We've all been there - stuck in traffic, inching along, running late and getting angry when suddenly everyone starts moving. Just like that, the road clears. No flashing lights, no mangled cars, no clue to suggest what went wrong. They're called phantom traffic jams, and mathematicians at MIT are determined to find out what causes them - and more importantly, how to prevent them.

Phantom jams are born of a lot of cars using the road. No surprise there. But when traffic gets too heavy, it takes the smallest disturbance in the flow - a driver laying on the brakes, someone tailgating too closely or some moron picking pickles off his burger - to ripple through traffic and create a self-sustaining traffic jam.

Massachusetts Institute of Technology mathematicians have created a model to describe how these frustrating snarls form. With this understanding, engineers could design build better roads to minimize the odds of them happening.

The mathematics of such traffic jams are strikingly similar to the equations that describe detonation waves produced by explosions, said Aslan Kasimov, a lecturer in MIT's Department of Mathematics. Realizing this allowed the reseachers to solve traffic jam equations that were first theorized in the 1950s. The MIT researchers even came up with a name for this kind of gridlock - "jamiton." It's a riff on "soliton," a term used in math and physics to desribe a self-sustaining wave that maintains its shape while moving.

The equations MIT came up with are similar to those used to describe fluid mechanics, and they model traffic jams as a self-sustaining wave.

"We wanted to describe this using a mathematical model similar to that of fluid flow," Kasimov said.

The researchers hit upon the equation after an experiment by Japanese researchers demonstrated the formation of jamitrons on a circular road. In that experiment, drivers were instructed to travel 30 kilometers an hour (18.6 mph) while maintaining a constant distance between cars. It didn't take long before disruptions occurred and phantom jams formed. Denser traffic brought quicker jams.

The MIT team found speed, traffic density and other factors can determine conditions that will lead to a jamiton and how quickly it will spread. Once the jam forms, the researchers say, drivers have no choice but to wait for it to clear. The new model could lead to roads designed with sufficient capacity to keep traffic density below the point at which a jamiton can form.

Kasimov found that jamitons have a "sonic point," which separates traffic flow into upstream and downstream components, much like the event horizon of a black hole. This sonic point prevents communication between these distinct components so information about free-flowing conditions just beyond the front of the jam can't reach drivers behind the sonic point. Ergo, there you sit, stuck in traffic and have no idea that the jam has no external cause, your blood pressure racing toward the stratosphere.

The MIT team plans to look more detailed aspects of jamiton formation, including how the number of lanes affects the phantom traffic jams. Perhaps they can then figure out what to do about people who won't hang up and drive.

Here's a video of the model at work:

Photo: Flickr user SignalPAD