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No Speed Limits
 > Models
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 Porosity

## Models

In science, when you're trying to study some phenomenon, one of the things you can do is make a model, a mathematical abstraction that describes whichever aspects of reality you deem relevant. I've studied a fair amount of science, and in doing so have seen many different models; and now, when I look at traffic, I see the same models waiting to be applied. The backward-moving waves that occur in traffic backed up at a stoplight, for example, are clearly due not to the forward motion of cars, but to the backward motion of anti-cars … just like holes moving in a semiconductor.

What I want to do in this essay is give an overview of the kinds of models I'm thinking of, and, hopefully, convey some of my excitement about them. I'll write some more specific essays later.

Others, of course, have thought about all this well before me. I've hardly even begun to see what's out there, but already I've found a reference to a book from 1971, Kinetic Theory of Vehicular Traffic. I'll report back as I find out more. In the meantime, if you'd like to look for yourself, I can recommend the phrase “car traffic phase transition” as a good starting point.

The idea of phase transitions comes from the thermodynamic model. The way I see it right now, traffic can exist in three phases, closely analogous to the solid, liquid, and gas phases of normal materials. In the gas phase, the cars travel as individuals, interacting with other cars only rarely; in the liquid phase, the cars are packed together, but still retain mobility, i.e., are still able to move relative to one another; and in the solid phase, the cars are packed together in essentially fixed relative positions, as in stop-and-go traffic.

There's more to thermodynamics than just identifying phases, of course. Just as a normal material has properties—temperature, pressure, and volume—and changes phase as its properties are varied, so also does traffic. I'm not sure traffic has temperature or pressure, but it certainly has volume, and then it has properties of its own as well, such as velocity, density, and maybe porosity. Velocity, I think, might play the role of temperature.

I should point out that the phrase “traffic volume” doesn't mean a volume in the thermodynamic sense, it means a number of cars per unit time, i.e., velocity times density.

When you combine thermodynamics with the idea that matter is made up of atoms and molecules, you get statistical mechanics, which aims to predict the thermodynamic properties of materials from the physical properties of the individual particles. Or maybe you get condensed-matter physics, which has the same goal, but deals with solids and liquids rather than gases. In any case, one can do the same for traffic, and try to predict the properties of traffic from the properties, or behavior, of individual cars.

In condensed-matter physics, one often has to simplify a problem by studying it in a lower number of dimensions. I don't think that will be necessary for traffic—I bet the association between cars and lanes is strong enough that we can regard the whole as a set of coupled one-dimensional systems. That may not always be the best model, but it's certainly true that adjacent lanes can have different properties, as with the third lane in a two-lane merge.

Another thing that comes from condensed-matter physics is the idea of anti-cars, or, more generally, quasiparticles. When you have a material made up of particles, and observe composite things moving around in it that aren't particles, those are quasiparticles. A quasiparticle can represent the absence of a particle, as with anti-cars, but it doesn't have to—it can also represent, for example, an increased density of particles, as with the waves of braking and congestion one sees in moderately dense highway traffic. (In that case, the wave is a sound wave, so the quasiparticle is a phonon, a particle of sound.)

Speaking of semiconductors and condensed-matter physics, I'd like to mention two other things: the idea of Fermi levels in parking lots, and a story I once read in Gene Wolfe's Book of Days.

Getting back to the idea of gases and liquids, there are some situations that beg for models from fluid dynamics. If you're at a toll barrier on a five-lane highway, and only one toll gate is open, in the middle, the pattern of cars on the other side might look a lot like a gas diffusing through a hole into a vacuum. Or, if you're driving down a highway in liquid traffic, and encounter a slow-moving wide load, you might see that the cars flowing by produce a turbulent wake.

Finally, there's a nice model that comes from chemistry. Once you start thinking of cars as atoms, it's not a large step to realize that there are different types of cars, and of drivers, so that the traffic has some particular chemical composition. There won't be a periodic table, of course, since the properties of cars and drivers are continuously variable, but there could still be practical applications. For example, just as a small amount of salt can melt ice by lowering its freezing point, so also might different behavior by a small fraction of drivers be able to melt frozen traffic, or effect various other large changes in its properties!