Computing Joint Delay Distributions for Trains in Railway Networks

Stochastic models for delay propagation in railway networks lead to promising results in the prediction of train delays. To respect waiting time policies, while preserving efficiency, these solutions assume that the departure and arrival times of trains are stochastically independent. We show, that the inherent error can become a significant problem. To tackle this problem, we first present formulas to calculate joint delay distributions for dependent trains in a basic structure. Using these distributions we can then calculate exact distributions for connecting trains. We then present a computational study comparing our calculation to a calculation, which uses the independence assumption, on a real world timetable of the German railway network (Deutsche Bahn AG). Our results show that, in the real world timetable, the error is negligible, but we still discuss how different structures could influence the result.