A model for the coordination between high-speed railway lines and conventional rail lines in a railway passenger transportation corridor

Transcription

1 Comptes in Railways XII 453 A model fo the coodination between high-speed ailway lines and conventional ail lines in a ailway passenge tanspotation coido Y. Bao School of Taffic and Tanspotation, Beijing Jiaotong Univesity, China Abstact With the constction of high-speed ailway lines in China, thee ae gowing concens abot the ational tanspot coopeation between high-speed ailway lines and conventional ail lines. A ational tanspot coopeation scheme can impove ailway capacity tilization, tain speed, sevice and the oganization qality of ailway tanspotation. The pevios eseach mainly focsed on the aspect of the management of ailway o passenge oganization, which ignoed the inteaction of them. Based on the planning of a ailway tanspotation coido and the stcte and distibtion of passenge flows, we addessed the poblem of ational coopeation of the ailway passenge tanspotation coido, aiming at identifying the tain vaieties, qantities and the otes of tains on high-speed ailway lines and existing conventional ail lines in a ailway tanspotation coido. A bi-level pogamming model fo the division is poposed. The ppe model is to minimize the total tanspotation cost, and the lowe one is an eqilibim model detemined by passenges. Then a soltion algoithm based on a genetic algoithm (GA) is designed. Finally, the application of the model and the algoithm ae illstated by a nmeical example. Keywods: high-speed ailway, ailway passenge tanspotation coido, coodination, bi-level pogamming, genetic algoithm. 1 Intodction The coodination of high-speed ailway (HSR) and conventional ailway (CR) is the isse to identify tain otes, tain qantity and the distibtion on the two WIT Tansactions on The Bilt Envionment, Vol 114, 2010 WIT Pess doi: /cr100421

2 454 Comptes in Railways XII lines in a ailway coido. The coodination is a mode choice poblem. Meanwhile, it is a ote choice poblem. Theefoe, the poblem of coodination is to identify the otes of diffeent tains on the two paallel lines. HSRs ae developing vey qickly in China, and they ae bilt between metopolises, bt thee ae aleady CRs between them, so the coodination between HSRs and CRs shold be eseach in ode to flly se esoces and avoid competition. An ageement was eached by the eseach of 1990s, and HSRs finished the tanspotation of passenges on HSR lines and most mid and long-distance passenges fom CR lines, and CRs finished feight tanspotation and the est of the passenges tavelling by the slow tains on CRs. Howeve, with the constction and opeation of HSRs, the eseach backgond and peeqisites have changed. Fo example, the eseach in the 1990s spposed that tain nits on HSRs wee boght fom othe conties, bt now, China can podce tain nits by heself. HSRs ae qite diffeent fom CRs in infastcte, opeation, and chaacte, so the altenative is diffeent. Theefoe, the coodination between HSRs and CRs is highly desiable. The coodination is concened with passenge tanspotation sevice qality, the evene and the development of ailway tanspotation. Pevios eseaches abot the coodination of HSR and CR cove diffeent aspects and emphases, inclding fom the aspect of passenges by the disaggegate model [1 4], o fom the aspect of the ailway opeato [5], o the above two aspects [6]. The eseach method contains the logit model [1 3], the passenge flows assessment model, based on the ailway netwok [7], the game model abot the selection of a competitive tanspotation coido [8, 9], the enmeation method, the satisfaction optimization, and so on. Howeve, most eseaches abot the coodination of HSR and CR ae fom the aspect of passenges o fom the aspect of the ailway opeato, and few eseaches have been done fom both aspects, and most stdies failed to eseach the feedback of the decision made by the ailway opeato fom passenges. This pape established a bi-level pogamming model to descibe the elationship between the decision made by the ailway opeato and the eaction fom the passenges abot the decision. The emainde of the pape is oganized as follows. Section 2 explains basic assmptions abot the poblem. In Section 3, individal ote choices and the ailway opeato s decision ae investigated by a bi-level pogamming model. Section 4 intodces a genetic algoithm to solve the poblem. A nmeical example is povided in Section 5 to illstate the application of the models. Section 6 pesents conclding emaks. 2 Basic assmptions The following assmptions ae made in this stdy: (a) whethe high level tain nits n on CR lines o whethe low level tain nits n on HSR lines is detemined by the pofit of the ailway opeato, and is not detemined by policy o othe factos; (b) passenges choices ae based on the maximm tavel tility; (c) the same type of tains (tain nits) have the same seating capacity and can be WIT Tansactions on The Bilt Envionment, Vol 114, 2010 WIT Pess

3 Comptes in Railways XII 455 assigned to HSR lines and CR lines; (d) the opeation of the two diections of a line is the same, so we only eseach one diection. 3 Bi-level pogamming model A ailway tanspotation coido consists of paallel ailway lines and some stations. Stations can by classified in to two types, 1) a tain cold n on anothe type of line at the station; 2) a tain cold not n on anothe type of line at the station. We establish a ailway netwok ( SE, ). Tables 1 and 2 ae the paametes and the decision vaiables sed in the model, espectively. The ppe level is to maximize the pofit of the ailway opeato, with the estiction of tain limited nning distance, the capacity of lines. The lowe level is to maximize passenges tility, since passenges tility is descibed by passenges cost, so the objective of the lowe level is to minimize passenges tavelling cost. The ppe level: X Max x ( ) (, ) Qijx M l Fl Cl dx i j (1) The lowe level: x 1 elab xe d lab x max (2) ab, S X x ( ) e e lab lab (3) MinZ x 1 m Qijx h ijpx Vp (4) xx h p1 Q Q P( x ) (5) ijx ij Vx Px ( ) e X x 1 The lowe level is the tility of passenges, and it detemines passenges tavelling scheme choice. Passenges tavelling scheme choice is the basis of coodination, since it affects the load facto of a tain, so it plays a vital ole of the coodination in a ailway tanspotation coido. Passenges tavelling scheme choice is affected by passenge time vale, fae, tavelling distance, tain feqency, tain depate time, the chaacte of HSR and CR lines, etc, and it is detemined by the tility the passenges get fom thei tavel; in addition to the tility of fae and tavelling time, it also incldes comfot, safety, pnctality, and so on. e Vx (6) WIT Tansactions on The Bilt Envionment, Vol 114, 2010 WIT Pess

4 456 Comptes in Railways XII Table 1: Definition of paametes and sets. Paamete and set Definition S The set of stations, station i, j S, and a,b ae the adjacent stations e Ac, line type l ( l 1, HSR line; 2, CR line) lab e lab The length of ac e lab ( e lab ) The maximm capacity of ac e lab Tain type, 1, tain nit only n on HSR lines; 2, tain nit on HSR lines which can n on CR lines; 3, tain on CR lines which can n on HSR lines; 4, tain only n on CR lines t The nning time of tain type Tain opeation scheme R The set of tain opeation schemes, R x Tain nmbe x of tain type, x 1, 2,, X VS Tain speed of type on line l l The occpation of tain type on line l l M The capacity of tain type F The fae of pe tain kilomete of tain type on l line l C The cost of pe tain kilomete of tain type on l line l C The fae of a passenge fom his oigin to his pa ailway tip stat station C The fae of a passenge fom his ailway tip end pe station to his destination t The time of a passenge fom his oigin to his pa ailway tip stat station t The time of a passenge fom his ailway tip end pe station to his destination Feqency of tain type f dx (, i j ) The nning distance of tain x T pi max x The tansfe time of passenge p at station i d The maximm tavelling distance of tain x Q ij The volme of passenges fom i to j WIT Tansactions on The Bilt Envionment, Vol 114, 2010 WIT Pess

5 Comptes in Railways XII 457 Table 1: Contined. Q The volme of passenges fom i to j by tain x ijx of scheme m The hieachy of passenges v Time vale of passenges with hieachy h h ( h 1,2,, m) Q Passenges of hieachy h fom i to j tavelling ijx h x of scheme by tain Table 2: Definitions of vaiables. Paamete and set Definition x Whethe tain Yes xe Whethe tain lab No;1, Yes ijpx x is opeated on scheme, 0, No; 1, x of scheme occpies ac lab Whethe passenge p chooses the tain pi scheme, 0, No; 1,Yes e,0, x of Whethe passenge p tansfe at station i, 0, No; 1, Yes; The pofit of ailway 3.1 Calclation of passenges tility Accoding to andom tility theoy, the tility of passenge p to the choice is U p. Up Vp p (7) U the tility of passenge p fo choosing tavelling scheme ; p V p the fixed tility of passenge p fo choosing tavelling scheme ; p the andom eo of passenge p fo choosing tavelling scheme. In this pape, passenges tavelling schemes ae the tavelling schemes of tavelling diectly by diffeent otes o by tansfeing at diffeent stations. Taking fig. 1 as example, thee ae 6 tavelling schemes fo passenges tavelling fom O to D, 1) passenges tavel diectly fom O to D by the tain nning on HSR line; 2) passenges tavel diectly fom O to D by the tain nning on CR line; 3) passenges tavel diectly fom O to D by the tain fist nning on HSR line, then changing to n on CR line at station A; 4) passenges tavel diectly fom O to D by the tain fist nning on CR line, then changing to n on HSR WIT Tansactions on The Bilt Envionment, Vol 114, 2010 WIT Pess

6 458 Comptes in Railways XII Fige 1: An illstation of passenges tavelling schemes. line at station A; 5) passenges fist tavel by the tain on HSR line to station A, then tansfe to the tain on CR line at station A; 6) passenges fist tavel by the tain on CR line to station A, then tansfe to the tain on HSR line at station A. Hee we define fo chaactes to calclatev p, economy ( X 1 ), expeditiosness ( X 2 ), comfot ( X 3 ) and accessibility ( X 4 ). Each tavelling scheme has a fixed tility by the fo chaactes. If we se V to eplacev p, then V1 11X1112X1213X13 14X14 (8) V 2 21X 21 22X 22 23X 23 24X 24 (9) Vn n1xn1n 2Xn2n3Xn3 n4xn4 (10) -paamete, the pefeence of passenge fo the chaacte q of q tavelling scheme, q 1, 2, 3, 4 ; X q - the chaacte q of tavelling scheme Calclation of tavelling scheme chaacteistics (1) Economy Passenges need to pay fo thei tavel, and the fae is sed to indicate the economy of the tavel. Fae consists of the access fae fom oigin to the stat station, the iding fae on the tain, and the egess fae fom the end station of the tavel to passenge s destination. X 1 C F d (, i j) C (11) pa l x ijpx pe (2) Expeditiosness Expeditiosness is an impotation facto affecting passenges choice, especially to bsinessmen. Hee, tavel time is sed to expess the expeditiosness of a tip. Pevios stdies se passenges tavelling distance divides tain speed. Howeve, thee ae two limitations in this method, 1) the vale to diffeent type of time shold be diffeent, i.e., passenges tansfe time fo waiting the connecting tain is diffeent fom the time iding on the tain; 2) tansfe beaks the contine tip, and it may take theat to passenges in thei mind. So we think we shold distingish diffeent types of time ding the tip. WIT Tansactions on The Bilt Envionment, Vol 114, 2010 WIT Pess

7 Comptes in Railways XII 459 Total tavel time incldes iding time on the tain, tain stop time and passenges tansfe time. Howeve, the addition time fo the late of the tain is not consideed. X 2 d (, i j)/ VS T (12) x l pi pi paamete of the tansfe time changed to iding time. (3) Comfot With the aise of living standad, people's consmption idea has changed. They pse mch moe comfotable tavelling envionment. Comfot is an impotant chaacte that affects passenges choice behavio. Since tavelling is a consming of passenges physical stength, additional time is needed to ecove fom the fatige, when the tavelling time is p to some hos. So passenge ecoveing time fom fatige eflects the comfot of a tip. The ecoveing time is associated with tavelling time and tavelling envionment, and tavelling envionment is detemined by tain type. Passenge ecoveing time is calclated by the following eqation (Peng [5]). g ( t) M/[1 exp( t)] (13) (14) ( t )/ t ( t )/ t (15) M - the limited ecoveing time, in geneal, M is 15 h; - nondimensional paamete, when tain type is, and t 0, the ecoveing time is M /(1 ) ; and - the stength coefficient of ecoveing time fo one tavelling ho, 0, 1 the nit is h. Fige 2: The illstation of passenges tavelling time and ecoveing time. WIT Tansactions on The Bilt Envionment, Vol 114, 2010 WIT Pess

8 460 Comptes in Railways XII Table 3: Passenges ecoveing time fom fatige when tavelling between Beijing-Shanghai by diffeent types of tains. Tain type Passenge tavelling time (h) Recoveing time (h) High-level tain on HSR Low-level tain on HSR Nomal tain on CR When M 15h, the ecoveing time tavelling by diffeent type of tains is as fig. 2. Fom the compaison we can see the advantage of HSR in ecoveing passenges fatige. Taking Beijing-Shanghai HSR line fo example, 1) if we assme that the tavelling time of high-speed tain is 5 h, the ecoveing time of passenges tavelling by HSR is 58 min; 2) if passenges tavelling by thogh tains (tain type Z) on CR line, the tavelling time is 13 h, and the ecoveing time will be p to 9 h; 3) if passenges tavelling by nomal tains on CR line, the tavelling time is 22 h and 43 min, and the ecoveing time will be p to 14 h 56 min, nealy to the geneal limited ecoveing time M. The above eseach is based on thogh tains, when passenges tansfe, if the tavelling time is t on tain type, in this case, paamete and shold be calclated by weighted aveage method. Theefoe, passenges comfot is calclated by eqn. (16). X 3 g () ( ) t (16) (4) Accessibility Most cent appoaches abot passenges choice behavio to diffeent tanspotation modes, in the mainland of China, focs on the chaactes of the mode itself, athe than eseach fom the whole tip. The sal methods to impove the maket shae of a mode ae enlaging the netwok, impoving the coveing aea of the mode, shoting the tavelling time, impoving the sevice, etc., bt ignoing the accessibility of the mode. Fom the eseach of aboad and Taiwan in China, accessibility is an impotation facto that affects the maket shae of diffeent tanspotation modes [10, 11]. With the development of highspeed tain nits, the iding time is lowe and lowe. Theefoe, the access time to the station and the egess time fom the station occpies a lage pat in the whole tavelling time, especially to those cities that ae always in heavy taffic. In this stdy, station accessibility is epesented by passenges agee time, egess time, the feqency of tains and the tansfe time. X 4 tpa Tpi pi / f tpe (17) - paamete of tain depate feqency. 4 Algoithm fo solving the model Genetic algoithm is intodced to solve the model, and the steps ae as follows. WIT Tansactions on The Bilt Envionment, Vol 114, 2010 WIT Pess

9 Comptes in Railways XII 461 Step 1: Repesentation and initialization of chomosomes fo the ppe-level model Select a feasible soltion N 0 fo the ppe-level model, let X { x } epesent a chomosome fo the ppe-level model. Each code in the chomosome is the vale of x, geneate POP _ SIZE _ U chomosomes, which is { X / X ( x 1, x 2... x n ), 1, 2,... POP_ SIZE_ U}. The steps sed to geneate chomosomes cold be descibed as below. Select a andom diection d fom R n ; If N 0 +d is feasible, let it be a new chomosome, othewise, geneate a new d, ntil N 0 +d is feasible; Repeat steps (1) and (2) to get POP _ SIZE _ U chomosomes. Step 2: Evalation and Selection Execte each chomosome to get each chomosome s fit vale based on step6, sot the chomosomes on the basis of fit vales. Select POP _ SIZE _ U chomosomes to execte the following steps. Step 3: Cossove Ceate a new poplation of POP _ SIZE _ U nmbe by applying the following opeations. The opeations ae applied to choose fom the poplation with a pobability based on fitness. (i) Dawinian Repodction: Repodce an existing chomosome by copying it into the new chomosome. (ii) Ceate two new chomosomes fom two existing chomosomes by genetically ecombining andomly chosen pats of two existing chomosome s sing the cossove opeation applied at a andomly (accoding to Pc _ U ) chosen cossove point within each chomosome. Step 4: Mtation Ceate a new poplation of POP _ SIZE _ U nmbe by applying the following opeations. The opeations ae applied to choose fom the poplation with a pobability based on fitness. (i) Dawinian Repodction: Repodce an existing chomosome by copying it into the new chomosome. (ii) Ceate one new chomosome fom one existing chomosome by mtating a andomly (accoding to Pm _ U ) chosen pat of the chomosome. Step 5: Iteations Iteatively pefom the above steps (2) ~ (4) ntil the temination citeion Gen _ Nm _ U has been satisfied. Step 6: Solving the lowe-level model based on the inpt fom the ppelowe model Step 6.1 Repesentation and initialization of chomosomes fo the lowe-level model Select a feasible soltion N 0 fo the ppe-level model, let X L { } epesent a chomosome fo the lowe-level model. Each code ijpx in the chomosome is the vale of ijpx, geneate POP _ SIZE _ L chomosomes, WIT Tansactions on The Bilt Envionment, Vol 114, 2010 WIT Pess

10 462 Comptes in Railways XII which is { X / X ( x 1, x 2... x n ), 1, 2,... POP _ SIZE _ L}. The steps sed to geneate chomosomes cold be descibed as below. Select a andom diection d fom R n ; If N 0 +d is feasible, let it be a new chomosome, othewise, geneate a new d, ntil N 0 +d is feasible; Repeat steps (1) and (2) to get POP _ SIZE _ L chomosomes. Step 6.2: Evalation and Selection. The same with step 2. Step 6.3: Cossove. The same with step 3. Step 6.4: Mtation. The same with step 4. Step 6.5: Iteations. The same with step 5. Step7: Retn the eslt Q by the lowe level to step 5. 5 Nmeical example ijx The ail netwok topology is shown in fig. 3. Capacity of each tain nit on HSR is 600 p (passenge), and 1220 p on CR. We assme that the occpation ate of each tain is 90% on HSR lines, and 85% on CR lines. The fae of each passenge pe tain-km is 0.30 and 0.14 CNY on HSRs and on CRs of highspeed tains, and 0.12 CNY on CRs of nomal tains. The cost of pe tain-km nit is and CNY of high-speed tains on HSRs and CRs, and 92.4 Fige 3: Illstation of the ail netwok sed in the nmeical example. Table 4: Passenges tavelling demand. A B C D E F G H A B C D E F G 2000 H WIT Tansactions on The Bilt Envionment, Vol 114, 2010 WIT Pess

11 Comptes in Railways XII 463 Table 5: The weight of sevices attibte fo diffeent types of passenges. Passenge hieachy Passenge income level/cny Pecentage/% Passenges time vale/ CNY Economy Expeditiosness Comfot Accessibility h=1 < h=2 2000~ h=3 3000~ h=4 > > WIT Tansactions on The Bilt Envionment, Vol 114, 2010 WIT Pess

12 464 Comptes in Railways XII Table 6: The nmbe of tains of diffeent sections. Section CR HSR Section CR HSR A-C 0 2 C-H 0 4 A-D 1 0 D-E 3 0 A-E 1 4 D-G 1 0 A-F 0 2 D-H 1 0 A-H 1 7 E-F 0 6 B-D 1 0 E-G 1 0 B-E 1 0 E-H 2 7 B-H 2 0 F-H 0 5 C-E 0 6 G-H 1 0 C-F 0 3 CNY of nomal tains on CRs. The oganization cost fo each passenge is Chinese Yan (CNY), when they tansfe. Meanwhile, we assme that the volme is not a constaint fo tain nits nning on CR lines. The genetic algoithm has been implemented by Micosoft Visal C (moe than 4200 code lines) and ns on a Pentim Do, 3.4GHz PC, with 512MB RAM memoy. The time cost is 56 seconds. The eslts ae given below. 6 Conclsions This pape addesses the coodination isse of HSR and CR in a ailway tanspotation coido fom the aspect of passenges and ailway opeato. A bilevel pogamming model is established to coodinate the diffeence of passenges' choice and the decision made by ailway opeato. A genetic algoithm is designed to solve the model. The model and algoithm is demonstated by a nmeical example. The poposed model can be extended in seveal diections. In the ppe-level level, feight tanspotation can be inclded, especially to those valable goods. Meanwhile, in the lowe level, passenges depate time can be added as a constiction. Anothe possibility is to add othe tanspotation modes in a tanspotation coido, sch as ai tanspotation, and feeway. Acknowledgements This stdy was jointly fnded by National Natal Science Fondation of China (No ) and Beijing Jiaotong Univesity (No ). The atho deeply appeciates the sppot. WIT Tansactions on The Bilt Envionment, Vol 114, 2010 WIT Pess

13 Comptes in Railways XII 465 Refeences [1] Saad N Aljaad & William R Black, Modeling Sadi Aabia-Bahain coido mode choice, Jonal of Tanspot Geogaphy, 3(4), pp ,1995. [2] Bhat C.R., A Heteoscedastic Exteme Vale Model of Intecity Mode Choice, Tanspotation Reseach Pat B, 29(6), pp , [3] Bhat C.R., Covaiance Heteogeneity in Nested Logit Models: Econometic Stcte and Application to Intecity Tavel, Tanspotation Reseach Pat B, 31(1), pp , [4] Chag-Ing Hs & Wen-Ming Chng, A Model fo Maket Shae Distibtion between High-speed and Conventional Rail Sevices in a Tanspotation Coido, The Annals of Regional Science, (31), pp , [5] Qiyan Peng, Tanspotation oganization of passenge special line, Science Pess, [6] Jie Tang, The coodination and optimization method between high-speed ailway and conventional ailway, Maste's Thesis, Cental Soth Univesity, [7] IljoonC hang, A Netwok-based Model fo Maket Shae Estimation among Competing Tanspotation Modes in a egion coido, Ph.D. thesis, The Univesity of Mayland, [8] Jianmei Zh, Game Model of Selection of Competitive Tanspotation Coidos, Jonal of Sothwest Jiaotong Univesity, 38(2), pp , [9] Ching-Wen Hs, Ysin Lee & Chn-Hsing Liao. Competition between high-speed and conventional ail systems: A game theoetical appoach, Expet Systems with Applications, 37, pp , [10] Cleve, Reinhad, Aipot and station accessibility as a deteminant of mode choice, Ph.D. thesis, Univesity of Califonia, Bekeley, [11] Matijn Bons, Moshe Givoni & Piet Rietveld. Access to ailway stations and its potential in inceasing ail se. Tanspotation Reseach Pat A, (43), pp , WIT Tansactions on The Bilt Envionment, Vol 114, 2010 WIT Pess