On busy congested rail networks, randomdelays of trains are prevalent, and these delays have knock-on effects which result in a signi®cant or substantial proportion of scheduled services being delayed or rescheduled. Here we develop and experiment with a simulation model to predict the probability distributions of these knock-on delays at stations, when faced with typical patterns of on-the-day exogenous delays. These methods can be used to test and compare the reliability of proposed

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... or schedule changes, before adopting them. They can also be used to explore how schedule reliability may be affected by proposed changes in operating policies, for example, changes in minimum headways or dwell times, or changes in the infrastructure such as, layout of lines, platforms or signals. This model generates a reliability analysis for each train type, line and platform. We can also use the model to explore some policy issues, and to show how punctuality and reliability are affected by changes in the distributions of exogenous delays.