Economics Mathematics

Traffic Physics 101: “The Jamiton”

I came across a cool article on Nautilus on the phenomenon of phantom traffic jams, where people slow down and cause backups for no discernible reason.


It turns out that the explanation for these event is fascinating. Moreover, as the author notes, these events are not just annoying, they can be dangerous. However, as the author notes:

phantom jams are not the fault of individual drivers, but result instead from the collective behavior of all drivers on the road. It works like this. Envision a uniform traffic flow: All vehicles are evenly distributed along the highway, and all drive with the same velocity. Under perfect conditions, this ideal traffic flow could persist forever. However, in reality, the flow is constantly exposed to small perturbations: imperfections on the asphalt, tiny hiccups of the engines, half-seconds of driver inattention, and so on. To predict the evolution of this traffic flow, the big question is to decide whether these small perturbations decay, or are amplified.

If they decay, the traffic flow is stable and there are no jams. But if they are amplified, the uniform flow becomes unstable, with small perturbations growing into backwards-traveling waves called “jamitons.” These jamitons can be observed in reality, are visible in various types of models and computer simulations, and have also been reproduced in tightly controlled experiments.

The author goes on to explain that we can imagine that every driver on the road is constantly running an unconscious optimization function: speeding up when traffic dissipates and slowing down when it accumulates. These two activities are usually balanced correctly, but sometimes our brains get it wrong:

The mathematical analysis of traffic models reveals that these two are competing effects. The delay before drivers reach their target velocity causes the growth of perturbations, while traffic pressure makes perturbations decay. A uniform flow profile is stable if the anticipation effect dominates, which it does when traffic density is low. The delay effect dominates when traffic densities are high, causing instabilities and, ultimately, phantom jams.

The transition from uniform traffic flow to jamiton-dominated flow is similar to water turning from a liquid state into a gas state. In traffic, this phase transition occurs once traffic density reaches a particular, critical threshold at which the drivers’ anticipation exactly balances the delay effect in their velocity adjustment. The most fascinating aspect of this phase transition is that the character of the traffic changes dramatically while individual drivers do not change their driving behavior at all.

The last sentence of this quote is what struck me: every driver seems to be doing the same thing she was doing before the jam and yet the traffic has gone from free flowing to congested. In the end, add the authors, the problem is not just with one person who slowed down:

Besides being an important mathematical case study, the phantom traffic jam is, perhaps, also an interesting and instructive social system. Whenever jamitons arise, they are caused by the collective behavior of all drivers—not a few bad apples on the road. 


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