A Practical Method for Timetable Rescheduling in Subway Networks During the End-Of-Service Period

Hindawi Journal of Advanced Transportation Volume 2018, Article ID 5914276, 9 pages https://doi.org/10.1155/2018/5914276 Research Article A Practical Method for Timetable Rescheduling in Subway Networks during the End-of-Service Period Wenkai Xu , Peng Zhao , and Liqiao Ning School of Trafc and Transportation, Beijing Jiaotong University, Beijing 100044, China Correspondence should be addressed to Peng Zhao; bjtu [email protected] Received 11 January 2018; Revised 30 April 2018; Accepted 8 May 2018; Published 27 June 2018 Academic Editor: Zhi-Chun Li Copyright © 2018 Wenkai Xu et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Tis study proposes a biobjective optimization method for timetable rescheduling during the end-of-service period of a subway network, taking all stakeholders’ interests into consideration. We seek to minimize the total transfer waiting time for all transfer passengers, meanwhile minimizing the deviation to the scheduled timetable. Te �-constraint method and linearization techniques are utilized to obtain the approximate Pareto optimal solutions within limited seconds, allowing for fguring out the trade-of between the two objectives. Te method is validated by numerical experiments for diferent delay scenarios based on a real-world case: the Beijing subway network. 1. Introduction before the end-of-service period, there is always a next connecting train which the transfer passenger can board. Recently, there are several contributions to the last-train But during the end-of-service period, the missed connecting timetabling problem of a subway system, which focused only train may be the last train of the connecting line; if so, the on the last train of each line in the network and expected transfer passenger cannot fnish his/ her trip via the subway to generate a more efciently scheduled timetable for all last system, which will bring a lot of inconvenience to the transfer trains [1–4]. However, it is very common that the scheduled passenger. timetable cannot be implemented because of unavoidable As a result, in order to deal with the disturbances occur- delays that occur at an operational level [5]. As a result, ring during the end-of-service period, the frst contribution this study is devoted to the timetable rescheduling problem of this study is that a timetable rescheduling model is during a specifc period: the end-of-service period. proposed from a stakeholder-oriented perspective with the Typically, most subway systems will be closed to the consideration of benefts of both passengers and operating public at midnight or thereabouts for maintenance. Owing to agencies. On the one hand, we seek to minimize the total the diferences in passenger fow characteristics between dif- transfer waiting time (TTWT) of all transfer passengers, and ferent lines in a subway network, the operational time frames a penalty time is adopted if transfer passengers miss their vary considerably among diferent lines. To be specifc, the last connecting trains, which benefts improving the level of end-of-service period in this study is defned as a period of service (LOS) afer disturbances. On the other hand, we try time from the scheduled departure time of the earliest last to minimize the deviation between the rescheduled timetable train from its originating station (among all last trains of all and the scheduled timetable, which also benefts passengers lines) to the time when all trains fnish their jobs. who do not need to transfer. Because of unavoidable disturbances in the daily opera- In addition, in contrast to previous studies that focused tion, a lot of contributions have been made to the timetable only on the last train of each line, there are multiple trains rescheduling problem during other periods (e.g., peak hours) running on each line during the end-of-service period, which [6]. But there is a considerable diference between the end-of- means that the train connection relationship in transfer service period and other periods. For example, if a transfer stations becomes much more complicated. But, the timetable passenger misses a connecting train due to a disturbance rescheduling is carried out through real-time adjustment of 2 Journal of Advanced Transportation an existing schedule, with a consequent need for fast compu- Schachtebeck and Schobel¨ [13], and Dollevoet et al. [14, 15] tation. In order to solve the practical problem of a large-scale by considering limited capacity of tracks, priority decisions, and complex network efciently, we utilize the �-constraint rerouting passengers, and limited capacity of stations. Binder method and some linearization techniques to convert the et al. [16] proposed an ILP model with three objectives: proposed model into an integer linear programming (ILP) the passenger satisfaction, the operational costs, and the model that can be solved by Cplex speedily, which constitutes deviation from the scheduled timetable. Strategies include the second contribution of this study. canceling, delaying, rerouting the trains, and scheduling Te third contribution of this study is that a real-world emergency trains. case study of the Beijing subway network is presented to More recently, there are several publications focusing validate the efectiveness of the proposed method. Historical on timetable rescheduling of a subway system. However, automaticfarecollection(AFC)dataoftheBeijingsubway methods were mostly proposed at a single-line level. Xu system is available to obtain the number of transfer passen- et al. [17] modeled the problem as a discrete event model gers of each connection, as an important input of our model. considering service balance performance of both directions Te approximate Pareto frontier is obtained by calculating on a double-track subway line. Te model is expected to the approximate Pareto optimal solutions, which helps us minimize the total delay time of all trains rather than all understand the trade-of of the two objectives. passengers. Gao et al. [18] integrated the skip-stop pattern Te rest of this study is organized as follows. Section 2 into the rescheduling model for a double-track subway line. reviews some recent studies about timetable rescheduling An iterative algorithm was proposed to solve the model and last-train timetabling. Te stakeholder-oriented model based on the model decomposition. Xu et al. [19] proposed for timetable rescheduling during the end-of-service period a passenger-oriented model for rescheduling on a subway is proposed in Section 3. Section 4 presents the model line considering the limited train capacity. Te delay time conversion and the solution strategy. Some experiments of alighting passengers and the penalty time of stranded based on a real-world case, the Beijing subway network, are passengers constitute the generalized delay time, which is carried out in Section 5. Section 6 draws some conclusions expected to be minimized. andfuturedirectionsinbrief. 2.2. Last-Train Timetabling. An enormous amount of litera- 2. Literature Review tures contribute to the timetabling problem, like Caprara et al.[20],ZhouandZhong[21],LeeandChen[22],Cacchiani Teliteraturereviewpresentedinthissectionfocusesontwo and Toth [5], and Yang et al. [23]. However, the last-train aspects: timetable rescheduling and last-train timetabling. timetabling problem of a subway system is an emerging issue Some recent publications are reviewed below in detail. in recent years. However, all related publications focused only on the last train of each line. Zhou et al. [1] developed an 2.1. Timetable Rescheduling. Terearealotofstudiesfocus- optimization model to reduce passengers’ transfer waiting ing on timetable rescheduling, which can be classifed by time for last trains and inaccessible passenger volume of disturbance or disruption, microscopic or macroscopic, and all origin-destination pairs. Coordinated departure times for passenger-oriented or train-oriented [6]. Various approaches all last trains are determined by the model. Kang et al. [2] have been developed in these previous studies. established a programing model with adjustable running From a train-oriented perspective, D’Ariano et al. [7] times and dwell times to obtain coordinated arrival and regarded the timetable rescheduling problem as a huge departure times of last trains at transfer stations. A genetic job shop scheduling problem with no-store constraints and algorithm was designed to solve the model. Kang et al. modeled the problem with an alternative graph formulation [3] modeled the problem as a mean-variance model to to minimize the deviation from the scheduled timetable. Tey improve the efciency of transfer passengers. Te model proposed a branch and bound algorithm with implication was solved by a genetic simulated annealing algorithm. rules enabling the speed up of the computation. Tornquist¨ Kang and Zhu [4] studied the same problem in Kang et and Persson [8] presented a MIP model to minimize a cost al. [2] and designed a new heuristic algorithm outper- function based on train delays considering reordering and forming both genetic algorithms and simulated annealing rerouting of trains. But for certain scenarios, it is difcult to algorithms. fnd good solutions within seconds. Terefore, Krasemann Based on all publications reviewed above, we present [9] designed a greedy algorithm to quickly fnd a good the focus of this study here.

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