This is a repository copy of Timetable coordination of first trains in urban railway network: A case study of Beijing.

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1 This is a repository copy of Timetabe coordination of first trains in urban raiway networ: A case study of Beiing. White Rose Research Onine URL for this paper: Version: Accepted Version Artice: Guo, X, Wu, J, Sun, H et a. ( more authors) (0) Timetabe coordination of first trains in urban raiway networ: A case study of Beiing. Appied Mathematica Modeing, 0 (-). pp ISSN 00-0X 0, Esevier. Licensed under the Creative Commons Attribution-NonCommercia-NoDerivatives.0 Internationa Reuse Uness indicated otherwise, futext items are protected by copyright with a rights reserved. The copyright exception in section of the Copyright, Designs and Patents Act aows the maing of a singe copy soey for the purpose of non-commercia research or private study within the imits of fair deaing. The pubisher or other rights-hoder may aow further reproduction and re-use of this version - refer to the White Rose Research Onine record for this item. Where records identify the pubisher as the copyright hoder, users can verify any specific terms of use on the pubisher s website. Taedown If you consider content in White Rose Research Onine to be in breach of UK aw, pease notify us by emaiing eprints@whiterose.ac.u incuding the URL of the record and the reason for the withdrawa request. eprints@whiterose.ac.u

2 Pease quote this paper as: Guo, X., Wu, J., Sun, H., Liu, R. and Gao, Z. (0) Timetabe coordination of first trains in urban raiway networ: a case study of Beiing. Appied Mathematica Modeing. In press. Timetabe coordination of first trains in urban raiway networ: a case study of Beiing Xin Guo a, Jianun Wu a, Huiun Sun b, Ronghui Liu c, Ziyou Gao b a State Key Laboratory of Rai Traffic Contro and Safety, Beiing Jiaotong University, Beiing 00 b Schoo of Traffic and Transportation, Beiing Jiaotong University, Beiing, 00 c Institute for Transport Studies, University of Leeds, Leeds LS JT, UK 0 Abstract A mode of timetabe coordination of first trains in urban raiway networs, based on the importance of ines and transfer stations, is proposed in this paper. A sub-networ connection method is deveoped, and a mathematica programming sover is utiied to sove the suggested mode. A simpe test networ and a rea networ of Beiing raiway networ are modeed to verify the effectiveness of our suggested mode. Resuts demonstrate that the proposed mode is effective in improving the transfer performance in that they reduce the connection time significanty. Keywords: Departure time; Timetabe coordination; First trains; Urban raiway networ 0. Introduction There is an increasing deveopment wordwide for urban raiway networ (URN) as an effective transportation mode to aeviate traffic congestion in cities. The denser an URN is, the more convenient it becomes to the traveers. However, having more ines and stations to an URN increases the compexity of timetabe optimiation for the system. What s more, the earier the departure times for first trains, the higher operation cost to the URN. There are therefore trade-offs to be made between traveers who want short transfer waiting time and operators who want to minimie operationa costs. Trade-offs are aso to be made between different departure times for different ines, such that the overa transfer connection times are sma. This is considered as the first train timetabing coordination probem. Generay, timetabe optimiation is to design a schedue which can hep transportation authorities to maximie their service eve (such as minimiing transfer time, maximiing transfer Corresponding author. E-mai addresses: wu@btu.edu.cn

3 0 0 0 accessibiity), or to minimie some generaied cost of a combination of the above. There are many studies focusing on the transfer time, and optimiation modes are proposed to design or adust a timetabe. For exampe, Jansen et a. (00) appied Tabu search method to adust the dispatching times of trains on a route to synchronie the timetabe by minimiing passenger transfer time. Cevaos and Zhao (00) aimed to change an existing timetabe by considering the coordination between ines. In their paper, the obective was to reduce the waiting time at the transfer stations. Chen and Wang (00) proposed a method for cacuating a reasonabe departure time by decreasing the waiting time at transfer stations during the day. Wong et a. (00) presented a mixed-integer-programming optimiation mode for schedue synchroniation probem which minimies the transfer waiting times of a passengers. They appied the method to the Mass Transit Raiway of Hong Kong. Shafahi and Khani (0) proposed two mixed integer programming modes to minimie the tota waiting time at transfer stations. Yang et a. (0) considered the optimiation of energy consumption and trave time as the obective based on a coasting contro method. Wu et a. (0) proposed a timetabe synchroniation optimiation mode to optimie passengers waiting time whie imiting the waiting time equitaby over a transfer stations in Beiing raiway networ. Nayeem et a. (0) proposed two agorithms on minimiing the waiting time and the number of transfers simutaneousy. Other researchers have concentrated on the aspect of the generaied cost to design the optimied timetabe. Yan and Chen (00) deveoped a mode for intercity timetabe setting. The mode is formuated as a mixed integer mutipe commodity networ fow probem. Zhao and Zeng (00) proposed a mode to minimie passengers transfer cost and presented a heuristic method to optimie transit networ panning. In the study, the transfer cost is separated into waing time between stops, the waiting time at transfer stations and transfer penaty time. Meanwhie, simutaneous approach of optima passenger cost and timetabing of transit systems has ony been superficiay expored, the synchroniation between schedues and operationa status is sti to be resoved. Gao et a. (0) examined the frequency optimiation probem under the assumption of eastic demand in a regiona metro system. The obective of the mode is to minimie the generaied cost which combines of transit user costs, car user costs, operator costs and externa costs. Sun et a. (0) formuated three optimiation modes to design a capacitated demand-sensitive pea and off-pea timetabes. There have been studies in dynamica re-scheduing in response to rea-time information to enhance the service quaity of URN. Taniguchi and Shimamoto (00) presented a dynamic vehice scheduing mode that incorporates rea-time information using variabe trave time. Dynamic traffic simuation was utiied to update trave time. Vansteenwegen and Oudheusden (00) proposed a inear programming mode considering deay time in the actua operation. They aimed to compute the idea buffer times for each connection, which was subsequenty used in the inear program mode for re-scheduing. Yan et a. (00) deveoped a scheduing mode which considers stochastic demand. They appied a simuation technique, couped with in-based and path-based routing strategies, to deveop two heuristic agorithms to sove the probem. Niu and Zhou (0) deveoped integer programming modes to optimie train timetabes in a heaviy congested urban rai corridor. Based on time-dependent, origin-to-destination trip records from an automatic fare coection system, a noninear optimiation mode was designed to sove the probem on a reaistic sied corridor. In timetabing probem, severa inputs are necessary, e.g., service time of day, departure time

4 for the first train, departure time for the ast train and schedue for during-the-day operation. Most of the existing iteratures on the subect of timetabing for URN have been concerned with the norma operation during the day, when the service can be considered infinite and there is not a start or an end of the service. Scheduing for during-the-day operation is different to that for the first or the ast trains. For during-the-day operation, the high service frequencies naturay reduce the connection time at transfer stations. A trains can connect to the feeder trains or be connected by other trains and within a reasonaby short period of time. For exampe, at transfer station (Fig.), for passengers from the q train in ine transferring to connecting q train in ine, their maximum connection time tends to be the headway of ine. During the pea period, when transit frequencies are high, Charoborty (00) demonstrated that missing a connection ony increases transfer connection time by a reativey short interva. On the other hand, during off-pea period, Yan and Chen (00) argued that when transit frequencies are ow, missing a connection means ong waiting times and the absence of synchroniation may even discourage peope from using pubic transport. In other words, it is important to study the synchronous timetabe in off-pea hour. Train qin ine Max{Connection time}=headway Connection time Headway Time Train q in ine Transfer station Train ( q ) in ine 0 Fig.. The connecting trains in norma operation trains. The first train timetabing probem which occurs in the morning off-pea hour becomes ever more important with the expansion of URN. The first train indicates the first operating train in each ine every day. Passengers usuay have to transfer to the other ine(s) to compete their trave within the networ. Therefore they are more concerned with service connectivity and transfer coordination. Trade-offs need to be made between passengers perspective and operator s perspective to set the departure times for first trains within reasonabe cost, without causing excessive ong connection time at any transfer station in the URN. To iustrate the probem, we assume that the first train in ine has to connect to the first train in ine in a transfer station (as iustrated in Fig.). An unbaanced departure time of first train wi ead to the foow situation: the departure time of first train in ine is much ater than the first train in ine, thus the first train can mae successfu transfer in ine to connecting trains in ine. The connecting trains

5 in ine can be the first train, the second train, etc. and the shortest connection time is severa times onger than headway in ine. Because of no train ahead of the first train in ine, and adustment the headways towards the ine to achieve the best synchroniation state is useess for the whoe performance of the system. First train in ine Unrestraint: {Connection time}> or = or <{Headway} Headway Connection time Time Second train in ine First train in ine Connecting trains Transfer station Fig.. The connecting trains in the first train probem. Taing the Beiing URN in Fig. for instance, six first trains depart from vehice depots in three bi-directiona ines (Line, Line and Line ). We present in the Tabe the current first train connection times. In Tabe, up to up means the first up train of ine can connect the first up train of ine. Simiary, up to down means the first up train of ine can connect the first down train of ine. The first train running in the up direction of ine arrives at HDHZ station at ::00 am, and the first train in the up train direction of Line departs at ::00 am. It taes passengers minutes to wa from ine to ine. As a resut, the transfer connection time is minutes which are a ong time for passengers to wait. In another exampe, the first train running in the down direction of ine arrives at HN station at ::0 am, and the first train in the down train direction of ine departs at ::00 am. It taes passengers minutes to transfer from ine to ine. Thus, the connecting train is ust eaving when the passengers come to the patform and they even can see the train eaving the patform. Therefore, we shoud aso avoid this situation that when passengers miss the connecting train for a few minutes. 0 Tabe. Transit panning process for the first trains in HDHZ station and HN station Station Transfer Transfer waing time (s) Arriving train First connecting train waiting (s) up to up 00 ::00 ::00 min HDHZ down to up 0 ::00 ::00 0 min 0 sec down to down 0 ::00 :0: min sec down to up 00 :0: ::00 min sec HN up to up :: ::00 min sec down to up ::0 ::00 0 min sec

6 down to down ::0 ::00 down to up ::00 :: min sec Line Line Up direction Down direction Transfer Line down arrives, 0: Line up arrives 0: Transfer HDHZ Line up arrives, 0: Transfer Line down arrives, 0: HN Transfer Line down arrives, 0:0: Line up arrives, 0: Transfer Line up arrives, 0: Transfer Line down arrives, 0: Line Fig.. The connecting first trains in a subset of the Beiing raiway networ. Tabe presents a snapshot of the connection time for first trains at some of the ey transfer stations in the entire Beiing raiway networ. It shows that the connection time for some of these ines is in hours, which are way beyond expectation. Such extremey ong connection time for first trains wi ceary ead to ow networ accessibiity and to discourage passengers from riding urban raiway transit. Tabe. A snapshot of the connection time for the first trains in Beiing raiway networ Station Number of transfer directions The connection time (h) HDHZ up to up up to down down to up down to down. ZCL up to up up to down down to up down to down. BTC up to up up to down down to up down to down. DZM up to up up to down down to up down to down. HN up to up up to down down to up down to down. In addition to minimie transfer time, timetabing is aso to formuate reasonabe headway, running time and dwe time so as to coordinate the departure times of trains at transfer stations. However, there are important differences in system characteristics between the norma during-the-day operation and the first trains. For the first trains, for exampe, the capacity of the trains is considered to be sufficienty high reative to the demand for such eary morning services. Secondy, the running time between any two stations and transfer time at station can be fixed

7 0 because there is no expected deay due to congestion. Thus, the train operation can be impemented stricty according to the train operation diagram. Thirdy, there are upper and ower bounds as to when the departure times of first trains can be schedued (due to the constraints of the day and the required operating time of the ine). Last but not east, there is an unbaanced distribution of passenger infows between the up direction and the down direction for the first trains in the morning when passengers are more iey to transfer from the suburbs to the downtown areas. So there are directions where transfer stations and ines are more important than the other directions. Scheduing for the first and ast trains has ony recenty begun to draw research interests. Xu and Zhang (00) proposed a muti direction transfer mode for first and ast train scheduing. Depending on the characteristics of passenger fow in the morning and evening, they presented the method to cacuate the departure time s domains of the first and ast trains. Zhou et a. (0) presented a coordination optimiation mode on first trains departure times to minimie passengers tota waiting time at origins and transfer waiting time for the first connecting trains. Chun et a. (0) put forward a dynamic passenger voume distribution method according to the generaied trave cost. Then a connection optimiation mode of ast train departure time is buit to increase accessibe passenger voume and reduce passengers transfer waiting time of a origin and destination (OD) pairs for ast trains. Kang et a. (0) estabished a ast-train networ transfer mode for Beiing URN to maximie passenger transfer connection headways, which refect ast-train connections and transfer waiting time. Kang and Zhu (0) proposed a first train coordination mode, whie Kang et a. (0) constructed an optimiation mode to minimie the running time and dwe time and to maximie the average transfer redundant time and networ transfer accessibiity of ast trains. Tabe. Literature on timetabing for the three different schedue types Scheduing type Obective Seected references Nachtiga and Voget (); Jansen et a. (00); Cevaos and Zhao (00); Chen and Wang (00); Minimie trave time Wong et a. (00) ; Shafahi and Khani (0); Yang et a. (0); Wu et a. (0); Nayeem et a. (0); Ibarra-Roas and Rios-Sois (0); Charoborty (00); Castio et a. (0); Castio et a. (0) During-the-day Yan and Chen (00); Zhao and Zeng (00); Gao et operation Minimie cost a. (0); Li et a. (0) ; Sun et a. (0) Taniguchi and Shimamoto (00); Vansteenwegen and Dynamic re-scheduing Oudheusden (00); Yan et a. (00); Niu and Zhou (0) maximie company profits Caprara et a. (0); Yaghini et a. (0) Minimie train deay Li et a. (0) Maximie transfer accessibiity Xu and Li (0); Kang et a. (0) Last train Maximie transfer connection operation headways Kang et a. (0); Zhou et a. (0) Minimie transfer time Chun et a. (0); Xu and Zhang (00)

8 First train operation Coordinate departure times of first trains Xu and Zhang (00); Zhou et a. (0); Kang and Zhu (0) Tabe summaries the ey iteratures for the three schedue types of URN: the norma during-the-day operation, the first and the ast train operations. It can be seen that the obectives of timetabe optimiation among the different scheduing types are quite distinct; the differences are aso highighted by the system characteristics in Tabe. Tabe. The characteristics of the three schedue types in URN Characteristics During-the-day operation The first train operation The ast train operation Sufficient train capacity May not be in rush hour Yes Yes Passenger fow consideration Yes No No Successfu passenger transfer Yes Yes Yes or No Transfer accessibiity High Low Low Consideration of ine coordination No Yes Yes Connection time short ong Long Thus far, studies on first train scheduing have been imited and none has distinguished the importance of ines and transfer stations in reation to transfer demand. A ines and transfer stations have been considered as equay important. In a arge URN, there is generay an un-even distribution of demand, especiay for first trains, which paces different weight on the utiiation of different ines and at different transfer stations. To fi this gap, in this paper, we propose a first train timetabing optimiation mode with expicit consideration of the importance of ines and transfer stations.. Ti0metabe coordination mode of first trains.. Assumptions 0 To faciitate the mode formuation, severa assumptions are made throughout the paper. They are isted beow. Assumption. The capacity of the first trains can meet the passengers trave demand according to the actua data statistics of passenger trave OD fow voume. Therefore, the effects of passenger fow on the timetabe coordination are not considered. Assumption. The running time between any two stations and transfer time at the transfer station are given. The running time is derived in advance by operators, based on the speed of the train and the ength of the ine section. The transfer time utiied in the actua case study is obtained by a fied survey and data processing. Assumption. The upper and ower bounds of the departure times of first trains are specified

9 by operators. To start the service too eary or too ate wi have an impact on the cost or performance of the raiway system directy. The bounds are given according to the practica experience of operators... Symbo notations The foowing ists the notations used in our first train transfer optimiation mode. Networ variabes: L: the set of ines, L, L,, m, where m is the tota number of ines in the URN, there are as many ines in this networ as there are sets of transfer stations generay S : the set of transfer stations in the networ, S S S S, S, S ; m, where n g g n S : the set of transfer stations in ine, S s s s, s, s number of transfer stations in ine ; q S : the set of transfer stations from ine to ine, S s s s, s, s q is the intersection number of ine and ine ; Z : the set of a stations in the URN, Z,, Z : the set of stations in ine, tota number of stations in ine ; s T : the transfer waing time at transfer station H : the headway in ine ; ; m p Z, Z,, is the tota, where,where p is the s from ine to ine. R : the running time of first train from station to the adacent station in ine ; 0 DW : the dwe time of first train at station in ine ; Decision variabes: D : the departure time of first train at station in ine ; A : the arriva time of first train at station in ine ; s C : the connection time at station s for passengers who transfer from ine to first

10 connecting train in ine successfuy;.. Importance of ine and transfer station For first train coordination, the maor concern ies not in the tota passenger transfer time in this period, but that no passengers shoud have to wait excessivey ong for their transfer. The directions of trave of the demand for first-trains (mosty from residentia to wor areas), rather than the absoute passenger voume, are more important factors to consider. For this reason, we define the importance of a station/ine connectivity in a URN. We introduce the concept of importance degrees to describe the connectivity of ines and transfer stations.... Importance of ine The importance of ine is affected by four topoogica properties of a URN: the number of transfer stations, the number of connection ines, the number of stations excuding the transfer stations, and the overa ength of the ine. Appying the muti-criteria decision method, we define the importance of ine as a weighted product of these structura factors: 0 where,, and represent the reative weights of importance of the four criteria, and.0. The vaues of these weights are drawn from expert experience. The weighted product mode of () has the property that a four contributing factors are benefit criteria, in that the higher the vaues are, the more importance they bring to the ine. For exampe, the addition of a new transfer station to the ine wi attract not ony more passengers using the ine, but aso passengers from other stations and ines. In addition, the four factors are a indispensabe components of the ine importance, e.g., if the number of transfer stations is ero, the ine s importance as far as train coordination is concerned, wi aso be ero.... Importance of transfer station In this study, according to the geographic position of a station, we consider that a URN can be divided into two areas: the downtown area (the inner, dashed area in Fig. ) and the suburb area (the outside area and the rest of the networ in Fig. ). Transfer stations in each area have distincty different importance degrees.

11 Line Suburb D Downtown Line Line Line Line Line Fig.. Sub-networs in URN. The importance of a transfer station is determined primariy by the importance of the ines it is connected to. In addition, we ran the importance of a station by its reative ocation in the URN: whether it is in the downtown or the suburb area, and whether it is connected to the most important ine in the URN. Using the same muti-criteria anaysis method, we formuate the station importance as: ( ) s s s s c s where c s is the number of ines connected to station s, and are the importance ' vaue for a transfer station in the downtown area and the suburban area respectivey, and is an importance vaue associated being on the most important ine. s and s are 0- integer variabes. If the station beongs to the downtown area s = station is connected to the most important ine in the URN, s = ; otherwise, s =0. Liewise, if a ; otherwise, s = Probem formuation and mode properties Scheduing of first trains in a URN can be formuated as a transfer optimiation mode. In this mode, the obective is to minimie tota connection time at transfer stations couped with the importance degree of the station. Generay, it is expected that the transfer demand are ow in the suburban area than that in the downtown area because of the ac of choices of other ines to tae in the suburban areas. This is especiay the case for the first trains. The ey is to give priority to minimie the connection time in ines with higher degree and at more important stations. The proposed importance degrees can assist in deaing with this probem effectivey, with ess important stations and ines in the suburb maing a negigibe contribution to the tota connection time. Thus, the obective of the first train optimiation probem can focus on the stations or ines which have high importance degree.

12 For each ine, the arriving time s A and the departure time be cacuated according to the departure time at the starting station s D at the station s can 0, accumuative running time and dwe time from the starting station to the current transfer station, and the dwe time at the current station (see Fig. ). This is represented in Eq. () and Eq. (). time of first train in ine at the starting station 0. 0 D is the departure 0 D s A s D DW R DW s DW 0 s Fig.. The cacuating progress of arriving time and departure time at station s. s s s 0 () A D R DW s s s D A DW () Let us consider a group of passengers transferring from ine to ine at transfer station s which is the same as station in ine and station in ine (see Fig. ). s 0 p 0 p Fig.. The transfer station s. Thus the successfu transfer connection time from ine to ine at the transfer station s can be described with the foowing formuation:

13 s s s s C D - ( A T () The minimum connection time is onger than the transfer waing time which can ensure the successfu transfers, and then the tota connection time from a transfer stations becomes: s CT ( C ) () L L ss In most previous iteratures on scheduing for norma during-the-day operations, the obective function is usuay to minimie the tota passenger waiting time where the number of transfer passengers is expicity considered. Giving our Assumption on the reativey ow demand for first trains, in this paper, we focus on minimiing the connection time between first trains. In fact, a maor novety of our mode is to appy the importance degrees of ines and stations in the obective function for optimiing first train coordination. Our obective can be formuated as foows: s () L L ss s s f min ( C ) st.. s s 0 () A D R DW B A D A D () s s s s C D ( A T () s s s M ( ) C M () 0 The obective function () foows a muti-criteria formuation of the contributing factors to transfer costs: the importance degree of the station at which a transfer happens, the importance degree of the ine from the transfer is made, and the transfer cost. The product within Eq. () is a measure of the cost-importance of an individua transfer at a station. The obective function sums the individua cost-importance measures of a transfer directions, and presents then a cost-importance measure of the whoe networ. Constraint () means that the departure time of first train at any stations cannot be earier than A and ater than B, where A and B are constants. The transfer waing time between two ines within a transfer station is fixed and given. It incudes the time of passenger getting off a vehice, waing to another vehice and getting on. Constraint () sets the timing order for the arriva and departure times in stations and. Constraint () ensures that missing a connection is prohibited. A binary variabe s is introduced. For a ines and stations, where M is a sufficienty arge positive number. Eq. () states that, if s = when passengers succeed in transferring, then 0 C M. On the other s 0 s hand, if passengers fai to transfer, C 0 and s =0, then M 0. s C Here we present a Mixed Inter Linear Programming (MILP) mode for the timetabing probem of Eq. (). To find an effective soution, we anaye the mathematica properties of the

14 proposed mode. Property. According to constraints ()-(), the feasibe domains of D and A can be bounded by time windows, which are expressed by the foowing expressions: A A A B A p max,,min, () p D max A, D,min B, D. () Proof. The procedures for obtaining the departure time window are described as beow. When A A, according to the constraint () and Eq. (), s s 0, thus 0 A D R DW A. The eariest arriva time in ine is A. The atest arriva time in ine is A p. If A B, the atest arriva time in ine is A p B. However, the constraint () bounds A p B. Thus, A p B and p, the station is the ast one in ine. Therefore, we can obtain Expressions () bounding the arriva time in ine, and Expressions () bounding the departure time D. Property. Let N be an integer and determined by 0 0 D D N max,0. Here, H the symbo [] represents the integer portion of the argument. Thus, N represents the number of trains that has operated in ine before the start of service in ine. The ower and upper bounds of the first connection time between the first trains and ine are N H H, respectivey. s T and Proof. We can easiy obtain the ower bound of vaid connection time between first trains is s T. According to constraint (), when the two trains arrive the station at the same time, that is 0 s s D A. Then we can get C s T s. Assume that the first train of ine ust eaving when the N th train of ine arrive the transfer station, thus the connection time between N th train of ine and first train of ine is H. Therefore, the connection time between the first trains of these two ines is N H H. If the N th train of ine can mae a connection with the first train of ine, the connection time between the first trains in two ines is N H, where H. Thus, we obtain the upper bounds of first connection time

15 . form first train in ine to first train in ine is N H H. Sub-networs Connection Method (SCM) 0 0 In this paper, the timetabing probem beongs to the NP-hard cass (Ibarra-Roas and Rios-Sois, 0; Kang et a., 0). Therefore, a mathematica programming sover is seected to sove the mode ensuring that the operation managers can obtain a soution within a reasonabe amount of time. Many of the mode variabes and constraints are cosey reated to the topoogy of the rai networ and panning period in the proposed mode. These can be cacuated prior to conducting the optimiation process. To further improve the efficiency of the soution method, we present beow a pre-processing method to reduce the computation time. Here we describe the Sub-networ Connection Method (SCM) beow and show how to derive the departure times of first trains at starting stations. Then, a mathematica programming sover, CPLEX Sover is used to sove the suggested mode. Additionay, we compare the performances of the CPLEX Sover with artificia inteigence agorithms in the first train timetabing probem. Step. Divide sub-networs According to the networ ayout, the URN is divided into severa sub-networs denoted by R { r R, r r,}, where r represents the number of sub-networs. In most cases, the URN is divided into the downtown area and the suburban area. Step. Choose the benchmar ine For each sub-networ, the first step is to choose benchmar ine and the base station. A benchmar ine, according to the principe of preference theory, is the ine that has the maximum number of connection ines. This is most iey to be found in the first ayer. A base station is the transfer station that has the maximum number of transfer passengers. In the exampe shown in Fig., ine wi be the benchmar ine and the transfer station D wi be the base station. In our mode formuation, the benchmar ine and the base station are the ey factors. We cacuate departure times and arriva times of a stations in the sub-networ r by using the departure time at the benchmar ine. Namey, the departure time at benchmar ine is the initia time stamp. Step. Cacuate departure times at stations in the benchmar ine According to the departure time at the base station in different directions (up and down), we can cacuate the departure times at a stations in the benchmar ine with Eq. (). Step. Cacuate the departure times at transfer stations in the first ayer In the first ayer, we tae the order of the ines importance degree as the computation sequence. Then, we cacuate the departure times at transfer stations in other ines by using the departure time at the base station. To ensure the connection of both directions, the departure time at transfer station is chosen on the ater of up direction time and down direction time. Step. Cacuate the departure times at ines which beong to the first ayer

16 In the first ayer, we determine the departure times at a stations according to the departure times at transfer stations cacuated in step. Step. Cacuate the departure times at ines which beong to the second ayer Choosing the departure times at transfer stations connecting the two ayers is crucia to cacuate the departure times at a stations in the second ayer. The departure times at ey transfer stations are then used as initia vaues to cacuate the departure times at the ines in the second ayer. Step. Verify Chec departure times at transfer stations. If it is in the reasonabe time range, repeat Step and Step. Otherwise, we choose the benchmar ine and the base station again and perform Steps - unti the departure times at a transfer stations are reasonabe. The reasonabe time range can stipuate in the subway operating company. Here, the reasonabe time means that the departure times of first trains must fit in a consoidated standard. For exampe, in the Beiing subway, the departure times of first trains sha not be earier than 0:00 and not ater than 0:0. The procedure of SCM is iustrated in Fig..

17 Start No Define sub networ Yes Downtown Yes Benchmar ine Yes Base station No No Departure time of base station Departure times of transfer stations in the benchmar ine Taing the ines into order in the downtown Transfer stations Departure times of transfer stations in ines Departure times of a stations in downtown Suburb Departure times of transfer stations in the connecting ines Departure times of a stations in the connecting ines Considering the suburban ineseft in order Departure times of a suburban transfer stations A ines' Departure times of first trains Not reasonabe Verify End Fig.. The fow diagram of SCM.

18 . Case study. A simpe URN... Networ parameters In this section, we iustrate the worings of our proposed agorithm through a sma test networ (see Fig. ) with three ines and five transfer stations. For this simpe networ, we did not need to divide it into two sub-networs. We foow the SCM procedure to cacuate the initia departure times in each ine. The initia departure times at a transfer stations are shown in Tabe. Both the average transfer time and the dwe time are assumed to be 0. minute. Line up direction down direction Line S Line S S S S Fig.. A simpe test transit networ. Tabe. Initia departure times for the test networ Line Direction S S S S S Line Line Line Up :0 :0 :00 Down :0 :0 :0 Up :0 : :0 : Down : :0 : :0 Up : : : Down :0 :0 :0... Optimiation resuts The experiments are tested using CPLEX Sover. on a persona computer with an Inte Core i,. GH CPU and GB RAM. We consider the up and down directions of a ine in Fig. networ as separate ines in our mode. The transfer directions incude the directions from the

19 suburban area to the downtown area. Appying the CPLEX Sover, we obtain the optimied tota connection time of s. Tabe shows the timetabe after optimiation for this numerica exampe. Tabe. Departure times at the test networ after optimiation Line Direction S S S S S Up :0 :0 :00 Line Down :00 :0 :0 Up :0 : :0 : Line Down : :0 : :0 Up : : : Line Down :0 : : As mentioned above, the departure time in ine is chosen as the benchmar. Therefore, departure times in other ines can be obtained with the suggested mode. In addition, connection time for a transfer stations is shown in Tabe. The resuts show that the tota connection time is decreased by.%. Tabe. The connection time at transfer stations (min) Station S S Transfer direction Before Optimiation Connection time After Optimiation Improved Vaue/min down to up up to down down to down 0 up to up 0 down to up 0 down to down - down to up up to up down to up S up to down - down to down - up to up down to up S S up to down - down to down - up to up down to up - up to down

20 down to down 0 up to up 0 Tota connection time... Comparison of soution methods In this section, we compare the performance of using CPLEX Sover with other aternative optimiation methods in soving the first train timetabing coordination probem. Three other inteigent agorithms examined are: simuated anneaing (SA), genetic agorism (GA) and Partice Swarm Optimiation (PSO). The tests are a conducted on the simpe networ shown in Fig.. The performances of the four optimiation resuts are presented in Tabe. Two concusions can be put forward here. () A methods reach simiar optimied resuts (in terms of obective function vaues). However, the CPU times are different. It too CPLEX Sover 0.s to obtain the optima soution, whie for GA, SA and PSO, the CPU times are.s, s and s respectivey. () A inteigent agorithms shoud test the parameters to get the more accurate soutions, the vaue of parameters have direct infuence on the optima resuts. The CPLEX Sover is not necessary to test parameters. () A methods improve the obective function from 00s in the origina timetabe to s. However, the CPLEX Sover reaches the optima soution much faster and more effective than the other three methods. Tabe. Resuts of first train scheduing by different methods Departure time Method CPU (s) Iterations Obective Upper Lower Origina :00 : SA :0 : GA. :0 : PSO. 00 :00 : CPLEX :00 : 0. Beiing raiway networ... Networ description In order to verify the proposed mode and soution agorithm, this paper taes Beiing raiway networ as a case study, which has ines, stations. (See Fig. ). A the transfer stations have been mared with bac dot. The downtown area of this URN is mared by the dashed area.

21 Line Line LiShuiQiao( LSQ ) up direction down direction Line Line HaiDian Huang Zhuang ( HDHZ) Line ZhiChunLu BeiTuCheng ( ZCL) ( BTC ) Yong HeGong ( YHG) XiZhiMen ( XZM ) XiDan Dong Dan ( XD ) ( DD) Fu XinMen ( FXM ) XuanWuMen ( XWM ) Line HuiNan ( HN) ChongWenMen ( CWM ) Wang Jing Xi ( WJX ) ShaoYaoJu ( SYJ ) DongZhiMen ( DZM ) GuoMao ( JGM) ( GM) JianGuoMen Line Line SiHui( SH ) Line BT SiHuiDong ( SHD) Fig.. Beiing raiway networ.... Line importance According to Eq. (), the importance of ine in Beiing raiway networ are cacuated and shown in Tabe. The parameters are given as 0., 0., 0., 0.. The expert nowedge suggests that: () the number of transfer station is the most important factor as it determines the passengers accessibiity especiay in the arge scae networ; () the number of stations is more important than the ine ength because more stations wi transport more passengers. The numbers of stations, the number of transfer stations, the number of connection ines and overa ength shoud pertain to the same order of magnitude. Thus, the ine ength is represented as ength/iometers and based on rea data obtained from the geographic information database of Beiing metro networ. Tabe. The importance of ine in Beiing raiway networ Line The number of transfer stations The number of stations Removing transfer stations The number of connection ines Length/m The ine importance Line.0.

22 Line. Line. Line.. Line..0 Line.. Line 0..0 Line BT.. As ine is the ony ine beonging to the downtown area, it is set as the benchmar ine. Then ordering ine importance from argest to smaest, we get: ine, ine, ine, ine, ine, ine, and ine BT... Transfer station importance From Fig., we can easiy obtain the vaue c s, i.e. the number of connection ines for each station. Except XZM station which is connected to three ines, a other stations are connected to ust two ines. Then setting the importance variabes 0., 0., 0., we can cacuate from Eq. () the importance of transfer stations in Beiing raiway networ and the resuts are shown in Fig.. It is found that XZM station is the most important transfer station in Beiing raiway networ.. Transfer Station Importance HDHZ ZCL BTC LSQ HN SYJ XZM YHG DZM FXM XD DD JGM GM SH SHD XWM CWM Transfer Station Fig.. Importance vaue of transfer stations in Beiing raiway networ.

23 ... Initia soution Foowing the MSC procedure, we cacuate the departure times at ines according to their order of importance, and seect a transfer station which has the argest importance degree as a base station in benchmar ine. For Beiing raiway networ, we seect XZM station as a base station to cacuate the departure time in ine. The initia departure times of first trains are shown in Tabe. Tabe. Initia departure times of first trains in Beiing raiway networ Line Line Line Line Line Line Line Line Line BT UP : : :0 : : : : : DOWN : :0 :0 : : :00 : :... The system performance of Beiing raiway networ Optimied resuts of Beiing raiway networ The upper bounds of departure times are :00 and ower bounds of departure times are :0. The optimied departure times are isted in Tabe. Tabe. The optima departure times of first trains in a ines Line Line Line Line Line Line Line Line Line BT UP 0: 0: 0: 0: 0: 0: 0: 0: DOWN 0:0 0: 0:00 0: 0: 0: 0:00 0: 0 The tota connection time Tabe shows the departure times in Beiing raiway networ, and the parts of connection time before and after optimiation are given in Tabe. After optimiation, the seected stations tota connection time is seconds (see Tabe ). Compared to the seconds in the current timetabe (see Tabe ), the optimied resuts reduce the seected stations tota connection time by seconds or %. For the whoe Beiing raiway networ, the improvement is % (from seconds to 0 seconds). The resuts indicate that the proposed mode is effective in soving the first train timetabing probem. Tabe. The departure times of first trains in actua operation of Beiing raiway networ Line Line Line Line Line Line Line Line Line BT UP 0:0 0:0 0: 0: 0:0 0: 0:00 0:

24 DOWN 0:0 0:0 0:00 0: 0: 0: 0:00 0: Tabe. The connection time before and after optimiation at seected transfer stations Transfer The connection time The waiting time Station Transfer waing before optimiation after optimiation Improvement (s) time (s) (s) (s) up to up HDHZ down to up 0 0 down to down 0 00 down to up up to up HN down to up down to down - down to up up to up FXM up to down 0 down to down up to down down to up 00-0 GM up to up 0 - down to up 0 up to down 00 Tota connection time Minimiing Just Missed The concept of ust missed describes the situation where the connecting train is ust eaving when the passengers come to the patform (Kang et a., 0). This situation shoud be avoided if at a possibe. If the connection time is ess than the transfer waing time, a count of ust missed is registered. Tabe presents the improvement on ust missed in the optimied resuts. It shows that the optimied schedue is effective in removing a ust-missed. Tabe. Comparison of origina timetabe and optimied timetabe in Just Missed, parts of Beiing raiway Transfer Connection time (s) Just Missed Station Transfer waing time (s) Origina Optimied Origina Optimied SYJ up to up XZM down to down 0 0

25 DD down to up 0 0 DD up to down JGM down to up GM down to up 00 0 HN down to down 0 The infuence to subsequent trains The service time and headway are two important indicators to iustrate the system performance in the timetabe. The infuence of first train timetabe optimiation for subsequent train operations in URN system can be evauated by these two indicators. () The service time To ensure that the vehice maintenance and equipment maintenance, scheduing shoud not change the ength of non-service time. Tabe reveas the service time of the actua operation timetabe and the optimied timetabe utiied the proposed mode. There is amost no change in the ength of service time by the proposed first train scheduing mode. The rate of service time change is 0.%, suggesting that the timetabe has a minima impact on the service time whie maing improvements in connection times and avoiding ust-missed. Tabe. Comparison of operation time in Beiing raiway networ Line Line Line Line Operation time Up Down Up Down Up Down Up Down Origina timetabe : : : : : :0 : : Optimied timetabe :0 : : :0 : : : : Operation time Line Line Line Line BT Up Down Up Down Up Down Up Down Origina timetabe :0 :0 : : : : : :0 Optimied timetabe : : :0 : : : : :0 () The mean headway and headway variance We utiie headway distributions as an indicator to measure the impact of the first train departures on subsequent trains. Tabe denotes the departure times of ines in actua operation of Beiing raiway networ, for the first six trains of the ine. Tabe. The departure times of trains in actua operation of Beiing raiway networ Origina departure time Line Direction st train nd train rd train th train th train th train Up :0:00 ::0 ::0 ::0 ::0 ::0 Line Down :0:00 ::0 ::0 ::0 :0:00 ::0 Line Up :0:00 ::0 ::0 :: ::0 ::

26 Down :0:00 :: :: :: :: :: Up ::00 ::00 ::00 ::00 ::00 ::00 Line Down :00:00 ::00 ::00 ::00 :: :: Up ::00 ::00 ::00 ::00 ::00 ::00 Line Down ::00 :0:00 :0:00 ::00 ::00 ::00 Up :0:00 ::0 ::00 ::0 ::00 :0:0 Line Down ::00 ::0 ::00 ::0 ::00 ::0 Up ::00 :: :: :0:0 :: :: Line Down ::00 :: :0:0 :0: ::0 ::0 Up :00:00 :0:00 ::0 ::0 :: ::0 Line Down :00:00 ::00 ::00 :0: ::00 :: Up ::00 ::00 :0:00 :0:00 ::00 ::00 Line BT Down ::00 ::00 ::00 ::00 ::00 :0:00 Tabe ists the optimied timetabe which has the schedued departure times of first trains is as proposed by the optimiation mode. It is worth mentioning that headways of subsequent trains are invariant. Comparison with the origina timetabe, the ight typeface represent invariant departure times, and the bod typeface represents the optimied departure times. Tabe. Optimied departure times of trains in Beiing raiway networ. The ones in bod mar the new trains foowing the optimiation. Line Direction Optimied departure time st train nd train rd train th train th train th train Line Line Line Line Line Line Line Line BT Up ::00 :0:00 :0:00 ::0 ::0 ::0 Down :0:00 ::0 ::00 ::0 ::00 ::0 Up ::00 ::0 :: ::0 ::0 ::0 Down ::00 :: :: :: :: :: Up ::00 ::00 ::00 ::00 ::00 :0:00 Down :00:00 ::00 ::00 ::00 :: :: Up ::00 ::00 ::00 ::00 ::00 ::00 Down ::00 ::00 :0:00 :0:00 ::00 ::00 Up ::00 ::00 :0:00 ::0 ::00 ::0 Down ::0 ::00 ::0 ::00 ::0 :0:00 Up ::00 ::00 ::00 :: :: :0:0 Down ::0 ::0 :0:00 ::0 ::0 :0:0 Up ::00 ::0 ::0 :: ::0 ::0 Down :00:00 ::00 ::00 :0: ::00 :: Up ::00 ::00 :0:00 :0:00 ::00 ::00 Down ::00 ::00 ::00 ::00 ::00 :0:00 We use train woring diagrams to further iustrate the changes of first train scheduing. There are three situations as iustrated in Figs. -. The first situation is showed in Fig.. The x-coordinate indicates the departure times of trains aong ine, and the y-coordinate indicates the stations in ine. The bac thin ines denote the trains in the origina timetabe and the red heavy

27 ines represent the adding trains in the optimied timetabe. It can be seen that the first train departs earier in the optimied timetabe than the origina timetabe. There are two trains added in the optimied timetabe and the trains after depart according to the origina timetabe. Station Yu Quan Lu ::00 :00:00 :0:00 ::00 ::00 :0:00 ::00 :0:00 ::00 :0:00 Origina Trains Adding Trains Ba Bao Shan Ba Jiao Fairground Gu Cheng Ping Guo Yuan st train nd train rd train th train th train th train ::00 :00:00 :0:00 ::00 ::00 :0:00 ::00 :0:00 ::00 :0:00 Time Departure time advance Fig.. Setch train woring diagram in ine up direction. The second situation iustrated in Fig., shows that the first four trains in the origina timetabe were canceed, so the departure time of the first train is postponed. The optimied timetabe suggests that it is not necessary to schedue these four trains, which can ead to significant cost savings. Origina Trains Canceed Trains Station :0:00 ::00 ::00 :0:00 ::00 :0:00 ::00 :0:00 Yu Quan Lu Ba Bao Shan Ba Jiao Fairground Gu Cheng Ping Guo Yuan st train nd train :0:00 ::00 ::00 :0:00 ::00 :0:00 rd train ::00 :0:00 Time Departure time postponed Fig.. Setch train woring diagram in ine down direction.

28 The third situation is shown in Fig., where both adding trains and canceing trains happened in the optimied timetabe compared to the origina timetabe. In this exampe, two trains are canceed and one train is added but at a ater departure time, resuting in overa cost savings to the operators. Chang Chun Jie Station Origina Trains Canceing Trains Adding Trains ::00 ::00 ::00 ::00 ::00 :0:00 ::00 ::00 Fu Xing Men Fu Cheng Men Che Gong Zhuang nd train rd train th train th train st train Xi Zhi Men ::00 ::00 ::00 ::00 ::00 :0:00 ::00 ::00 Time Departure time postponed Fig.. Setch train woring diagram in ine up direction. The mean and variance for the headway of the first six trains are presented in Tabe. The overa rate of change in the mean headway is 0.% and in the headway variance is.%, suggesting that the departure times of first trains optimied by the proposed mode has minima impact on subsequent trains. Tabe. Comparisons of headway between origina timetabe and optimied timetabe Origina timetabe Optimied timetabe Line Direction The mean Headway The mean headway Headway headway (hour) variance (hour) variance Line Up 0:0: 0.0 0:0: 0.0 Down 0:0: :0: Line Up 0:0: :0: 0.0 Down 0:0: 0.0 0:0: 0.0 Line Up 0:0: 0.0 0:0: 0.00 Down 0:0: 0.0 0:0: 0.0 Line Up 0:0: 0.0 0:0: 0.00 Down 0:0: :0: 0.0 Line Up 0:0: 0.0 0:0: 0.0 Down 0:0: 0.0 0:0: 0.00 Line Up 0:0: 0.0 0::0 0.0 Down 0:0: 0.0 0::0 0.00

29 Line Up 0:0: 0.0 0:0:0 0.0 Down 0:0: 0.0 0:0: 0.0 Line BT Up 0:0: :0: Down 0:0: 0.0 0:0: 0.0 Average 0:0: :0: 0.0 The infuence to Transfer passengers The mean and variance for the headway of the first six trains are presented in Tabe. The overa rate of change in the mean headway is 0.% and in the headway variance is.%, suggesting that the departure times of first trains optimied by the proposed mode has minima impact on subsequent trains Concusion The first train probem becomes an important issue with the expansion of urban raiway networs. Passengers usuay have to transfer to other ine(s) to compete their ourna within a URN. The coordination of first trains is important because extremey ong connection time for first trains wi ead to ow networ accessibiity and discourage passengers from riding urban raiway transit. On the other hand, the earier the departure times for first trains, the higher operation cost to the URN. There are therefore trade-offs to be made between traveers who want mae a good coordination between first trains so that they can transfer smoothy and operators who want to minimie operationa costs. In this paper, a timetabe coordination optimiation mode of the first trains departure time is proposed whie minimies the connection time based on the importance of transfer stations and ines in URN. The CPLEX Sover is combined with a practica method of SCM to sove this probem. To verify the effectiveness of the proposed mode, a case study of Beiing raiway networ is performed. The resut shows that the tota transfer connection time is significanty reduced and the ust-missed situations avoided. For further research, we suggest that the extra traveing time shoud be considered as a non-deterministic factor in research of transfer optimiation. The first train groups probem (This was a timetabing probem invoving not ony the first train, but consecutive trains in the morning period) that are compatibe with passenger voume can be cacuated by considering the transfer coordination. In addition, in rea ife operations, parameters are difficut to caibrate due to the compexities of the networ structure and the ine characteristics. More empirica wor is obviousy required. Finay, a toerance eve can be considered for train departure time to increase the robustness of the schedue, the toerance eve represents the bounds of first train groups departure time to ensure a successfu transfer, cruciay, no redundancy trains. Acnowedgments This paper is party supported by China Nationa Funds for Distinguished Young Scientists (0), the Nationa Basic Research Program of China (0CB00), NSFC (), Research Foundation of State Key Laboratory of Rai Traffic Contro and Safety (RCS0ZT00), and the UK Rai Safety and Standards Board (Proect RSSB-T). In