# Ivars Peterson's MathTrek

November 22, 2004

## Cruise Control and Traffic Flow

You're whizzing along the highway, when the driver of the car in front of you suddenly slams on the brakes, perhaps to let another vehicle merge into the lane. You respond by braking, too, as does the driver of the car behind you, and so on. And your tendency is to brake harder—just to be on the safe side—than the driver in front of you did.

This effect can propagate backward for long distances, depending on the traffic volume and speed, creating waves of congestion.

The trouble is that people take time to respond to changes in speed. Such sluggish reaction times mean that extra spacing is needed between vehicles for safe travel.

One potential solution is to equip a car with adaptive cruise-control technology. Such a system uses radar and a computer to maintain a safe distance from another car or truck. Its advantage is that it can respond much more quickly and precisely than human drivers can to any change in speed. A vehicle using adaptive cruise control typically brakes sooner and more smoothly than one without the system.

Physicist L. Craig Davis of the University of Michigan has used computer simulations, applying concepts from statistical mechanics, to study how the use of adaptive cruise-control technology might affect traffic flow. He reports his results in the June Physical Review E.

The computer model developed by Davis shows that, if all vehicles on a highway had adaptive cruise control, perturbations due to changes in the lead vehicle's velocity would not translate into propagating pockets of traffic congestion. Traffic would flow smoothly.

Intriguingly, at an average speed of 67 miles per hour, if only one in five vehicles used adaptive cruise control, no traffic jams would form and traffic would generally flow freely. At lower concentrations, however, intermittent episodes of traffic congestion would still be an issue.

The situation is more complicated when highways speeds are less than 50 miles per hour or when drivers are caught in stop-and-go traffic or face a heavy volume of merging vehicles. In such cases, adaptive cruise control has less impact and can even make the situation more difficult.