# Alan McKee

*"I thoroughly enjoyed getting stuck into the project and will definitely be considering a career in academia and research."*

Alan McKee is a student at Cambridge University, but for Summer 2008 he joined Dr Mark McCartney and his team at the University of Ulster investigating the **mathematical analysis of a model for how vehicles behave on a stretch of road**.

In the model, drivers attempt to follow the vehicle in front while also attempting to drive at their own preferred speed. In such mathematical models there are parameters which represent how the driver responds to perceived relative velocities between himself and the driver in front, and the difference between his actual velocity and his preferred velocity. For some choices of these parameters the model leads to traffic flow breakdown. The project sought to discover which of these parameters led to such breakdown.

Talking about the outcome of the project, Dr McCartney commented: *"I had initially expected that any solutions regarding the stability of the model would have to be found mostly by numerical methods. However, a very pleasing result was that we were able to find the set of analytic boundaries for any set of n vehicles and also find a single analytic boundary in the limit as n approached infinity."*

Alan has already had his work submitted to the journal Physica A. His supervisor, Dr McCartney said: *"It was a pleasure to work with such a bright student! Alan’s findings have made a very useful contribution to the ongoing research of the group, and opened up new questions for us to investigate further."*