Robustness Improvements in a Train Timetable with Travel Time Dependent Minimum Headways

In a railway network with dense traffic, trains’ scheduled arrival and departure times are highly dependent on each other and even a small delay easily propagates to subsequent trains using the same infrastructure resources. In the current paper a given timetable is compared to a modified timetable, where the assigned minimum time slot in the traffic for a service is linearly increasing with the service’s travel time. The underlying assumption is that trains lose precision as they travel longer and catching a fixed-size time slot is easier at the beginning of the journey. Real world observations confirm this assumption as well. The aim of this study is to verify the improvement in the robustness of those timetables that are modified with respect to the idea of travel time dependent reserved time slots for the arrival times of trains and to compare the results with the initial timetables. Numerical experiments are conducted on a selected double track segment of the Swedish Southern mainline. Four timetable case studies are considered for the experiments: off-peak hours and peak hours in 2011 and 2014, respectively. Each timetable is tested for various disturbance scenarios. Several performance measures are used to evaluate delay propagation in the timetables, including deviations from the initial timetable, total delays, total number of delayed trains at destinations, number of punctual trains with 5 minutes arrival delay tolerance at destinations and number of violations in trains’ overtaking orders. Results show that the modified timetables outperform the initial ones for small disturbances.