The formation of a phantom traffic jam.

The formation of a phantom traffic jam.

The most frustrating sort of traffic jam may be the one that has, apparently, no cause. Think road rage with no one to blame.

MIT mathematicians have been working on the problem. No, they didn’t find someone to blame. Instead, they have developed a model that describes the circumstances that prompt such jams to form. This model could help road designers minimize the odds of their formation. 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

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. The equations, similar to those used to describe fluid mechanics, model traffic jams as a self-sustaining wave.