Flexible Connections in PESP Models for Cyclic Passenger Railway Timetabling

In this paper we describe how rolling stock and passenger connections in a cyclic railway timetable can be modeled in a flexible way within the model for the Periodic Event Scheduling Problem (PESP). The PESP model was introduced by Serani and Ukovich (1989). Usually, PESP-models assume that the constraints for rolling stock or passenger connections specify in detail which trains should connect with each other. However, the flexibility described in this paper allows the model to choose which trains should connect with each other in a rolling stock or passenger connection. We express the required number of train compositions in terms of the integer cycle variables of the constraint graph. We also describe an abstract framework, demonstrating that, under certain conditions, the extra flexibility can be modeled purely in terms of PESP constraints. The concept of flexible rolling stock and passenger connections is illustrated by an example based on three intercity lines of Netherlands Railways.