Dynamic and Robust Timetable Rescheduling for Uncertain Railway Disruptions

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Unexpected disruptions occur frequently in railway systems, during which many train services cannot run as scheduled. This paper deals with timetable rescheduling during such disruptions, particularly in the case where all tracks between two stations are blocked for a few hours. In practice, the disruption length is uncertain, and a disruption may become shorter or longer than predicted. Thus, it is necessary to take the uncertainty of the disruption duration into account. This paper formulates the robust timetable rescheduling as a rolling horizon two-stage stochastic programming problem in deterministic equivalent form. The random disruption duration is assumed to have a finite number of possible realizations, called scenarios, with given probabilities. Every time a prediction about the range of the disruption end time is updated, new scenarios are defined, and the model computes the optimal rescheduling solution for an extended control horizon, which is robust to all these scenarios. Based on the model, uncertain disruptions can be handled with robust solutions in a dynamic environment. The stochastic method was tested on a part of the Dutch railways, and compared to a deterministic rolling-horizon method. The results showed that compared to the deterministic method, the stochastic method is more likely to generate better rescheduling solutions for uncertain disruptions by less train cancellations and/or delays, while the solution robustness can be affected by the predicted range regarding the disruption end time.