The Formula For Traffic

"Many traffic jams leave drivers baffled as they finally reach the end of a tail-back to find no visible cause for their delay.

Now, a team of mathematicians from the Universities of Exeter, Bristol and Budapest, have found the answer and published their findings in leading academic journal Proceedings of the Royal Society.

The team developed a mathematical model to show the impact of unexpected events such as a lorry pulling out of its lane on a dual carriageway. Their model revealed that slowing down below a critical speed when reacting to such an event, a driver would force the car behind to slow down further and the next car back to reduce its speed further still.

The result of this is that several miles back, cars would finally grind to a halt, with drivers oblivious to the reason for their delay. The model predicts that this is a very typical scenario on a busy highway (above 15 vehicles per km). The jam moves backwards through the traffic creating a so-called ‘backward travelling wave', which drivers may encounter many miles upstream, several minutes after it was triggered. "

Thanks to Justin Emond