Passage IV

NATURAL SCIENCE: This passage is adapted from the "The Physics of Gridlock" by Stephen Budiansky (©2000 by The Atlantic Monthly Company.)

American traffic engineering has been a practical, level-headed field. Its mathematical and computer models indicate that when traffic jams occur, they are the result of bottlenecks (merging lanes, bad curves, accidents), which constrict flow. Find a way to eliminate the bottlenecks and flow will be restored.

Then a few years ago, several German theoretical physicists began publishing papers on traffic flow in publications not normally read by civil engineers. The physicists had noticed that if one simulated the movement of cars and trucks on a highway using the well-established equations that describe how the molecules of a gas move, some distinctly eerie results emerged. Cars do not behave exactly like gas molecules, to be sure: for example, drivers try to avoid collisions by slowing down when they get too near another car, whereas gas molecules have no such aversion. But the physicists added some terms to the equations to take the differences into account, and the overall description of traffic as a flowing gas has proved to be a very good one. The moving-gas model of traffic reproduces many phenomena seen in real-world traffic. When a flowing gas encounters a bottleneck, for example, it becomes compressed as the molecules suddenly crowd together — and that compression travels back through the stream of oncoming gas as a shock wave. That is precisely analogous to the well-known slowing and queuing of cars behind a traffic bottleneck: as cars slow at the obstruction, cars behind them slow too, which causes a wave of stop-and-go movement to be transmitted "upstream" along the highway.

The eeriest thing that came out of these equations, however, was the implication that traffic congestion can arise completely spontaneously under certain circumstances. No bottlenecks or other external causes are necessary. Traffic can be flowing freely along, at a density still well below what the road can handle, and then suddenly gel into a slow-moving ooze. Under the right conditions a small, brief, and local fluctuation in the speed or spacing of cars — the sort of fluctuation that happens all the time just by chance on a busy highway — is all it takes to trigger a system-wide breakdown that persists for hours after the blip that triggered it is gone. In fact, the physicists' analysis suggested, such spontaneous breakdowns in traffic flow probably occur quite frequently on highways.

Though a decidedly unnerving discovery, this was very much of a piece with the results of mathematical models of many physical and biological systems that exhibit the phenomena popularized under the heading "chaos theory." In any complex interacting system with many parts, each of which affects the others, tiny fluctuations can grow in huge but unpredictable ways. Scientists refer to these as nonlinear phenomena — phenomena in which seemingly negligible changes in one variable can have disproportionately great consequences. Nonlinear properties have been discovered in the mathematical equations that describe weather, chemical reactions, and populations of biological organisms. Some combinations of variables for these equations give rise to sudden "phase shifts," in which the solution to the equation jumps abruptly from one value to another; others set off truly chaotic situations in which for a time the solution to the equation fluctuates wildly and without any seeming pattern, and then suddenly calms down.

In the case of traffic, the physicists found that given a certain combination of vehicle density and vehicle flow rate along a highway, the solution to their equations undergoes a sudden phase shift from freely moving traffic to what they call "synchronized traffic." Cars in all lanes abruptly slow down and start moving at the same speed as the cars in adjacent lanes, which makes passing impossible and can cause the whole system to jam up for hours.

Such a leap from one state to another is like what happens when a chemical substance changes phase from vapor to liquid. It often happens that water in a cloud remains in the gas phase even after temperature and density have reached the point where it could condense into water droplets. Only when a speck of dust happens along, providing a surface on which condensation can take place, does the transition finally occur. The physicists basically found that free flow and synchronized flow can occur under the same conditions, and that under such "metastable" conditions a small fluctuation in traffic density can act as the speck of dust causing the shift from one to the other.