Resolving instability in railway timetabling problems

A significant growth of the railway transportation demand is forecasted in the next decades which needs an increase of network capacity. Where possible, infrastructure upgrading can provide extra capacity; although in some cases, this is not enough to satisfy the entire transportation demand even if optimised timetabling is performed. We propose a heuristic model to develop a stable timetable which maximises the satisfaction of transportation demand in situations where network capacity is limited. In case the demand cannot be fully satisfied, the model relaxes the given line plan and timetable design parameters. The aim is to keep as many train services as possible and reduce the level of service minimally. We develop a mixed integer linear programming (MILP) model for minimising the cycle time to find an optimised stable timetable for the given line plan. The heuristic iteratively solves the MILP model and applies relaxation measures. We tested the model on the Dutch network. The results showed that the model can generate stable timetables by removing train services from the critical circuit, and also, higher transportation demand can be satisfied by additionally relaxing timetable design parameters.