# 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.

Return to previous page

Contact:
Richard G. Clegg (richard@richardclegg.org)
or
Keith Briggs
()