Curing Congestion

Stay close, don't pass, and we'll all get there somehow.

By Robert Kunzig|Monday, March 01, 1999
RELATED TAGS: MATH
There is nothing quite like a congested highway to make your fellow human beings seem dispensable. You don't even have to be stopped dead--it's enough just to drive into one accordion after another, breathing exhaust, eyeing the other lanes to see if you should dart into them because they're moving just a wee bit faster. Worse is passing an on-ramp, grinding your teeth as a fresh stream of enemies flows onto your road. Perhaps you accelerate a bit to avoid giving way.

Bernardo Huberman understands, but he might call you uninformed. A little more traffic, he says, might be all it would take to transform the whole mess into a state of crystalline harmony, one that moves everyone to his destination reliably, steadily, and safely.

Huberman is not a woolly-headed New Ager; he is a theoretical physicist at the Xerox Palo Alto Research Center who makes his living thinking about social dilemmas. Until recently he spent most of his working hours pondering congestion on the Internet. But one day he got a visit from Dirk Helbing of the University of Stuttgart in Germany. Helbing is a theoretical physicist who spends all his working hours pondering congestion on highways. And he's far from alone: traffic physics is a hot subject these days, especially in Germany, home to fast cars and crowded autobahns. Working together, Helbing and Huberman say they have found a way to unclog highways everywhere. "I think it would be very simple," says Huberman.

Their discovery is based on computer models, which have gotten a lot better at capturing the intricacies of traffic. Old models, Helbing says, used a complicated equation for each vehicle, which consumed gobs of computer time. As a practical matter that made it hard to be realistic.

The newer ideas that Helbing and other physicists have developed simplify matters. One method treats cars on a highway as molecules in a gas, but molecules that want to move in one direction at a certain velocity. The computer thus must solve fewer equations to describe the cars' aggregate behavior. Another method considers the cars individually, but as "cellular automatons" that follow simple rules--"I am going too slow; there is a vacant cell in the adjacent lane that would allow me to pass this pig in front of me; therefore I shall pass." Fudge factors--one of Helbing's takes into account dawdling--endow the automatons with erratic, humanlike behavior.

The data that anchor these models to real conditions come from those electric highway cables that cars must sometimes thump over. They're called induction-loop detectors, and they measure the number, size, and speed of passing vehicles. The German highway network has lots of them. A couple of years ago, studying the data from a set of detectors on a stretch of highway north of Frankfurt, another Stuttgart physicist, Boris Kerner of the Daimler-Benz Research Institute, made a surprising discovery. Between free-flowing traffic and traffic jams, he identified another pattern, slower than free-flowing but still steady, in which cars in all three lanes moved at the same speed.

Kerner observed that this "synchronized traffic" occurred most often near on-ramps. A peak in the number of cars coming off the ramp could cause the traffic on the highway to synchronize suddenly, like water vapor condensing to a droplet around a particle of dust. The effect often spread up and down the highway from the ramp and could persist for hours after the burst on the ramp had subsided.

By modeling traffic as a gas, Helbing has been able to reproduce Kerner's synchronized traffic pattern--and to show that it can be caused by other disturbances, like one truck creeping past another, slowing the flow behind. The synchronizing can even be caused by a small trough in the number of cars merging onto a highway. ("That is surprising," he says.) Moreover, he has shown that there are many distinct phases of congested traffic--at least five--between free-flowing and a jam. Just as chemists construct a phase diagram for an element, showing the temperatures and pressures at which it is solid, liquid, or gaseous, so Helbing has constructed a phase diagram for highway traffic. It suggests how different combinations of flow on the highway and flow on a ramp can produce the different types of congestion--and how easily one phase can flip into another.

"At certain traffic densities, small causes have large effects," Helbing says. "In particular, most types of congestion are avoidable--they aren't caused by overloading of the highway but by small disturbances that grow and at some point cause the traffic to break down."

Which is where the study he recently did with Huberman comes in. Using Helbing's cellular automaton model, they simulated a realistic mix of cars and trucks on a highway, moving at different speeds and passing one another at every opportunity. They computed the times it took the vehicles to cover six miles of road under a wide range of traffic conditions. At one critical traffic density--about 35 vehicles per mile of highway--they observed something dramatic: the passing rate plummeted. "All of them start becoming one," says Huberman. "The whole thing locks in, and suddenly the traffic is basically moving like a solid block."

Although he and Helbing haven't yet proved this happens on a real highway, data from Dutch roads seem to confirm their predictions. At the critical density, the cars and trucks adopt the same speed, and both types of vehicle seem to maintain that speed for a long stretch of road. That is a desirable situation, say Helbing and Huberman: a steady speed makes for reliable travel times and less passing, which can cause accidents. The solid-block state is fragile, however; increase the vehicle density a bit and the fast-moving block dissolves into sluggish and aggravating stop-and-go traffic.

Fortunately, there are ways of keeping the block intact. All you have to do, say Helbing and Huberman, is put computer-controlled stoplights at each on-ramp. Instead of allowing cars onto the highway according to a preset schedule, as is done, for example, on the Long Island Expressway, the lights must respond to real-time data on traffic conditions collected by wires the cars pass over. When the data indicate gaps in a block of traffic passing an on- ramp, the light there turns green, filling the gaps and keeping the flow smooth. When the density threatens to shift the traffic into stop-and-go, the light turns red again.

At rush-hour peaks, traffic would still slow to a crawl. But at intermediate densities, says Huberman, commuters would move smoothly and contentedly as a solid block. "When people act in selfish ways, it's very hard to achieve a common goal," he says. "But here the interesting thing is you have a rather large group of people, they're all being selfish, and yet they all achieve a very smooth state of running through the freeway. It's an unintended, global cooperation. And it's a very comfortable way of driving. I've experienced this at around 50 miles per hour or so. The cars are at a distance at which you could pass, and yet you don't. Somehow you just feel that this is okay--everybody seems to feel that they're optimizing, and they're all better off."

Nirvana on the freeway?
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