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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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humans
By xsilver on 6/10/2009 11:30:15 AM , Rating: 2
Im not sure how it is in the US, but here in australia on the freeways there are LED signs that light up during peak hours in order to take advantage of this fluid dynamics.
eg. speed is reduced to reduce stop start.

Only problem is, humans are greedy/inconsiderate and many ignore the speed sign anyways only to stop 3 cars in front and ruin the fluid dynamics model.

I always love hearing how people complain WHY speed limits are reduced when its peak hour rather than sped up. lol.

RE: humans
By mdogs444 on 6/10/2009 11:31:43 AM , Rating: 2
Studies have shown that accidents are more likely to happen at lower speeds than at higher speeds. That is also why we have minimum speed limits on freeways.

No matter which way you look at it, its better to stay with traffic, even if that means speeding. When I lived in Chicago, the speed limit was 60, but if you were not doing 80 then you had people 6" from your rear bumper blasting the horn. In that case, the slow driver is the danger because 90% of the cars are going over the limit. Staying with traffic is safer, causes less congestion, and gets you where you need to go faster.

RE: humans
By mmcdonalataocdotgov on 6/10/2009 11:40:18 AM , Rating: 2
True to that. It is not speed, but variations in speed that cause density waves. The people who go slow force other people to go around them, which forces people in the other lanes to slow and try to go around further, which forces etc. Density wave.

RE: humans
By radializer on 6/10/2009 8:03:46 PM , Rating: 2
On those lines, when I was living in the Phoenix metro area, I was once pleasantly surprised when the speed limits of a certain stretch of the Loop 202 freeway increased (yes increased! ) from 55pmh to 65pmh.

As for the reasons behind this ... everyone used to drive that stretch of freeway at speeds of 70mph, and rumor has it that those who actually stuck to the 55pmh speed limit were causing a traffic hazard - so I guess ADOT (or whoever sets these limits) figured they'd up the limit to 65mph to improve traffic flow.

By the way, if you drive out on I-10 headed east from Tucson towards El Paso ... the posted Minimum Speed Limit is 65mph almost through all of New Mexico.

RE: humans
By GaryJohnson on 6/10/2009 11:41:09 AM , Rating: 2
That doesn't compute. The higher the speed the more cars per second a roadway can hanlde. Lower speed = fewer cars per second = more traffic.

RE: humans
By mmcdonalataocdotgov on 6/10/2009 11:45:13 AM , Rating: 2
The more cars on the road, the more cautious and overcorrecting the drivers become, and the slower the traffic. The net affect is that the roadway can handle lower car counts at higher speeds, and higher car counts at lower speeds. Its called Rush Hour.

RE: humans
By Chernobyl68 on 6/10/2009 11:50:35 AM , Rating: 2
not really true. At high speeds, the headway increases, and you while your vehicles are travelling faster, there is more space needed between them.

2400 vehicles per hour per lane is about the maximum theoretical capacity of a freeway lane. This volume gets reduced by a host of factors, including:

Truck percentage
driver familiarity
Interchange spacing
lateral clearance
lane width

just to name a few.

RE: humans
By Seemonkeyscanfly on 6/10/2009 3:47:05 PM , Rating: 2
that's only if you want to be safe and live.... :)

RE: humans
By Ratwar on 6/10/2009 7:01:39 PM , Rating: 1
Look, if you want a real world example of why your explanation is... well... bullshit, come drive around Atlanta, GA for awhile. Going ~70 mph with maybe a car length behind you and a car length in front of you is kinda standard.

Going slower may ease traffic on roads that aren't going to be over capacity anyways, but on roads that are already well beyond capacity, they only make the situation worse.

RE: humans
By Xerstead on 6/10/2009 3:33:19 PM , Rating: 2
In theory, yes. You may be able to get more vehicles along a road all travelling at high speed but can the road/drivers handle it safely? Faster traffic requires increased spaces between vehicles and at higher speeds with heavy traffic these 'phantom' traffic jams become more likely. Also there is an increased risk of a collision. The aim is to create the highest (within reason) average speed which is done by keeping everybody moving even if this means starting at a slower speed.

RE: humans
By micksh on 6/10/2009 4:57:29 PM , Rating: 2
There is a way to measure distance in time units and this can be found in some safety guidances.
Theoretically if all cars keep distance considered safe (3 seconds to the next car) the distance will be proportional to speed and highway throughput will stay the same at any non-zero speed.
But, that is only if we don't count car length. Safe distance between cars increases with the speed but cars don't elongate. So the throughput should increase with the speed unless drivers increase safe distance measured in time units (which is probably the case).

On the side note, people just don't seem to use gas pedal here, in North California. I see a lot when people enter highways at 45-50 mph where limit is 65 mph, and these are not grandmas, these are otherwise normal-looking young and middle-aged men. Maybe they are trying to save on gas that way?
And then "inverse race" starts with some car in right lane. The car on highway which is already well below speed limit slows down trying to yield to entering car. And the entering car slows down trying to yield to the car on highway. At around 40 mph they finally settle this desperately slowing down all right lane. And all that when highway is not crowded, there is a lot of room to merge into it.
Many people just can't estimate at what point they need to merge and they think the slower the safer.

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