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Published online: 26 November 1998; | doi:10.1038/news981126-8

Further on down the road

Phillip Ball
You know the situation. You're sitting there in the rush-hour traffic, trying to calm yourself with the radio, breathing in the fumes, and edging forward in little jumps. For perhaps twenty yards you experience the joy of second gear, and then it's back to a halt.

And you thought you were just a poor, down-trodden commuter. Little did you know that you are in fact taking part in an experiment on the physics of self-organization. It's an experiment that is replayed day after day on the highways of the world - but now physicists are beginning to unravel the complex interplay of factors that lead to spontaneous jams in heavy traffic.

Everyone is familiar with the puzzling, not to say vexing, phenomenon of spontaneous jams. You've been held up for a good half-hour or so in traffic that is barely moving - but when you get to the apparent source of the obstruction, there's nothing there. It is as if the jam suddenly just 'evaporates'. Lest you imagine that this is the same kind of idealization that leads to the infamous physicists' model of spherical race-horses running in a vacuum, consider for a moment what a traffic flow looks like. On a sparsely populated highway the cars are generally far apart, moving at whatever speed they choose, and free to manoeuvre from lane to lane. To a physicist, this is reminiscent of a gas - a low-density fluid in which particles move about at random and encounter each other only very rarely.

Then comes rush hour, and the traffic density rises suddenly. There is less room for manoeuvre without risk of collision, and the average speed decreases. The traffic has become more akin to a liquid. If the density becomes too great, things start to freeze up: clusters of "solid" form, where the vehicles are packed closely in regular fashion, unable to move because of their immobile neighbours. Crudely speaking, a traffic jam is akin to freezing -the phase transition between a liquid and a solid.

But as B. S. Kerner from the Daimler Benz Research Institute in Stuttgart, Germany, shows in Physical Review Letters, things are more complicated than that. The formation of a major traffic jam seems to involve a sequence of smaller transitions from free flow to increasingly constrained and synchronized traffic states. Kerner has analysed data collected from several years of traffic rumbling along German highways, and he reports characteristic patterns that presage the appearance of the dreaded stop-start behaviour encountered in tailbacks.

First, the traffic flow undergoes a transition from free to synchronized as the vehicle density (the number of cars per kilometre, say) increases. In synchronized flow, all of the vehicles travel at close to the same average speed. This is already a precarious state, because it means that the vehicles become highly dependent on one another - in physicists' terms, their motion is correlated. When the motion of electrons in metals becomes correlated, strange things happen - such as the transition to a state of superconductivity. When traffic speed becomes correlated, meanwhile, you're heading for trouble.

And here it comes - in the form of "narrow jams" which appear spontaneously in the synchronized flow. That is to say, every so often a tiny perturbation in the flow, such as a single vehicle slowing down slightly while the driver changes the cassette tape (do not try this on the way home!) sends repercussions upstream of the flow that leads to a drastic, localized drop in speed. These narrow jams can appear anywhere in the flow, but not surprisingly they are more common at junctions where vehicles enter or exit the highway, since it is here that temporary slowing down is more likely.

So steady synchronized flow gives way to a series of narrow jams. This state can persist indefinitely if the volume of traffic remains the same - but if it gets too large, says Kerner, the next crisis that delays your dinner is a phenomenon he calls the "pinch effect". Basically, this means that narrow jams bunch up in a region called the 'pinch' region, becoming ever closer as the average vehicle speed declines. This is the stop-go situation - you leave one narrow jam only to encounter another a little further down the road. Eventually narrow jams in the pinch region coalesce into wide jams, and you're sitting there impotently drumming your fingers on the wheel. Welcome to solid-state traffic.

Synchronized traffic can get snarled into a whole series of wide jams, but they will always maintain a certain distance apart - narrow jams just outside a wide jam will either be absorbed by it or will become dissipated. So the heavy traffic has the curious feature of organizing itself into a series of wide jams with a roughly even spacing between them, just as desert sand is ruffled into a series of equally spaced ripples by the wind.

For all that they think they are acting of their own accord, each driver becomes a mere particle arrayed according to the broader plan of the self-organized flow. Those car advertisements that promised to set you free have instead ensnared you into the life of a grain of sand.

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