PASSENGER FLOW ANALYSIS FOR TRAIN RESCHEDULING AND ITS EVALUTION

Transcription

1 * * * Internatonal Symposum on Speed-up, Safety and Servce Technology for Ralway and Maglev Systems 009 (STECH 09) Ngata JAAN ASSENGER FOW ANAYSIS FOR TRAIN RESCHEDUING AND ITS EVAUTION Shunch Tanaka*, Kazumasa Kumazawa* and Takafum Kosek* of Informaton and Communcaton Engneerng, Graduate School of Informaton Scence and Technology, The Unversty of Tokyo, tanaka@kosek.t.u-tokyo.ac.jp of electrcal engneerng, Graduate School of engneerng, The Unversty of Tokyo, kumazawa@kosek.t.u-tokyo.ac.jp of Informaton and Communcaton Engneerng, Graduate School of Informaton Scence and Technology, The Unversty of Tokyo, takafumkosek@eee.org ABSTRACT Tran reschedulng durng dsrupted servce s a substantally sgnfcant task for urban ralway operators. Ths task typcally depends on the experences and personal decsons of the professonal operators. The operators use nether systematc methodologes for modfyng tran schedules nor quanttatve crtera for measurng the qualty of the rescheduled plans. Thus, operators have requested assstance n the form of a computer-aded tran-reschedulng program. The authors have created a computer-aded tran reschedulng system that seeks to mnmze passenger nconvenence. The method of passenger flow for tran reschedulng s dscussed for realstc analyss.. INTRODUCTION Reschedulng tran operaton s often needed when tran operaton s dsordered by varous malfunctons or accdents. Man tasks for t are presently taken by tran dspatchers wth ther experence and ntutons. It s very dffcult, snce there are many factors to be consdered such as locaton of trans and rollng stocks, tracks and tran layout, locaton of drvers, passengers demand, and so on. Correspondng to hgh-speed and hgh-densty tran operaton, dspatchers have requested an assstance system to make reschedulng tran operaton plans quckly and precsely. The authors proposed a method to rate tran operaton plans quanttatvely from the passengers' pont of vew. Based on t, the authors formulate an assstance system that chooses an approprate method to modfy a tran schedule[]. In ths paper, the method of passenger flow analyss that s used for evaluatng the reschedulng plan s ntroduced. assengers tend to behave to decrease ther dscomfort, but the dscomfort of congeston can be evaluated only after passenger flow s determned. That s to say, they cannot always behave wth ther mnmum costs. Therefore the multple routes that has comparatvely low costs are consdered n passenger flow analyss, so that the passengers could select ther routes stochastcally..train RESCHEDUING SYSTEM Ths computer-aded tran reschedulng system makes a reschedulng plan based on the nformaton of delay and varous restrctons. The system conssts of two man parts, one s creatng a tran plan and the other s evaluatng the plan. In the part of creatng a tran plan, change of tran dagram and determnaton of tran arrval and departure are executed. In evaluatng the plan, estmaton of passengers behavor and calculaton of evaluaton ndces are carred out. The tran reschedulng plan s made by repeatng process of adopton judgment of a new modfcaton based on the evaluaton ndces. And the tran reschedulng plan s presented to the tran dspatchers. Fg. shows a composton of the computer-aded tran reschedulng system. Fg. A composton of the computer-aded tran reschedulng system

2 Ngata JAAN Table Constrants for tran operaton Constrans Content Regular schedule A Tran must not run earler than regular schedule. Regular runnnga tran requres longer tme defned by tme tran type. Regular A tran must stop at a staton for more Stoppng tme than defned tme. Conflctng A certan nterval requred between routes trans that routes conflct at a staton. Blockage Trans more than defned number can t run at the same tme between statons..creation OF TRAIN RESCHEDUING AN The part of creatng tran operaton plan n the system receve a regular tran schedule and nformaton about delay, and try to apply tran reschedulng method to meet the constrants for tran operaton as shown by Table. For decson on arrval or departure tme of each tran at each staton under these constrants, the authors use graph theory as shown by Fg., and use ERT (rogram Evaluaton & Revew Technque) for the longest path search algorthm to fnd the longest path to each node from the node expressng tme orgn. 4.EVAUATION OF THE RESCHDUING AN The part of evaluatng tran operaton plan n the system receve the arrval/departure tme of each tran at each staton from the part of creatng tran operaton plan, and smulate passengers act to decde the numbers of passengers between neghborng statons. The detals about passenger flow smulaton are descrbed n the next secton. After passenger flow analyss, the reschedulng plan s evaluated. There are many methods to evaluate tran schedule, although the authors use the evaluated value based on passengers pont of vew. The evaluated value s defned crteron for passengers loss consderng the followng three evaluaton ndces; travelng tme, burden of transfer, and congeston. These values are calculated wth the result of passenger flow analyss. Travelng tme s the amount of tme requred from departure staton to destnaton. Travelng tme s defned as follows: = N t = () where N s the number of passengers, t s the travelng tme of passenger. Fg. An example of a graph representng tran operaton Burden of transfer vares accordng to constructon of each staton. For example, the transfer wth stars has a hgh cost. These burdens are calculated as passengers loss n addton to the real tme for transfer. = N M r () j = j= where r j s tme equvalent to the burden of passenger s j-th transfer and M s the number of transfers passenger needs. Congeston s also consdered as passengers loss because passengers n congested tran feel dscomfort. Ths evaluaton uses nonlnear functon to convert passengers dscomfort, as shown n Fgure[]. Congeston loss s defned as follows: q n Sk ks = f c qkstks k= s= c () ks where n s the number of statons, S k s the number of trans whch arrve at staton k. q ks, t ks, and c ks are the number of passenger n the tran, the tme requred, and the capacty of the tran between k-th and (k+)-th statons respectvely. f c s the nonlnear functon. Fg. Relatonshp between congeston rate and congeston cost per mnute

3 Ngata JAAN Fg6. Change of passenger flow Fg.4 An example of a graph representng passenger flow STE: Search the shortest path wth Djkstra 7 0 The mnmum cost from node0 : to node7 = to node0 = Reduced cost of ark (7,0) =-+= STE:Defne the reduced-cost for every ark STE: Consder the branches for the shortest path Rcost: 0 Rcost:6 0 6 Rcost: 0 4 Rcost: Rcost: STE4: Select the mnmum reduced-cost as nd path, consder the branches for nd path and repeat STE,4 Fg.7 the flow of MS algorthm Fg.5 Model of passenger overflow The total passengers loss s the sum of above three types of loss. = + + (4) 5.ASSENGER FOW ANAYSIS 5. Graph of passenger flow assenger flow analyss s based on graph theory. Ths graph conssts of nodes and lnks. The nodes show arrval and departure of each tran at each staton, and the lnks show boardng, tran stoppng, and transfer. Boardng lnks and tran-stoppng lnks contan tme, and transfer lnks contan total of tme and dscomfort as weght of lnks. The example of passenger flow graph s shown n Fg Conventonal model assengers would get on tran n order to assure that ther dscomfort become mnmum. As a result, passengers routes are descrbed as routes from start nodes to destnaton nodes wth mnmum cost. In the precedng study[], the shortest paths from each departure node to arrval node are calculated wth Djkstra s algorthm. However, congeston s not consdered n ths passengers dscomfort. Congeston cannot be used as a barometer of passenger flow analyss because congeston s determned after decson of passenger-flow. For ths reason, passengers n the smulaton tend to choose rapd trans as compared to local trans. Therefore passengers could get on more than capacty of the tran as shown n Fg.5. Ths caused volence of causalty. The passengers behavor was not correctly estmated and evaluaton crtera could not be accurately calculated. If each passenger over flow s ndependent, passengers who cannot get on the tran can adjust ther travel plans after the next tran leaves the staton. But under the crcumstances that more than one passenger overflows have relatonshps, t s very dffcult to calculate the passenger- flow accurately. Moreover, all passengers mght transfer the tran even f ther dscomforts show a slght declne as shown n Fg.6. It s not realstc that behavor of all passenger s drastcally affected by slght dfferences n the dscomfort, and passenger overflow occurs because many passengers are concentrated n a rapd tran. 6.MUTIE ATHS OF ASSENGER FOW 6. Introducton of k-th paths algorthm K-th shortest paths algorthm was developed for fndng a path between two nodes such that the sum of weght of ts consttuent edges s k-th smallest. MS algorthm[4] s one of the k-th shortest paths algorthm. The flow of ths algorthm s shown n Fg.7. In the graph of passenger flow proposed by us, nodes represent destnaton and arrval of the trans. Calculaton of mult-paths from one destnaton node to arrval node can fnd only the paths wth the same tran at the start staton and the same tran at the goal staton. Ths method

4 Ngata JAAN Fg.8 Introducton of the staton arrval nodes Fg.0 Calculaton tme of MS Algorthm Fg9 Comparson of passengers loss cannot fnd an effectve soluton. The node that brngs tran arrval nodes of each staton s ntroduced as shown n Fg.8. Wth the search for the mult-paths from the tran departure node to staton arrval node, effectve multple paths can be found. 6. Keepng the result of Djkstra s algorthm As another method, keepng the result of Djkstra s algorthm can be consdered. In conventonal graph of passenger flow, Djkstra s algorthm can fnd the paths from one tran-destnaton node to multple tran-arrval nodes at one staton. In conventonal method, the paths except for the shortest path are dscarded. By keepng these paths, the nformaton would be useful for mult-path search though there s no guarantee of k-th shortest paths accuracy. 6. robablty of passenger flow Two methods to fnd mult-paths are ntroduced. The number of passengers that use each path s determned wth dsaggregate demand model as follows: = n exp( θc ) j= exp( θc ) where s probablty that passenger select the path, and θ s parameter of ogt model, C s dscomfort of travelng tme and transfer, and N s the number of paths. assengers act under ths probablty. j (5) Fg. The example of napproprate path 6.4 Effect of multple paths Both k-th path algorthm and keepng the result of Djkstra s algorthm reduce the dscomfort of congeston although the dscomfort of travelng tme and transfer s ncreasng as shown n Fg.9. The total passengers loss s ncreasng, but the gap of the number of passengers between rapd and local trans has been mtgated. Based on calculaton tme, the method of keepng the result of Djkstra s algorthm s about the same tme as fndng only sngle path. On the other hand, the method of k-th path algorthm requres tme as k ncreases. Fg.0 s relatonshp parameter k and calculaton tme on certan tran network. 7.CONCUSION Consderng multple paths n passenger flow analyss ultmately results n the numercal ncrease of passenger penalty functon. But the problem n the analyss only wth sngle path can be elmnated. On fndng the multple paths, an napproprate path could sometmes be found as shown n Fg.. Such paths must be removed from the canddates. One of the methods for more realstc passenger flow analyss to nclude plannng tme n the analyss for explct consderaton of causalty[5]. The combnaton of these method and multple paths would result n more useful evaluaton of the passenger flow n practce.

5 Ngata JAAN REFERENCES [] Nagasak, Y., Eguch, M. and Kosek, T.: Automatc Generaton and Evaluaton of Urban Ralway Reschedulng lan, roc. of Int. Symp. on Speed-up and Servce Technology for Ralway and Maglev Systems. STECH 0., pp.0-06 (00). [] Mtan, K., Ieda, H., and Hatanaka, H.: Evaluatng Method of Congeston Cost by the Model of assenger s Boardng Behavor, Infrastructure lannng Revew (n Japanese), no. 5, pp (987). [] Hara, K., Kumazawa, K. and Kosek, T.: Effcent Algorthm for Evaluatng and Optmzng Tran Reschedules by Takng Advantage of Flexblty of Quadruple Track, The Thrd Internatonal Conference on Ralway Tracton Systems (RTS007). pp.9-97 (007). [4] E.Q.V. Martns, M.M.B. ascoal and J..E. Santos: An algorthm for rankng loopless paths, Research Report, Unv. de Combra. (999). [5] Kumazawa, K., Hara, T., and Kosek, T.: A Novel Tran Reschedulng Algorthm for Correctng Dsrupted Tran Operaton n a Dense Urban Envronment, Eleventh Internatonal Conference on Computer System Desgn and Operaton n the Ralway and Other Transt Systems (COMRAI008), pp (008).