## Mathematicians develop model to solve traffic-jam mystery

December 20th, 2007 - 4:05 pm ICT by admin

Washington , Dec 20 (ANI): Mathematicians have solved the mystery behind traffic jams and have developed a model to show how major delays occur on our roads, with no apparent cause.

A number of traffic jams leave drivers puzzled as they finally reach the end of a tail-back and realize there was no evident cause for their delay.

This research was carried out by a team of mathematicians from the Universities of Exeter, Bristol and Budapest .

This team developed a mathematical model to demonstrate the impact of unexpected events such as a lorry pulling out of its lane on a dual carriageway.

The model disclosed that if a driver slows down below a critical speed while reacting to such an event, he would force the car behind in order to slow down further and the next car back to reduce its speed further still.

As a result, several miles back, cars would finally come to a halt, with drivers ignorant of the reason for their delay.

The model also predicted this to be a very typical scenario on a busy highway (above 15 vehicles per km).

The jam moves backwards through the traffic and creates a so-called backward travelling wave, which drivers may encounter many miles upstream, after several minutes it was triggered.

As many of us prepare to travel long distances to see family and friends over Christmas, were likely to experience the frustration of getting stuck in a traffic jam that seems to have no cause, said Dr Gabor Orosz of the University of Exeter .

He added: Our model shows that overreaction of a single driver can have enormous impact on the rest of the traffic, leading to massive delays.

Previously, drivers and policy-makers did not know why jams like this occur, though many owe it to the sheer volume of traffic.

Although this plays an evident part in this new theory, the main issue is around the smoothness of traffic flow.

According to the model, heavy traffic will not automatically result into congestion but can also be smooth-flowing.

This model considers the time-delay in drivers reactions, leading to drivers braking more heavily than would have been necessary if they had identified and reacted to a problem ahead a second earlier.

When you tap your brake, the traffic may come to a full stand-still several miles behind you. It really matters how hard you brake - a slight braking from a driver who has identified a problem early will allow the traffic flow to remain smooth,continued Dr Orosz.

He added: Heavier braking, usually caused by a driver reacting late to a problem, can affect traffic flow for many miles.

The research team is now planning to develop a model for cars equipped with new electronic devices, which could cut down on over-braking as a result of slow reactions.

These findings are published in leading academic journal Proceedings of the Royal Society

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