Math Model Says Some Traffic Jams Act Like Self-Sustaining Waves

June 19, 2009

Mathematicians have developed a model that could help road designers minimize phantom traffic jams—those that can occur even when no accident, stalled vehicle, or closed lane disturbs the flow.

Such phantom jams occur in heavy traffic when small disturbances, such as a driver hitting the brake too hard or getting too close to another car, escalate into a self-sustaining traffic jam.

To model such a traffic jam, termed a "jamiton," researchers at the Massachusetts Institute of Technology turned to equations in fluid mechanics for self-sustaining waves. "We wanted to describe this using a mathematical model similar to that of fluid flow," MIT's Asian Kasimov said.

Kasimov and his collaborators were inspired to tackle the problem after Japanese researchers created a jamiton experimentally on a circular roadway. Even though drivers tried to travel only 30 kilometers per hour and maintain a constant distance from one another, disturbances occurred and phantom jams formed. The denser the traffic, the faster the jams formed.

Basing their work on an analogy to detonation waves produced by explosions, the mathematicians took aim at solving hyperbolic, continuum traffic equations. They found that, like a detonation wave, a jamiton will contain a "sonic point" below which traffic would slow dramatically. The results were reported in the article "Self-Sustained Nonlinear Waves in Traffic Flow," published in May 26 in Physical Review E.

Having considered examples of traffic flow on open and closed roadways, the team, which included Morris Flynn (University of Alberta) and MIT mathematicians Jean-Christophe Nave, Benjamin Seibold, and Ruben Rosales, has indicated that it plans to investigate how the number of lanes and other factors affect the formation of a jamiton.

Source: Massachusetts Institute of Technology, June 9, 2009.