Mathematically modelling phantom traffic jams

You know how high traffic density always seems to lead to self-perpetuating traffic jams that have no visible cause other than the fact that everyone has slowed down? There's math to describe it:
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...

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.

MIT Hopes to Exorcise 'Phantom' Traffic Jams (via Futurismic)