Rob Goverde: Railway infrastructure capacity analysis using stochastic max-plus algebra

Max-plus algebra is a very efficient tool to model and analyse periodic railway timetables and their infrastructure consumption, both in a microscopic and a macroscopic way. In particular, the eigenvalue problem in max-plus algebra relates to the UIC timetable compression method of capacity consumption calculations when the timetable is modelled microscopically with blocking times. In a max-plus setting this capacity method is easily generalized to networks including connections at stations. This presentation shows how these max-plus models can be analysed efficiently in the general-order form, without first having to translate the model to a pure first-order model x(k)=Ax(k-1). The max-plus models can be generalized to stochastic systems, where the process times follow arbitrary stochastic distributions. In this case, the mean cycle time can be computed as a measure of capacity consumption showing the effect of variations in the process times over deterministic values. The algorithms apply to large-scale systems using a sparse matrix representation of the max-plus models.