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

Yao Chen,Baohua Mao,Tin Kin Ho,Yun Bai,Zhujun Li

doi:10.1155/2019/9692024

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.

Highlights

Urban rail transit plays a very important role in the public transportation system to alleviate road congestion and reduce pollution, through the high requirements on safety and reliability and the service provision of mass capacity and environment-friendliness
This paper proposes three optimization models on the timetable coordination among last trains of different lines on an urban rail network
Model (A) fine-tunes the running and dwell time of last trains with the given lower and upper bounds, which is formulated as a mixed integer linear programming

Summary

Introduction

Urban rail transit plays a very important role in the public transportation system to alleviate road congestion and reduce pollution, through the high requirements on safety and reliability and the service provision of mass capacity and environment-friendliness. The transfer walking time of different passengers are assumed to be a point value for the purpose of simplification in previous studies [2,3,4, 7, 8] Such an assumption is unlikely to be valid at a real-life transfer station. This paper attempts to design a last train timetable that enables the two-way transfer accessibility with considering the heterogeneity in transfer walking time. With the consideration of both transfer passengers and onboard passengers, the maximal transfer accessibility is achieved at the minimal cost of the increased dwell time This is the first attempt to address the last train coordination under the heterogeneity of transfer walking time.

Literature Review

Last Train Timetable Modelling

Case Study

Conclusions