Modelling Delay Propagation in Railway Networks

In this paper we study the accumulation and propagation of delays in (simplified) railway networks. More precisely, we want to estimate the total expected arrival delay of passengers as a cost criterion to be used in a timetable optimisation. Therefore, we want to determine the delay distributions analytically from given source delay distributions. In order to include accumulation and propagation of delays, the source delay distribution must belong to a family of distributions that is closed under appropriate operations. This is the case if we can represent the distribution functions by so called theta-exponential polynomials. A drawback of this representation is the increasing number of parameters needed to describe the results of the operations. A combination with moment approximations allows to solve this problem with sufficient accuracy. Generally, the calculation of propagated delays requires a topological sorting of arrival and departure events. That excludes cyclic structures in the network. We present a relaxation of the topological sorting that allows to (approximately) calculate long run delays in cycles.