Rebecca Haehn: Satisfiability Checking for Optimisation of Timetables in Railway Engineering under Consideration of Uncertainties

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Railway traffic is steadily increasing. Since changes in the railway infrastructure are expensive and take a long time, it is also increasingly important to optimize the exploitation of the available infrastructure capacity. At the same time the quality of service should still be satisfying. Unfortunately, with increasing traffic volume, the time intervals between consecutive trains are smaller, which makes it more likely that even small delays sensitively propagate and have a strong negative impact on other trains’ punctuality. Rebecca Haehn’s project aims at developing an approach to examine the robustness of a given timetable under consideration of probabilistic primary delays (i.e., the original sources of delays, not caused by the delays of other trains), and to use this approach to schedule additional freight trains such that certain cost functions are minimized while the probabilities to cause additional delays to the given fixed timetable stays below given specified limits. As a starting point, Haehn first developed an elegant method for freight train scheduling, without considering delays. The second milestone was the development of a symbolic simulation method to estimate the probabilities of delays in a fixed timetable under given probabilities for primary delays. Whereas that method neglected stochastic dependencies, current work in an advanced status (implementation nearly finished) considers also those dependencies and is thus able to provide exact results. The last steps will be the schedule of freight trains using the developed symbolic simulation and the completion of a user interface to ease the usage of the developed methods and the visualization of the analysis results. The dissertation has been delayed by unexpectedly time-consuming processing of real-world data provided by the Deutsche Bahn.