sttus of vehicle is one of bsic tsks for opertors to conduct when running vehicles in rel time. Unfortuntely, it is still problem for reserches nd opertors to figure out how to obtin more ccurte prediction of trvel time. In order to increse the ctul occurrence of synchronized trnsfers, some reserches chose connectionl vehicle running sttus s comprison. It cn mke two or more vehicles meet successfully t trnsfer point, without considering the problem whether vehicles run on time or not. From the perspective of public trnsit system, obtining synchronized time-tble is the mjor gol. Hence, the synchronized time-tble will be chosen s preference in this pper. The opertionl time devition, which is defined s the difference between predictive nd plnned rrivl time t time-point, is regrded s predictive indictor. Consequently, the time devition of vehicle t time-point k+1 cn be determined s formul (1): d ( k 1) T ( k 1) T ( k 1) (1) The predictive rrivl time t time-point k+1 cn be got s formul (2). T ( k 1) T ( k) t( x) L V i Pi The dwell time t time-point or stop x cn be obtined s formul (3). (2) b B B( x) A A( x), single-door, if Bx ( ) 0 or Ax ( ) 0 0, single-door, if B( x)= A( x )=0 t( x) b mx( B B( x), A A( x)), double-door, if Bx ( ) 0 or Ax ( ) 0 0, double-door, if B( x)= A( x )=0 Hence, ccording to the formul (1)~(3), the opertionl time devition of vehicle rrivl t time-point k+1 cn be predicted with some rel-time public trnsit informtion. 4.4 Deployments of opertionl tctics (3) With the use of the predictive model, it is extremely effortless to gin the opertionl time devition rrivl t every time-point. The rel-time speed opertionl tctics, including speed chnge, skipping stop nd vehicle holding t trnsfer point, will be recommended to driver bsed on the outcome of predictive model The dynmic speed djustment model

6 The updte rules for verge running speed djustment re given s follows: Sitution 1: running lte, nmely, d( k 1) 0 If ( k) d ( k 1) V L( L V t) Ri i i Pi i else ( k) d ( k 1) V V Ri imx Sitution 2: running erly, nmely, d( k 1) 0 If ( k) d ( k 1) b V L ( L V t ) Ri i i Pi i else ( k) d ( k 1) V b V Ri imin Sitution 3: running on time V Ri End V Pi Where, ) is the chnge of trvel time, which is obtined by decomposing time devition ti in proportion, it cnnot exceed to the rnge of trveling time, b) ( k ) nd ( k) re the b rnge of trvelling time in ech section if vehicle trvel with mximl nd miniml speed respectively, which cn be determined s following: ( k) ( Li VPi Li Vi mx ) (4) b( k) ( Li Vi min Li VPi ) (5) Skip stopping tctics In sitution 1, if the vehicle is still running lte with the ppliction of speed chnge tctics, the skip stop tctic should be deployed t some stops. The rules of choosing stop to be skipped re: ) compre the number of lighting pssenger t every stop, nd choose the stop hving the lest number to implement skipping tctic, b) otherwise, in order to decrese the dditionl wlking time of pssengers who wnt to light t skipped stop, two consecutive stops cnnot implement skip stop tctic t the sme time Holding vehicle t trnsfer point In sitution 1, if the vehicle is still running lte with the deployment of speed chnge nd stop skipping, the connecting vehicle should be held, nd in sitution 2, if speed chnge cnnot meet the devition, the current vehicle should use holding tctic t the trnsfer point. The holding tctic cn be implemented t the trnsfer point until it s time to leve ccording to pln or be kept longer if the trnsfer vehicle is required, but the holding time cn t exceed the mximum llowble vlue.

7 5 Cse study A cse study is dopted to ssess the effectiveness of the djustment model nd its potentil deployment. This cse study reltes to rel-time PT network in Beijing, Chin, which hs been used in previous studies (To Liu, 2014). The PT network of the cse study is illustrted in Figure 2. It consists of 2 bus routes with trnsfer point. Route 694 runs from north to south nd Route 728 runs from west to est. Time-point 5 is trnsfer point, which provides trnsferring service for the pssengers of the two Routes. Figure 2 Schemtic digrm of cse study bus routes TPX XXX Route 694 Route 728 Time Point NO. Time Point Stop Stop NO. TP TP2 201 TP TP TP TP TP TP6 5.1 Dt collection The dt include informtion on routes, vehicles, nd pssengers. It is worth to note tht in this study some dt re collected from the reserch by Liu et l (2014) Route informtion Route informtion comprises route ID, route direction, the number of stops, stop ID, the distnce between two consecutive stops, nd plnned synchronized timetble Vehicle informtion All vehicles of the two routes re equipped with GPS devices, so they cn shre their reltime loction nd speed informtion with the control center. The informtion is updted in intervls of 30s. The collected informtion of vehicle includes vehicle ID, driver ID, plnned hedwy, vehicle loction, nd verge running speed in ech segment. Mximl nd miniml verge trveling speed ought to be predicted with trffic condition nd vehicle chrcter.

8 5.1.3 Pssenger informtion Pssenger informtion comprises the number of pssengers lighting nd bording t ech stop nd the number of pssengers trnsferring t ech trnsfer stop. In prctice, the pssenger informtion should be forecst with the history pssenger demnd dt, for simplicity, the dt collected from IC or smrtcrds ws regrd s predictive. The collected dt re shown in Tble Principles Tble 1 Route, vehicle nd pssenger Informtion of PT Routes Plnned timetble Pssengers Distnce Stop between Arr. Time Dep. Time Bording Alighting stops(km) Route694, Hedwy=10 min, Vehicle ID: TP1 8:01:00 8:04: :07:15 8:08: :10:33 8:11: TP2 8:15:24 8:16: :19:50 8:20: TP3 8:23:26 8:25: :29:10 8:29: :33:58 8:34: TP4 8:38:19 8:40: :47:39 8:48: :52:18 8:52: :54:40 8:55: :57:53 8:58: TP5 9:06:28 9:07: Route728, Hedwy=9 min, Vehicle ID: TP6 7:59:20 8:00: :05:26 8:06: :09:10 8:09: :14:50 8:15: TP7 8:27:10 8:28: :32:10 8:32: :35:10 8:35: TP8 8:40:41 8:42: :47:36 8:48: :53:35 8:54: :57:03 8:57: :02:03 9:02: TP5 9:06:35 9:07: Tking the ctul opertionl sitution into considertion, the following principles will be used: Vehicle s ctul deprture time cnnot be erlier thn plnned t ny time-point. However, t ny stop, if vehicle s dwell time meets the demnd for pssenger lighting nd bording, vehicle is permitted to deprt stop erlier thn plnned. For simplicity, 120% nd 50% of plnned verge trveling speed re regrded s mximl nd miniml verge trveling speed, respectively. Besides, the mximl holding time of the two cse study routes re sme

9 with 60s. All vehicles hve single door for pssenger lighting or bording, nd the cpcity of vehicles re 60, including 40 sets nd 20 stnding. 5.3 Evlution of performnce As mentioned bove, in the predictive model, it dopts the plnned synchronized timetble s reference to forecst the opertionl time devition of the vehicle. Therefore, it is necessry to develop n evlution indictor, which cn describe how the opertionl sttus of vehicle chnges in reltion to the plnned schedule fter deploying the rel-time tctics. With the concept of opertionl time devition, the opertionl devition rtio is defined to ccess the deployment effect of tctics. The opertionl devition rtio cn be determined s following: R AT dg b( x) d ( x) 100% d ( x) b g (6) It is pprent tht the bigger the opertionl devition rtio is, the better the optimiztion is. If the opertionl devition rtio is equl to 100%, the running sttus of vehicle is coincident with the plnned schedule. 5.4 Implementtion nd results In the cse study, rel-time tctics re recommended to the current vehicle using the dynmic speed djustment model in vrious scenrios with different deprture time devition t the first stop of the route, menwhile, it is ssumed tht the trnsferring vehicle is ble to rrive t trnsfer point s plnned. Tking the vehicle deprture on time s reference, dd or reduce the devition of deprture time with n intervl of 30s every time. For erly deprture, tke the ctul sitution into considertion, the mximl devition is controlled s 10 min. For lte deprture, the intervl is dded to the devition grdully, until the direct trnsfer cn t be chieved t trnsferred point with ny of the rel-time tctics. The outputs of ech scenrio re segments deployed with the speed chnge, skipped stop, or holding time tctics t the trnsfer point, whether direct trnsfer or not, nd time devition of vehicle rriving t the trnsfer point. Here, the text includes two situtions; route 694 hs deprture devition nd 728 on time; nd route 728 hs deprture devition nd 694 on time. All the outputs re shown in tble 2 nd 3, respectively. It is worthy to note tht some devitions, which hve common tctics, re not listed in the tbles considering the spce limits for this pper.

10 Tble 2 outputs of cse study (trnsfer from route 694 to 728) R694 R728 Performnce Dep. time dev. t 1th stop (sec) Rel Time Tctics Direct trnsfer? Time Dev. t trnsfer point Dev. Rtio (%) Speed chnge segment Skipped stop Holding time with without with without -600 YES NO TP1-TP3(d)/TP4-TP5(u) YES NO TP1-TP2(d)/TP3-TP5(u) YES NO TP1-TP2(d)/TP3-TP5(u) YES NO TP1-TP2(d)/TP3-TP5(u) YES NO TP1-TP2(d)/TP3-TP5(u) YES YES TP1-TP2(d)/TP3-TP5(u) YES YES TP1-TP2(u)/TP3-TP5(u) YES NO TP1-TP2(u)/TP3-TP5(u) 101 YES NO TP1-TP5(u) 101 YES NO TP1-TP5(u) 101 YES NO TP1-TP5(u) 101\201 YES NO TP1-TP5(u) 101\201\301 YES NO TP1-TP5(u)) 101\201\301 YES NO TP1-TP5(u) 101\201\301 YES NO TP1-TP5(u) 101\201\301\402\404 YES NO TP1-TP5(u) 101\201\301\402\404 3 YES NO TP1-TP5(u) 101\201\301\402\ NO NO NOTE: 1) the sign (u) mens speed up; nd 2) the (d) mens speed down, the sme in Tble 3. Tble 3 outputs of cse study (trnsfer from route 728 to 694) R728 R694 Performnce Dep. time dev. t 1th stop (sec) Rel Time Tctics Direct trnsfer? Time Dev. t trnsfer point Dev. Rtio (%) Speed chnge Holding Skipped stop segment time with without with without -600 YES NO TP6-TP7(d) YES NO TP6-TP7(d) YES NO TP6-TP7(d) YES YES TP6-TP7(d) YES YES YES 0 n 90 TP6-TP7(u) YES YES 0 0 n 180 TP6-TP7(u) YES YES 0 0 n 240 TP6-TP7(u) YES YES TP6-TP7(u) 603 YES YES TP6- TP8(u) 603 YES NO TP6- TP8(u) 603\701 YES NO TP6- TP8(u) 603\701 YES NO TP6- TP9(u) 603\701 YES NO TP6- TP9(u) 603\701 YES NO TP6- TP9(u) 603\701\802 1 YES NO TP6- TP9(u) 603\701\802\ YES NO TP6- TP9(u) 603\701\802\ NO NO

11 The nlysis of results cn be divided into the two situtions: 1) Route 694 hs deprture devition nd 728 on time The deprture time devition of route 694 s vehicle rnges from -600s to 480s. the rrivl time devition t the trnsfer point is 78s without using tctics while the vehicle deprts on time t first stop, direct trnsfer fils becuse the vehicle needs more dwell time thn plnned for to permit pssenger lighting or bording. The direct trnsfer only cn be obtined when the deprture time devition rnges from -138s to -18s without tctics. However, using rel-time tctics, the direct trnsfer cn be successfully mde while devitions rnge from -600s to 477. The length of intervl increse is lmost 797.5%. Besides, the vehicle cn rrive t the trnsfer point s plnned with deployment of rel-time tctics while the deprture time devition rnges from -600s to +417s, clerly this is n importnt strtegy to improving the relibility of vehicle. 2) Route 728 hs deprture devition nd 694 on time As tble 3 shows, the deprture time devition of route 728 s vehicle rnges from -600s to 930s. If the vehicle deprts from first stop on time, it cn rrive t the trnsfer point s plnned without using ny tctics. The direct trnsfer cn be obtined when the deprt time devition rnge from -62s to 273s without tctics. After using rel-time tctics, the rnge is from -600s to 917. The length of intervl expnds by lmost 352.8%. Wht s more, the vehicle cn rrive t the trnsfer point s plnned with deployment of reltime tctics while deprture time devition rnges from -600s to 839s. 6 Conclusions Plnned synchronized trnsfers do not lwys mterilize due to the stochstic chrcter of trffic flow, driver behvior nd fluctution of pssenger demnd on feeder bus routes. Missed trnsfers frustrte pssengers s well s reducing the potentil for encourging new users onto the public trnsport system. This work presents n optimiztion procedure with rel-time opertionl tctics to decrese or eliminte vehicle opertionl devition, nd thus to increse the ctul occurrence of synchronized trnsfers in plnned PT networks. An rrivl time devition-bsed dynmic speed djustment model is proposed for updting vehicle speed. Three opertionl tctics, chnging speed, holding nd skip stopping, re used in the optimiztion with rel-time vehicle speed nd loction informtion. The cse study tests how close the vehicle keeps with plnned schedules nd how much delys chnge fter deploying tctics. Results show tht by pplying the proposed methodology, for the two routes explored, the length of devition intervl for direct trnsfer cn be significntly incresed 797.5% nd 352.8%, respectively. Vehicles lso cn rrive t trnsfer point s plnned with ppliction of proposed methodology while deprture time devition rnge from -600s to 417s for route 694, nd from -600s to 839s for route 728. The methodology described in this pper is first step in wider project which ims to develop new pproches to optimising the doption of rel time strtegies in bus services to improve relibility nd trnsfer synchronistion. There re number of wys tht methods of this kind

12 cn be improved. Clerly wider ppliction of the pproch to lrge set of dt would improve our understnding of the performnce of the pproch developed. There re lso wider rnge of potentil opertionl tctics which might be employed including express opertion nd in terms of fleet deployment pproches such s ded heding. In ddition the nlysis might consider rel time provision of dt to drivers wherever they re on route, rther thn t timing points s hs been used in this pper. In theory, dopting GPS nd rel time in cb communictions with bus drivers, it my be possible to updte bus drivers on how they my djust opertions to better drive to trnsfer points to chieve better synchronistion. Indeed if one considered possible future involving utonomous vehicles including driverless buses, procedures s described in this pper might be deployed to inform vehicle driving instructions using direct communictions with the driving control system. Overll the methods described in this pper provide the bsis to improve bus opertions by mking the most of new technologies to provide nd rect to rel time informtion. Advnced pproches of this kind hve the potentil to significntly improve relibility nd network performnce of trnsit systems into the future. Acknowledgements The study is supported by the key project of Ntionl Nturl Science Foundtion of Chin (No ) nd the Ntionl High-Tech Reserch nd Development Progrm of Chin (No. SS2014AA110303). The study visit of Mr Wu to the Institute of Trnsport Studies is lso supported by Monsh University. The uthors would lso like to thnk the reviewers of ATRF for their inputs on the reserch. Reference Ceder, A. 2007, Public Trnsit Plnning nd Opertion: Theory, Modeling nd Prctice. Butterworth-Heinemnn, Elsevier, Oxford, United Kingdom,. Ceder, A., Wilson, N.H.M., Bus network design. Trnsporttion Reserch Prt B 20, Ceder, A., Public Trnsit Plnning nd Opertion: Theory, Modeling nd Prctice. Butterworth-Heinemnn, Oxford, UK. Ceder, A. 2015, Public Trnsit Plnning nd Opertion: Modeling, Prctice nd Behvior, 2nd ed. CRC Press, Tylor & Frncis Group, London. Chowdhury, S. J., nd A. Ceder. 2013, Definition of Plnned nd Unplnned Trnsfer of Public Trnsport Service nd Users Decision to Use Routes with Trnsfers. Journl of Public Trnsporttion, Vol. 16, No. 2, pp Zho, F., nd I. Ubk. 2004, Trnsit Network Optimiztion Minimizing Trnsfers nd Optimizing Route Directness. Journl of Public Trnsporttion, Vol. 7, No. 1, pp Domschke, W. 1989, Schedule Synchroniztion for Public Trnsit Networks. Opertions Reserch Spektrum, Vol. 11, No. 1, pp Voss, S. 1992, Network Design Formultions in Schedule Synchroniztion. Computer-Aided Trnsit Scheduling. Springer Berlin Heidelberg, pp

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