The Railway Rapid Transit frequency setting problem with speed-dependent operation costs

In this paper we deal with the problem of determining the best set of frequencies in a Railway Rapid Transit network considering convex non-linear variable operation costs at segments. The operation cost at each track will depend on the train model characteristics operating each line, the passenger load on trains and the average train speed. Given the network topology and the passenger mobility patterns, we propose a methodology to determine the best regular timetable, taking into account both, users' and service provider points of view. Since the frequency setting and the passengers assignment are intertwined problems, the proposed procedure solves a succession of interrelated transit assignments and frequency setting models. At each iteration, given a transit assignment, the resultant frequency setting problem turns into a Mixed Integer Non-Linear model which is solved to optimality in a sequential way, both considering the different train models and the passenger load on trains. The proposed methodology is illustrated on a real-size scenario.