Researchers Bring Chaos Theory To Rush Hour Traffic

At the Texas Transportation Institute at Texas A and M University, researchers calculated that in 2011, traffic delays cost the U.S. economy $121 billion in lost productivity — in addition to 2.9 billion gallons of wasted gasoline. And in major cities around the world, severe traffic congestion paralyzes cities for hours each day, causes fatal car crashes, and disrupts the transportation industry.

In many ways, the calculus of traffic jams is straightforward: too many vehicles on the road, plus an aging roadway system, multiplied by time, equals headache-inducing rush hour traffic. But this July, a team of researchers from Colombia and Chile are investigating the effect of a new variable on this system; specifically, the team is exploring how chaos affects traffic.

Already, countries around the world have several different models for analyzing traffic patterns. In Germany, drivers benefit from the “Grüne Welle,” or “Green Wave,” when traffic lights are synchronized to give drivers multiple consecutive green lights. And in the United Kingdom, the advanced Motorway Incident Detection and Automatic Signaling system allows real-time control of motorway traffic.

The South American team hopes their research will shed new light on this global phenomenon. The researchers created a “discrete mapping” model of a bus moving through a digital city under ideal traffic conditions, and the results of the study were presented in the July issue of the mathematics journal Chaos. If a hypothetical bus has a “chaotic trajectory,” then it will be virtually impossible to predict its itinerary, whereas a bus with “non-chaotic-trajectory” would be easy to track.

“Systems with chaotic dynamics have a very short time horizon for predictability — which helps to explain scheduling problems with buses,” said Jorge Villalobos, the study’s lead author.

Much of the paper is beyond the understanding of mathematics amateurs; however, Villalobos’s team did reach one simple, if disappointing, conclusion.

“Pretending to optimize bus systems — in the sense of minimizing travel times — is physically impossible,” said Villalobos.

Ultimately, the researchers concluded that chaos plays an integral role in shaping traffic patterns.

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