The Physics of Gridlock

What causes traffic jams? The depressing answer may be nothing at all.

 


Illustration by Maris Bishofs
 

 

 

BERTRAND Russell once observed that animal behaviorists studying the problem-solving abilities of chimpanzees consistently seemed to detect in their experimental subjects the "national characteristics" of the scientists themselves. A divergence in the findings of the practical-minded Americans and the theoretically inclined Germans was particularly apparent.

Animals studied by Americans rush about frantically, with an incredible display of hustle and pep, and at last achieve the desired result by chance. Animals observed by Germans sit still and think, and at last evolve the solution out of their inner consciousness.

In science, Germans tend to come up with things like the uncertainty principle. Americans tend to come up with things like the atomic bomb.


The latest field to host this conflict of national styles is one that seems at first glance to offer little prospect of a sporting contest. Bigger and better highways are as American as fast-food restaurants and sport utility vehicles, and when it comes to making the crooked straight and the rough places plain, the practicality of American traffic engineers is hard to argue with. As an American academic discipline, traffic engineering is centered in civil-engineering departments, and civil engineers tend to believe in solving problems by going at them head on. A recent study funded by nine state departments of transportation to examine the doubling in congestion on urban highways and primary roads that has occurred over the past two decades listed in its final report various ways that traffic engineers have tried to alleviate the problem. These included "add road space" and "lower the number of vehicles." This would not, as the saying goes, appear to be rocket science.

Even when American traffic engineers have ventured closer to rocket science, with computer simulations of traffic flow on multi-lane highways, the results have tended to reinforce the American reputation for practicality and level-headedness. The 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.

SUCH was the happy, practical, and deterministic state of affairs up until a few years ago, when several German theoretical physicists began publishing papers on traffic flow in Physical Review Letters, Journal of Physics, Nature, and other publications not normally read by civil engineers. The Germans 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 Germans' 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.

Such mathematical discoveries do seem to be borne out in the real world. Biological populations often exhibit erratic booms and busts that cannot be explained by any external cause. Long-term weather patterns defy prediction by the most powerful supercomputers. And a whole class of chemical reactions has been discovered in which the chemicals do not merely react and create a product, as they did in high school chemistry class, but oscillate back and forth between reactants and products. (Some especially nice ones cause color changes in the solution, so you can sit there and watch the stuff in the beaker go back and forth every few seconds.) The consistent story in all these discoveries is that the components of the system and their interactions themselves -- rather than any external cause -- give rise to the nonlinear behavior of the system as a whole. A rough analogy is a dozen dogs standing on a water bed. If one dog moves, he starts the bed sloshing around, which causes another dog to lose his balance and shift his weight, which sets up another wave of disturbance, until true chaos is reached.

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