Sensitivity analysis of a railway station track layout with respect to a given timetable

An important step in the process of designing a railway station track layout is the verification of the robustness of the layout with respect to the timetables it is based on. For this purpose we develop in this paper an algorithm to randomly perturb a given timetable such that the perturbation is feasible and has the same structure as the given timetable. Mathematically, in this paper we study the problem of, given a set of integer variables and a set of binary relations stating minimal and maximal differences between the variables, to generate solutions uniformly at random. The algorithm involves the simulation of a Markov chain whose state space is a particular subset of the set of feasible timetables and whose limiting and equilibrium distribution is the uniform distribution. Whereas this idea seems simple, some technical pitfalls need to be overcome to make it sound.