When traffic congestion becomes a problem, new bridges or bigger roads might seem like the obvious solution. But sometimes the opposite is true, according to John Hubbard, professor of mathematics: Closing roads can actually speed up traffic.

Hubbard discussed this apparent paradox in his talk, "The Price of Anarchy," as part of Math Awareness Month in Malott Hall's Bache Auditorium April 30. He examined the time cost of "selfish routing," in which each driver pursues his own advantage. Citing studies by Stanford mathematician Tim Roughgarden and Cornell computer scientist Eva Tardos, he said that selfish routing results in as much as one-third more time spent in travel than the optimum "social routing," in which total travel time is minimized. Thus the "price of anarchy," he said, is the ratio 4/3.

He provided a simple model: a town and factory divided by a winding river. When there were just two bridges, everyone takes an hour and a half to commute, but if a third, large bridge is built, everyone takes two hours.

"Building the bridge and giving people free choice had the result that everybody took more time," he said.

Real-life situations support this theory, he said. When 42nd Street in New York City was closed, he said, "everyone expected the traffic was going to be terrible, and to everyone's amazement, the traffic was actually faster everywhere. There's every reason to think that turning 42nd Street into a pedestrian mall would, in fact, speed up everyone's traffic."

Hubbard used a model of strings, springs and weights to show that the mathematics underlying the price of anarchy is not psychological: Physical systems behave the same way. The weight was supported by two springs and one taut string, with two other strings connected, but hanging slack. When he cut the taut string, the weight moved up, not down as expected.

Although closing roads appears to be the logical solution to some traffic congestion problems, Hubbard said, it is unlikely that policies like these will be implemented. "It's very counterintuitive. … You try convincing a traffic engineer, never mind a politician, that this is a good idea, and then you'll know why they don't do it."

The Department of Mathematics sponsors an annual public lecture in keeping with each year's national theme; this year the theme is Mathematics and Complexity.

Joyce Wu '13 is a writer intern at the Cornell Chronicle.