Modelling reliability of train arrival times

This paper deals with the scheduling of trains so as to minimise train trip times, whilst maximising reliability of arrival times. The amount of risk of delay associated with a schedule is used as the reliability component of a constrained schedule optimisation model. The paper outlines the model developed to quantify the risk of delays to individual trains, as well as to specific track segments and to the schedule as a whole. The risk model, which deals with single track operations, can be used to estimate the likely impact on reliability of arrival times of changes in train frequencies and operating practices; track and station infrastructure investment strategies; and train technology upgrading. An application of the model to the optimisation of schedules on a track corridor is described. The results obtained using the model are compared with the schedules used by train operations planning staff, in terms of overall delay and timetable reliability. The results highlight the significance of including a measure of timetable reliability, such as risk of delays, in the objective function for scheduling optimisation