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MIT mathematicians model traffic jams like detonation waves

Most drivers have been stuck in a traffic jam at one point or another. Some of the jams are caused by an accident or closed lanes. Other traffic jams crop up with seemingly no reason.

A group of mathematicians at MIT is working on the development of a new model to explain how and why these so-call phantom traffic jams form. According to the researchers, these types of phantom traffic jams form when there are a lot of cars on the road and small disturbances like a driver hitting the brakes too hard or getting too close to another car. These little disturbances can escalate into a self-sustaining traffic jam.

The model developed by the team of researchers may help road designers build roads to minimize the possibility of phantom traffic jams. The key to the study is the discovery that the mathematics of these jams called jamitons are very similar to the equations used to describe the detonation waves produced by explosions.

The discovery of the jamitons allowed the researchers to solve traffic jam equations first theorized in the 1950's. The equations are reportedly similar to those used in fluid mechanics and model traffic jams as self-sustaining waves. The equations allowed the researchers to calculate the conditions that case a jamitons to form and how fast the jamiton will spread.

According to the researchers, once this type of jamiton forms it is nearly impossible to break up and a driver’s only choice is to wait the jamiton out. The researchers say that the new model can help road designers to determine speed limits that are safer and find stretches of road where accidents are more likely.

One of the researchers, Aslan Kasimov, said, "We wanted to describe this using a mathematical model similar to that of fluid flow." Kasimov and his team say that they discovered that jamitons have a sonic point that separates traffic flow into upstream and downstream components. Communication of the cause of the jamiton to drivers it the downstream segment of traffic is impossible say the researchers.

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RE: The source is pretty simple really
By drycrust on 6/10/2009 1:31:18 PM , Rating: 2
True. One of the basic laws of physics is the speed of a car is less than or equal to that of the car in front.
As the density of cars on any given road goes up, the cushion between cars gets smaller. Since a car cannot travel faster than the car in front, when the car in front brakes or misses a gear change, the car behind must brake equal to or greater than the car in front.
As the average gap between cars gets smaller, so the need to brake harder than the car in front goes up. These two factors (speed car behind <= car in front, braking car behind >= braking car front) causes speed oscillations, which is really just classical wave theory. As with a normal amplifier, where the amplifying device cannot exceed its power supply's capability, so the traffic problems really start to happen when the physical bounds of the environment (speed limit or grinding to a halt) are approached.
This is why you get congestion around areas with merging traffic, because cars merging into a dense traffic stream with no extra lanes is just like an impedance mismatch. If the merging stream is also dense then really the only way to fix it without causing congestion is to have the merging traffic have their own lane.
However, it is important to note that if a line of cars is long enough, as happened when they were evacuating New Orleans, then you will get vehicle speeds that oscillate, which will cause vehicles to grind to a halt for no apparent reason.

By Xerstead on 6/10/2009 3:01:45 PM , Rating: 2
I was sure I'd seen a video of this effect before so i had a look and found one on YouTube:
This is like a mini version of the M25 motorway around London. This is one of the busiest roads in the UK and frequently has major traffic jams for miles. There is a variable speed limit around much of it indicated by overhead signs and speed camera enforcement. Traffic is slowed down at peak times to 40/50/60/70mph to help prevent and controll the problem.
The example is a circular road but it will have the same effect on a straight one.

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