# Phantom Traffic Jams

## Mathematicians Explain How Traffic Jams Form Without Apparent Cause

May 1, 2010

Mathematicians explain how traffic jams that seem to have no cause, or phantom traffic jams, get their start. Because the volume of cars on a highway can be heavy at times, the slightest disturbance in the flow can cause a back-up. This includes actions such as a driver tapping a brake too often, getting too close to another car or hitting the brake too hard. The researchers used equations similar to those used in fluid dynamics to design a model based on traffic volume and density to explain this phenomenon. The model explores under what conditions these jams form, intending to help road designers minimize their chances of occurring.

## Science Insider

TRAFFICKING IN PHYSICS: On sparsely populated highways the cars are generally well-separated, and can move at whatever speed they choose while freely maneuvering between lanes. A physicist would compare this to molecules in a gas, which are spaced further apart and move around randomly, only occasionally encountering other molecules. During rush hour, traffic density is much greater, so there is less room for cars to maneuver without risking collision, and the average speed is lower. Traffic is more like a liquid at that point. If the density of cars on the highway becomes too great, the flow of traffic freezes up: clusters of a "solid" can form, where cars are packed so closely together they can't move -- a traffic jam.

ABOUT FLUID DYNAMICS: The study of the physics of fluids -- matter in liquid, plastic, gaseous, and plasma states -- is called fluid dynamics. Understanding the behavior of matter under different temperature and pressure conditions is important to applications such as the aerodynamics of aircraft and automobiles, the flow of petroleum through pipelines, weather prediction, and even traffic engineering. Other concepts important to solving problems in this discipline include the velocity and density of a fluid.

The American Mathematical Society and the Mathematical Association of America, The Institute for Operations Research and the Management Sciences, The Human Factors and Ergonomics Society, and the Division of Fluid Dynamics - American Physical Society contributed to the information contained in the TV portion of this report.

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Phantom Traffic Jams

To Go Inside This Science:
Jean-Christophe Nave
Postdoctoral Associate
Dept of Mathematics
617) 253-4989
jcnave@mit.edu

Ivars Peterson
Mathematical Association of America
Washington, DC 20036-1358
ipeterson@maa.org
1-800-741-9415

Lois Smith
Human Factors and Ergonomics Society
Santa Monica, CA 90406
lois@hfes.org
310-394-1811

Mike Breen and Annette Emerson
American Mathematical Society
Providence, RI 02904-2294
paoffice@ams.org
1-800-321-4267

Institute for Operations Research and the Management Sciences
www.informs.org
Barry List
443-757-3560
barry.list@informs.org

Division of Fluid Dynamics - American Physical Society
Dr. James Brasseur
The Pennsylvania State University
814-865-3159
brasseur@psu.edu