Timetable Mapping Model and Dynamic Programming Approach for High-speed Railway Rescheduling

In railway systems, rescheduling trains in case of delays or disruptions occur is a critical and challenging task to remain the punctuality of railway traffics. Solving the railway traffic rescheduling problem is complex, computation-intensive and time-consuming from practical and computational perspectives. The problem has typically a very large search space, making it time-consuming to solve even for state-of-the-art optimization solvers. In this paper, a dynamic programming (DP) approach is used to address the issues of high computation costs in rescheduling railways traffics under various delays, in order to map the arrival and departure time of the train to the state of DP, we develop a timetable mapping model for the real-time train rescheduling (TTR) problem. Each section is modeled as a stage in the action space and the state of each stage is represented by the departure sequence of all the trains at the station for timetable mapping. And we further obtain the state transfer equation and construct the Bellman equation with the goal of minimizing the total delay time and use the Bellman equation inverse to derive the solution. Finally, numerical experiments of TTR are conducted. The advantage of the proposed DP is illustrated from the perspective of the strategy compared with the widely used First-Come-First Serve (FCFS) and the First Schedule-First-Serve (FSFS). It shows that the proposed DP can effectively solve the TTR problems, especially for primary delay problems.