A variable trip time model for cyclic railway timetabling

In this paper we describe how variable trip times can be included into an existing cyclic railway timetabling model based on the well-known periodic event scheduling problem (PESP). Thereby we provide an extension of the existing model because in the existing model it is assumed that the trip times of all trains on all tracks of the railway network are known a priori. However, the latter may be too restrictive in practice. The solution space of the extended model that we present is larger because small deviations from the fixed trip times are allowed. This is especially useful when a feasible solution to the fixed trip time model does not exist. The solutions obtained from the extended model are proven to be correct under certain necessary and sufficient conditions. Furthermore, the extended model has the same general structure as the original model. Therefore, solution methods developed for the original fixed trip time model can be applied to the extended model as well.