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 humanbeings seemdispensable. You don't even have to be stopped dead--it's enough just todrive into oneaccordion after another, breathing exhaust, eyeing the other lanes to seeif you should dartinto them because they're moving just a wee bit faster. Worse is passing anon-ramp,grinding your teeth as a fresh stream of enemies flows onto your road.Perhaps youaccelerate a bit to avoid giving way.

Bernardo Huberman understands, but he might call you uninformed. A littlemore traffic,he says, might be all it would take to transform the whole mess into astate of crystallineharmony, one that moves everyone to his destination reliably, steadily, andsafely.

Huberman is not a woolly-headed New Ager; he is a theoretical physicist atthe Xerox PaloAlto Research Center who makes his living thinking about social dilemmas.Until recentlyhe spent most of his working hours pondering congestion on the Internet.But one day hegot a visit from Dirk Helbing of the University of Stuttgart in Germany.Helbing is atheoretical physicist who spends all his working hours pondering congestionon 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 andHuberman saythey have found a way to unclog highways everywhere. "I think it would bevery simple,"says Huberman.

Their discovery is based on computer models, which have gotten a lot betterat capturingthe intricacies of traffic. Old models, Helbing says, used a complicatedequation for eachvehicle, which consumed gobs of computer time. As a practical matter thatmade it hard tobe realistic.

The newer ideas that Helbing and other physicists have developed simplifymatters. Onemethod treats cars on a highway as molecules in a gas, but molecules thatwant to move inone direction at a certain velocity. The computer thus must solve fewerequations todescribe the cars' aggregate behavior. Another method considers the carsindividually, butas "cellular automatons" that follow simple rules--"I am going too slow;there is a vacantcell in the adjacent lane that would allow me to pass this pig in front ofme; therefore I shallpass." Fudge factors--one of Helbing's takes into account dawdling--endow theautomatons with erratic, humanlike behavior.

The data that anchor these models to real conditions come from thoseelectric highwaycables that cars must sometimes thump over. They're called induction-loopdetectors, andthey measure the number, size, and speed of passing vehicles. The Germanhighwaynetwork has lots of them. A couple of years ago, studying the data from aset of detectorson a stretch of highway north of Frankfurt, another Stuttgart physicist,Boris Kerner of theDaimler-Benz Research Institute, made a surprising discovery. Betweenfree-flowingtraffic and traffic jams, he identified another pattern, slower thanfree-flowing but stillsteady, in which cars in all three lanes moved at the same speed.

Kerner observed that this "synchronized traffic" occurred most often nearon-ramps. Apeak in the number of cars coming off the ramp could cause the traffic onthe highway tosynchronize suddenly, like water vapor condensing to a droplet around aparticle of dust.The effect often spread up and down the highway from the ramp and couldpersist forhours after the burst on the ramp had subsided.

By modeling traffic as a gas, Helbing has been able to reproduce Kerner'ssynchronizedtraffic pattern--and to show that it can be caused by other disturbances,like one truckcreeping past another, slowing the flow behind. The synchronizing can evenbe caused bya small trough in the number of cars merging onto a highway. ("That issurprising," hesays.) Moreover, he has shown that there are many distinct phases ofcongested traffic--atleast five--between free-flowing and a jam. Just as chemists construct a phase diagram foran 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 suggestshow differentcombinations of flow on the highway and flow on a ramp can produce thedifferent typesof congestion--and how easily one phase can flip into another.

"At certain traffic densities, small causes have large effects," Helbingsays. "In particular,most types of congestion are avoidable--they aren't caused by overloadingof the highwaybut by small disturbances that grow and at some point cause the traffic tobreak down."

Which is where the study he recently did with Huberman comes in. UsingHelbing'scellular automaton model, they simulated a realistic mix of cars and truckson a highway,moving at different speeds and passing one another at every opportunity.They computedthe times it took the vehicles to cover six miles of road under a widerange of trafficconditions. At one critical traffic density--about 35 vehicles per mile ofhighway--theyobserved something dramatic: the passing rate plummeted. "All of them startbecomingone," says Huberman. "The whole thing locks in, and suddenly the traffic isbasicallymoving like a solid block."

Although he and Helbing haven't yet proved this happens on a real highway,data fromDutch roads seem to confirm their predictions. At the critical density, thecars and trucksadopt the same speed, and both types of vehicle seem to maintain that speedfor a longstretch of road. That is a desirable situation, say Helbing and Huberman: asteady speedmakes for reliable travel times and less passing, which can causeaccidents. The solid-blockstate is fragile, however; increase the vehicle density a bit and thefast-moving blockdissolves into sluggish and aggravating stop-and-go traffic.

Fortunately, there are ways of keeping the block intact. All you have todo, say Helbingand Huberman, is put computer-controlled stoplights at each on-ramp.Instead of allowingcars onto the highway according to a preset schedule, as is done, forexample, on the LongIsland Expressway, the lights must respond to real-time data on trafficconditions collectedby wires the cars pass over. When the data indicate gaps in a block oftraffic passing an on-ramp, the light there turns green, filling the gaps and keeping the flowsmooth. When thedensity threatens to shift the traffic into stop-and-go, the light turnsred again.

At rush-hour peaks, traffic would still slow to a crawl. But atintermediate densities, saysHuberman, commuters would move smoothly and contentedly as a solid block. "Whenpeople act in selfish ways, it's very hard to achieve a common goal," hesays. "But here theinteresting thing is you have a rather large group of people, they're allbeing selfish, andyet 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'veexperienced this ataround 50 miles per hour or so. The cars are at a distance at which youcould pass, and yetyou don't. Somehow you just feel that this is okay--everybody seems to feelthat they'reoptimizing, and they're all better off."

Nirvana on the freeway?--Shanti Menon
Posted 3/8/99


RELATEDWEB SITES:

DirkHelbing
Dirk Helbing's Traffic Simulator
News story from the American Institute of Physics
U.S. Department of Transportation
National Highway TrafficSafety Administration
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