Timetable Synchronization of Last Trains in an Urban Rail Network to Maximize Service Accessibility and Minimize Transfer Waiting Time

Approaching operation closure of an urban rail network, the service accessibility gradually decreases and the headway becomes longer. Timetable synchronization of last trains is an effective way to improve the service accessibility of crucial original-destinations (SACOD) and reduce the waiting time of transfer passengers. The service accessibility is determined by the transfer connections of trains, while the waiting time of transfer passengers depends on train arrival and departure times. In this regard, this paper proposes a two-phase model which seeks best transfer connections of last trains firstly and then attains the most appropriate departure times of last trains contributing to reducing passenger waiting time. The first phase is to find the range of departure times of last trains, with the objective of maximizing the number of passengers reaching their destinations successfully through metro service. Constrained by range obtained in the first phase, the second phase is to choose specific departure times of last trains on all metro lines to minimize the total waiting time of transfer passengers at transfer stations. A binary tree traversal algorithm (BTTA) is developed to attain the optimal solution of the first phase model, while a genetic algorithm (GA) is applied to solve the second phase model. Case studies on Wuhan metro network show that the optimized timetable improves the service accessibility of crucial ODs by 49.08% in comparison with the practical timetable and reduces passenger transfer waiting time by 2.48%. Additionally, BTTA is able to quickly find the optimal solution of the first phase and the timetable obtained by the developed algorithm performs much better than the solution using GA in both the first and the second phases.