Dynamic and robust timetable rescheduling for uncertain railway disruptions

Unexpected disruptions occur frequently in the railways, 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 hours. In practice, a disruption may become shorter or longer than predicted. To take the uncertainty of the disruption duration into account, this paper formulates the 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 a two-stage stochastic model computes the optimal rescheduling solution to all these scenarios. 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.