Stochastic Delay Propagation

In daily operation, railway traffic always deviates from the planned schedule to a certain extent. Primary initial delays of trains may cause a whole cascade of secondary delays of other trains over the entire network. In this project, we develop a  stochastic model for delay propagation and forecasts of arrival and departure events which is applicable to all kind of public transport (not only to railway traffic). Our model is fully realistic,  it includes general waiting policies (how long do trains wait for delayed feeder trains), it uses driving time profiles (discrete distributions)  on travel arcs which depend on the departure time, and it incorporates the catch-up potential of buffer times on driving sections and trains stops. The model is suited for an online scenario where a massive stream of update messages on the current status of trains arrives which has to be propagated through the whole network.

Efficient stochastic propagation of delays and forecasts for the likelihood  that planned transfers between connecting trains are feasible have important applications in online timetable information, in delay management and train disposition, and in stability analysis of timetables.

The proposed approach has been implemented and evaluated on the German timetable of 2011 with waiting policies of Deutsche Bahn AG. A complete stochastic delay propagation for the whole German train network and  a whole day can be performed in less than 14 seconds on a PC. We tested our propagation algorithm with artificial discrete travel time distributions which can be parameterized by the size of their fluctuations. We compare our forecasts with real data for different types of days, namely a weekday and a day on the weekend. As can be expected, the range of the support of the distributions increases with the size of fluctuations and an increase of the time horizon, but all scenarios turned out to be computable in almost real time. Hence, stochastic simulation of delays is efficient enough to be applicable in practice, but the forecast quality requires further adjustments of our artificial travel time distributions to estimations from real data.

Details can be found in the Technical Report 2011/1: Stochastic Delay Prediction in Large Train Networks.

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