MIT takes aim at ‘phantom’ traffic jams
June 9, 2009
(PhysOrg.com) -- Countless hours are lost in traffic jams every year. Most frustrating of all are those jams with no apparent cause — no accident, no stalled vehicle, no lanes closed for construction.
Such phantom jams can form when there is a heavy volume of cars on the road. In that high density of traffic, small disturbances (a driver hitting the brake too hard, or getting too close to another car) can quickly become amplified into a full-blown, self-sustaining traffic jam.
A team of MIT mathematicians has developed a model that describes how and under what conditions such jams form, which could help road designers minimize the odds of their formation. The researchers reported their findings May 26 in the online edition of Physical Review E.
Key to the new study is the realization that the mathematics of such jams, which the researchers call “jamitons,” are strikingly similar to the equations that describe detonation waves produced by explosions, says Aslan Kasimov, lecturer in MIT’s Department of Mathematics. That discovery enabled the team to solve traffic jam equations that were first theorized in the 1950s.
The equations, similar to those used to describe fluid mechanics, model traffic jams as a self-sustaining wave. Variables such as traffic speed and traffic density are used to calculate the conditions under which a jamiton will form and how fast it will spread.
Once such a jam is formed, it’s almost impossible to break up — drivers just have to wait it out, says Morris Flynn, lead author of the paper. However, the model could help engineers design roads with enough capacity to keep traffic density low enough to minimize the occurrence of such jams, says Flynn, a former MIT math instructor now at the University of Alberta.
The model can also help determine safe speed limits and identify stretches of road where high densities of traffic — hot spots for accidents — are likely to form.
Flynn and Kasimov worked with MIT math instructors Jean-Christophe Nave and Benjamin Seibold and professor of applied mathematics Rodolfo Rosales on this study.
The team tackled the problem last year after a group of Japanese researchers experimentally demonstrated the formation of jamitons on a circular roadway. Drivers were told to travel 30 kilometers per hour and maintain a constant distance from other cars. Very quickly, disturbances appeared and a phantom jam formed. The denser the traffic, the faster the jams formed.
“We wanted to describe this using a mathematical model similar to that of fluid flow,” said Kasimov, whose main research focus is detonation waves. He and his co-authors found that, like detonation waves, jamitons have a “sonic point,” which separates the traffic flow into upstream and downstream components. Much like the event horizon of a black hole, the sonic point precludes communication between these distinct components so that, for example, information about free-flowing conditions just beyond the front of the jam can’t reach drivers behind the sonic point. As a result, drivers stuck in dense traffic may have no idea that the jam has no external cause, such as an accident or other bottleneck. Correspondingly, they don't appreciate that traffic conditions are soon to improve and drive accordingly.
“You’re stuck in traffic until all of the sudden it just clears,” says Morris.
In future studies, the team plans to look more detailed aspects of jamiton formation, including how the number of lanes affects the phantom traffic jams.
The research was funded by the U.S. Air Force Office of Scientific Research, the National Science Foundation and the (Canadian) Natural Science and Engineering Research Council.
Source: Massachusetts Institute of Technology (news : web)
Jun 05, 2009 |
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Make a critically dampened wave out of the flow by intelligent buffering. It works.
It is most likely caused by those drivers who are always late and think that zooming in and out of other cars is going to make a difference in getting to where they are going, thus causing everyone else to slam on thier brakes.
There are also those who drive side by side, and won't get into the slower lane when there are cars behind them.
I see this kind of driving every day, in places where the roads are straight, with no on or off ramps, and the trucks are all in the slow lanes.
The problem is that a traffic jam represents a compression of the time between arrival of succeeding vehicles. The compression then acts as a restricted-source of those same vehicles, slowing the release of the lead vehicles depending on actual speed, spacing, capacity of the vehicles to accelerate, and inclination of the drivers. The jam happens because vehicles arrive at the rear faster than they are released at the front.
The reason the jam occurs is a flinch - some driver slows. Maybe because someone cut him off, maybe because he dropped his iphone or donut. If the vehicles following are too close - they have to flinch, too, comressing the distance they follow and slowing their speed.
It is the combination of dependent events - if the car ahead slows, you have to, too - and statistically varying events - each vehicle accelerates at a different rate, so they give a randomly varying time to the vehicle behind, before that vehicle proceeds when released from the jam. A vehicle is released from the jam when no vehicle ahead impedes the driver.
The solution doesn't help the driver at all - keep back the safe following distance according to the posted speed limit - regardless of the actual speed of the vehicle ahead. Maintaining the distance reduces the risk of transferring a flinch to the vehicle behind - and starting or continuing a traffic jam.