Rescheduling Trains Using Petri Nets and Heuristic Search

Railway systems may be interrupted by unforeseen events that require quick replanning to a feasible new schedule. This paper deals with the train rescheduling problem on double-track lines. The rescheduling problem is regarded as a conflict detection and resolution procedure. Timed Colored Petri nets are adopted to model the railway system: places represent rail resources, and tokens represent trains. A conflict detection rule is established in accordance with the safety principles of railway operations to predict potential conflicts. A Petri-net-based conflict resolution algorithm adapted from the A* algorithm is designed to search for an optimal or a near-optimal feasible schedule. The algorithm takes into account the railway operational principles when generating new markings, so that the new schedule has less train delays and respects the safety principles. The approach is applied in a case study to a double-track corridor from the Dutch railway network. For small delays, the algorithm can make delayed trains recover to their scheduled timetable within seconds. For large perturbations, the solutions generated by the algorithm can effectively reduce train delays while ensuring traffic safety.