MoN9: Ninth Mathematics of Networks meeting, 18th June, St Andrews University

Keith Briggs (BT Research) - Optimal trip-planning in transport systems with random delays

This is joint work with Peter Kin Po Tam, Birmingham University

Public transport systems are likely to be always subject to delays, and a disincentive to passengers is the complexity of planning journeys in the presence of such uncertainty. Most people, especially when making an important journey, want to arrive at a specific time, with a bounded probability of being a specific number of minutes late. This kind of planning is impossible with current ticket-purchase systems.

We have developed a precise mathematical model of such a system. There are two main difficulties to be tackled - to develop an appropriate mathematical model of the transport system incorporating the delay data, and to implement the resulting optimization algorithm efficiently. Our mathematical model uses data collected from the real-time website to build a separate stochastic model of train performance on every route. This is a kind of “learning” phase, which runs continually in the background. We then have a generic model that computes probability distributions for passengers passing through the system and changing trains. The result is a new concept of the Green’s function of a railway station. This is the kernel of an integral transform which is used to propagate probability distributions through stations.

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Contact: Richard G. Clegg ( or Keith Briggs (mailto:keith.briggs_at_bt_dot_com)