Finding Delay-Tolerant Train Routings through Stations

Abstract

Currently, many railway operators are increasing the frequencies of their trains. By condensing the timetable, routing trains becomes increasingly difficult as the chosen routes not only have to meet safety restrictions, but also guarantee some stability if delays occur.

We address the problem of routing trains through railway stations for a given timetable and outline two algorithms. The first algorithm searches for a feasible solution for the train routing problem based on an independent set modeling that is solved using a fixed-point iteration method. The initial solution is then amended by applying the second algorithm in order to increase the time slot of a chosen route, i.e. the time interval during which a train may arrive and find its designated route open. This algorithm is based on a local search optimization scheme.

Results showed that the fixed-point iteration found feasible solutions within minutes even for difficult cases, i.e. tight timetables. Though more time-consuming, the second algorithm allowed the average time slot length to be doubled, thus implying that it is possible to find routings which are more delay-tolerant. This helps to decrease impacts of late trains.