Stochastic delay propagation in railway networks and phase-type distributions

It is difficult to analyse stochastic models for the propagation of delays in railway networks. It seems that the choice is between very global mathematical (queueing) models at one extreme and simulation models at the other. In this paper we discuss a (fairly general but not too detailed) model for delay propagation and show that in a world of so-called phase-type distributions it is possible to derive secondary delay distributions from primary delay distributions. We shall explain why phase-type distributions and the delay propagation model are suited for each other and show by an example that it is possible to develop algorithms that analyse such networks.