If you plan to hit the roads like the zillions of other drivers this holiday weekend, Avi Polus has a word of advice: patience.

A transportation engineer at Technion-Israel Institute of Technology in Haifa, Prof. Polus's concern isn't drivers' collective blood pressure but traffic flow. Like the growing number of other engineers and physicists who are hubcap-deep in the science of traffic, he is determined to explain infuriating mysteries such as phantom traffic jams (There's no bottleneck or accident at the front of this jam, so why weren't we moving?) and why a brief drop in volume can, paradoxically, trigger a long-lasting traffic jam.

Impatience on two-lane roads actually improves traffic flow, as antsy drivers pass slowpokes rather than letting a convoy form. On highways, however, "passing, aggressive behavior and lane changing is greatly detrimental to the flow," says Prof. Polus.

The reason is that chronic lane changing simulates the "weaving section" of a highway. If an off-ramp lies just beyond an on-ramp, entering drivers merge left (assuming ramps are on the right) and exiting drivers merge right, causing traffic to crisscross like mobile braids. When, in heavy traffic, many drivers change lanes again and again, trying to find the one that is moving faster, the same weaving effect kicks in, reducing the capacity of that section of road.

"Weaving is the worst condition for traffic flow," says Prof. Polus. Because drivers in heavy traffic brake when a car pulls into their lane, and because it takes time to get back up to speed, there are larger and constantly-changing gaps between vehicles. That invites yet more cars to change lanes, propagating a wave of stop-and-go traffic that cuts the number of cars in a stretch of road by about 10 percent, calculates Prof. Polus, who will present his work at the 16th International Symposium on Transportation and Traffic Theory at the University of Maryland this month. That may not sound so dire, but in rush hour the result is a five-mile backup, his calculations show. In congestion, be content with the lane you're in.

More and more scientists are modeling traffic with equations from the branch of math called nonlinear dynamics, which describes systems that suddenly jump from one state to another. Like water that suddenly freezes, flowing traffic can spontaneously seize up, beginning at a single point of crystallization (the idiots who braked to rubberneck) and causing a wave of high density to spread backward.

Lane closures, on ramps, uphill, chronic lane changing and other "inhomogeneities" in traffic flow can all trigger a density wave, Martin Treiber of Dresden University of Technology has shown in mesmerizing simulations (www.traffic-simulation.de/). One result can be "phantom" jams, which occur so far upstream of the bottleneck that the congestion there has long cleared by the time drivers at the back of the pack reach it. As a result, they never see the snafu that flipped smooth flow into a stop-and-go mess. By one estimate, three-quarters of traffic jams are phantoms.

Carlos Daganzo of the University of California, Berkeley, was puzzled by what highway sensors showed: When congested traffic forms upstream of a bottleneck, the rate at which cars at the front leave the congested area decreases. "It's as if, when a line forms at the popcorn stand, the server slows down, so people leave with their popcorn at a slower rate just because there are more people waiting," he says.

Yet the counterintuitive effect is seen time and again, and in a recent study he and colleagues figured out why. The congestion causes cars to jockey across lanes, ever on the lookout for the faster one. Lane changing increases the gaps between cars, as drivers slow down when someone barges in front of them. Bigger gaps means fewer cars per second leaving the front of the jam.

If that seems counterintuitive, consider that briefly reducing volume can trigger a stop-and-go wave. Within the region with suddenly fewer cars, perhaps because a long funeral cortege just exited, the emptier road entices drivers to speed up ("Open road -- yes!"). But sooner or later, Prof. Treiber notes, these drivers catch up to a denser, slower-moving region. The ensuing braking can trigger the dreaded density wave.

Most jams occur way before a road reaches its capacity, and the culprits are all around you. Even in heavy but moving traffic, inhomogeneities would have much less effect if drivers had faster reaction times. When merging traffic causes the driver in front of you to brake, you do so as well, unless you enjoy fender benders. But because braking takes time, the gap between you and the car ahead shrinks, explains Prof. Treiber. You slow even further until the gap reaches a size you are comfortable with. Result: You are now traveling even more slowly than the car whose braking triggered the stop-and-go wave in the first place. The car behind you does the same, and the effect propagates backward, often for miles.

You can lessen this effect, however. Prof. Treiber suggests looking a few cars ahead so you know when and how much to brake. "If you brake just in time, you can usually safely brake less," he says, "which improves the flow." Consider it a good deed.

First Published: July 1, 2005, 4:00 a.m.