A practical model for last train rescheduling with train delay in urban railway transit networks

• A last train operation model is proposed to minimize the running time and the dwell time, and to maximize the average transfer redundant time and the network accessibility.
• The transfer directions and the delay time in the subway are analyzed.
• The most sensitive section in a subway line can be identified. If the last train delay is less than the permitted time, the system can neutralize the effect of the delay.

Last train timetable rescheduling aims at coordinating the arrival and departure times of feeder trains with connecting trains at transfer stations to eliminate the effect of unexpected incidents in train operations. It has become a challenging problem in the operations and management of urban railway transit networks because of high complexities in coordination among lines. In this paper, we propose a rescheduling model for last trains with the consideration of train delays caused by incidents that occurred in train operations. In the model, two aspects are considered. On one hand, we try to minimize the running time and the dwell time, and to maximize the average transfer redundant time and the network accessibility. On the other hand, we expect to minimize the difference between the original timetable and the rescheduled one. A genetic algorithm is developed to solve this problem. The case study of Beijing railway transit network shows that once a delay occurs in a section, the most effective way to adjust the timetable consists of adjusting the running time of trains that have strong transfer relationships with the delay section. If the delay is not substantially long, the suggested model would neutralize the influence of the delay.