Modelling Delay Risks Associated with Train Schedules

The overall timetable reliability is a measure of the likely performance of the timetable as a whole, in terms of schedule adherence. The reliability of arrivals is a critical performance measure for all rail markets. This paper presents analytically based models designed to quantify the amount of delay risk associated with each track segment, train and the schedule as a whole. Three main types of delays are modelled, namely: terminal/station delays; track related delays; and rolling stock related delays. The models can be used to prioritise investment projects designed to improve timetable reliability. For example, a comparison can be made between track, terminal and rolling stock projects, in terms of their likely impact on timetable reliability. The effect of timetable changes on likely reliability can also be modelled. Using the risk models developed here, it is possible to assess the likely effect of removing/adding sidings for passing and crossing purposes, under single line train operations. The paper illustrates the use of the models using a series of tests with a timetable consisting of nine trains and six stations. The effect of changing assumptions regarding delays due to terminal congestion; track related problems; and rolling stock, are modelled and the results are summarised. Also modelled is the impact of changes to the timetable.