A stochastic timetable optimization model in subway systems

With fixed running times at sections, cooperative scheduling (CS) approach optimizes the dwell times and the headway time to coordinate the accelerating and braking processes for trains, such that the recovery energy generated from the braking trains can be used by the accelerating trains. In practice, trains always have stochastic departure delays at busy stations. For reducing the divergence from the given timetable, the operation company generally adjusts the running times at the following sections. Focusing on the randomness on delay times and running times, this paper proposes a stochastic cooperative scheduling (SCS) approach. Firstly, we estimate the conversion and transmission losses of recovery energy, and then formulate a stochastic expected value model to maximize the utilization of the recovery energy. Furthermore, we design a binary-coded genetic algorithm to solve the optimal timetable. Finally, we conduct experimental studies based on the operation data from Beijing Yizhuang subway line. The results show that the SCS approach can save energy by 15.13% compared with the current timetable, and 8.81% compared with the CS approach.