|Ivars Peterson's MathTrek|
September 10, 2001
From a physicist's point of view, traffic flow can be regarded as a "many-body system of strongly interacting bodies." Various studies have revealed that such systems can show wavelike behavior and abrupt transitions from one state to another. The shift from freely moving to jammed traffic, for example, corresponds to a phase transition from gas to liquid.
Using such models, researchers have identified various factors that induce traffic jams. These factors generally correspond to everyday situations: mistimed traffic signals, a blocked lane, the narrowing of a freeway to fewer lanes, a busy exit or entry ramp, a truck slowly grinding its way up a hill.
The models indicate that what happens typically depends on traffic volume--a combination of vehicle density and average speed. At low volume, cars move more or less independently, achieve a preferred speed, and change lanes as required. At high volume, small disturbances can trigger congestion.
Computer simulations also suggest that at moderate traffic volumes when vehicle flow should be relatively stable, a single car moving at randomly fluctuating speeds within a steady stream of traffic along a single lane can by itself create waves of congestion that propagate down the road behind it. Cars far from the offending vehicle can find themselves unexpectedly caught up in localized traffic jams that have no apparent cause.
The amount and type of congestion induced by an erratic driver depend on how much the leading car's velocity fluctuates, even when the average speed matches that of the rest of the traffic. For moderate fluctuations, for instance, an erratically driven car can trigger a train of density waves, which move upstream like shock waves. The situation worsens when the average traffic speed is slower. Isolated, moving clusters quickly grow into a nearly continuous jam of congested traffic as the average speed decreases.
The simulations clearly suggest that, under the right circumstances, an individual driving erratically enough can readily cause the sorts of traffic jams normally associated with much heavier traffic.
Copyright 2001 by Ivars Peterson
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You can check out various types of traffic simulations at http://sunsite.utk.edu/winners_circle/unlimited/UNAL2I6J/applet.html, http://www.math.toronto.edu/mathnet/carcompet/simulation.html, and http://www.theo2.physik.uni-stuttgart.de/helbing/RoadApplet/.
Comments are welcome. Please send messages to Ivars Peterson at email@example.com.