Periodic Railway Timetabling with Event Flexibility

Abstract. This paper addresses the problem of generating conflict-free periodic train timetables for large railway networks. We follow a two level approach, where a simplified track topology is used to obtain a macro-level schedule, and the detailed topology is considered locally on the micro level. To increase the solution space in the interface of the two levels, we propose an extension of the well-known Periodic Event Scheduling Problem (PESP) such that it allows to generate flexible time slots for the departure and arrival times instead of exact times. This Flexible Periodic Event Scheduling Problem (FPESP) formulation considerably increases the chance to obtain feasible solutions (exact train routings) subsequently on the micro level, in particular for stations with dense peak traffic. Total trip time and the time slot sizes are used as multiple objectives and weighted and/or constrained to allocate the flexibility where it is most useful. Tests on a medium size instance of the Swiss Federal Railways 2007 service intention demonstrate the advantage of the FPESP model, while it only moderately increases its solution time in most cases.