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The Basics of the Problem

It has long been said that if you can't describe something mathematically, then you don't truly understand it. I think the lack of success of chemical attractors of the opposite sex (pig hormones sold in the gas station) is relative evidence that some issues should forever be out of the reach of the scientific method. But traffic is not such a beast.

A surprising number of models of vehicular traffic have been constructed through the ages. These range from basic continuum mechanical models that treat traffic flow (rather than individual vehicles), to the latest efforts of government supercomputers at Sandia turning their sights from nuclear explosion behaviors and kill-ratios to the construction of intelligent driver "agents" to assist city planners in prioritizing infrastructure projects. All very enlightening and surprisingly accurate.

Even a basic discrete model (treating individual cars) can predict the conditions under which an accident is all but unavoidable. This doesn't require braking distance or acceleration data on the latest products from Detroit; it only requires the assumption that not every car on the road will be simultaneously traveling in the same direction at the same speed. It predicts that if a driver has no knowledge of car behavior at least six seconds ahead, virtually any change in conditions will result in a crash.

In other words, stare at the rear bumper of the car in front of you, and you will eventually be dining on that very safety device. Obvious enough, right?

It was this soft spot of simple real-world modeling that allowed a team in Sweden to finally derive the optimum "car density" on a roadway, based on typical lane changes, accidents, and other behaviors.

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