Optimisation of train schedules to achieve minimum transit times and maximum reliability

The overall timetable reliability is a measure of the likely performance of the timetable as a whole, in terms of schedule adherence. The concept is a critical performance measure for both urban and non-urban rail passenger services, as well as rail freight transportation. This paper deals with the scheduling of trains on single track corridors, so as to minimise train trip times and maximise reliability of train arrival times. A method used to quantify the amount of risk of delay associated with each train, each track segment, and the schedule as a whole, is used as the reliability component of the constrained optimisation model. The methodology used to estimate the risk of delay is put forward. The paper also describes a number of alternative solution techniques for the scheduling problem. These techniques include exact optimal solutions using branch and bound, and heuristic approaches, such as genetic algorithms, nearest neighbourhood heuristic and tabu search. Some of the results of using these alternative approaches are briefly described. The schedule produced using risk of delay in the objective function, will be the most efficient in terms of delay due to train conflicts and delay that may occur due to unexpected events. The model and solution techniques are applied to the problem of determining improved positions of sidings on a single track corridor, with respect to a given schedule.