Optimal Coordination of Last Trains for Maximum Transfer Accessibility with Heterogeneous Walking Time

Abstract

Last train coordination aims to synchronize the arrival and departure times of the last feeder trains and the last connecting trains at transfer stations to improve the transfer accessibility of urban rail networks. This study focuses on the transfer accessibility between last trains with considering heterogeneous transfer walking time. Three mathematical models are developed on the last train timetable optimization. The first model fine-tunes the last train timetable under the given bound of the dwell time. The second one aims to allow the mutual transfers with the prolonged dwell time to maximize the transfer accessibility. A biobjective function is proposed to seek the trade-off between the maximal transfer accessibility and the minimal extension of dwell time. The third model considers the heterogeneity of transfer walking time that is represented as a random variable following a probability distribution. A discrete approximation method is proposed to reformulate the nonlinear model. The embedded Branch & Cut algorithm of CPLEX is applied to solve the models. A real case on the Shenzhen metro network is conducted to demonstrate the performance of the models. The three models all provide better last train timetable than the current timetable in practice. The sensitivity analysis manifests that the third model are always advantageous in the optimization of successful transfer passengers.

First-Train Timetable Synchronization in Metro Networks under Origin-Destination Demand Conditions

“…Cevallos and Zhao [4] presented a system-wide approach to minimize the total transfer times by shifting existing timetables. Considering heterogeneous transfer walking times, Chen et al [5] proposed a mixedinteger quadratic programming model to maximize the number of transfer passengers for last train services on metro networks. A mixed-integer programming model was established by Chen et al [6] to improve passenger accessibility.…”

A Stochastic Programming Approach for Scheduling Extra Metro Trains to Serve Passengers from Uncertain Delayed High-Speed Railway Trains

“…Since these two problems are quite different (see also erefore, it is necessary to develop a new mathematical model to describe this problem, which is challenging due to its stochastic and biobjective nature as discussed in Section 1. Finally, worth mentioning are also studies that focus on the specific timetabling aspect of synchronizing the last trains in railway or metro systems, recent examples of which include Yang et al [22]; Chen et al [23]; and Long et al [1]. Although the last metro train synchronization problem also considers factors such as the successful transfer of passengers and the running time of the last trains, this problem is conceptually very different than the extra train scheduling tackled in this paper, where the main decision is about how many additional trains to add at night to serve delayed HSR passengers.…”

Coordination of Last Train Transfers Using Potential Passenger Demand From Public Transport Modes

“…Few studies considered actual passenger demand during the last train period. Some research studied the last train problem without the consideration of passenger demand [5]- [8], [14], [15], while others [9]- [12], [16], [17] assumed that the demand is given or generated randomly. But the assumption might nitrogen be suitable because the hypothetical demand used may lead to completely different results compared to realistic situations.…”

“…Some researches focused on the passenger destination accessibility for metro last trains. The destination accessibility indicates the percentage of passengers using last trains at origins who can reach their destinations successfully [9], [10]. Yao et al [11] put forward a dynamic accessibility index of urban rail transit to optimize the last train schedule.…”