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Thu, 09 Oct 2008
Braess' Paradox says that adding extra capacity to a network can sometimes reduce its efficiency. In electronics, removing wires can sometimes increase the conductivity of the circuit. In road networks, it means opening a new road or new lanes can actually increase how long it takes the average person to complete their trips. Usually not, but sometimes.
The problem is well known in Game Theory: when everyone is trying to maximize their own personal advantage, the overall solution may not be the best one. This can be the case with road networks. If everyone tries to take the route that is quickest for themselves, you may end up with a situation where eveyone is slowed down.
Say for instance that you add a link that gives some people a shortcut via a short highway access road, saving a few people 10 minutes to get somewhere. Say that the extra traffic caused by these people and their turns onto an off the shared road causes an extra 9 minutes of slowdown on that road. These people still come out ahead by 1 minute so they keep using the shortcut. But a lot of other people are being slowed down by 9 minutes. Of course road networks are complex and interlinked, and people's behaviour is not exactly predictable so it is not simple to predict when a new road will slow traffic.
Last year I read an article in Vancouver Magazine and later went to a talk about the same story. To quote the story,
LaClaire heard about Braess' Paradox from a visiting traffic scholar in a Wall Centre conference room back in 2000. He remembers the equation, and the epiphany it brought. His blue eyes twinkle as he recalls the moment he raised his hand.Closing roads to reduce congestion has been a wacky theory, based on guesswork and potentially expensive trial and error, against the stern advice of traffic engineers. Until a few weeks ago.
In a paper to be published in Physical Review Letters, Korean physicists and an American computer scientist calculate the "price of anarchy" (PoA) that results from individual decisions which increase the travel time of others. And in a well considered algorithm and methodology, they can point out exactly which roads should be shut down and what travel time savings would occur as a result.
The next step is experimental confirmation. The paper points to 25 specific roads in Boston, New York, and London that could be shut down. Although the paper doesn't seem to point to specific software that they could make available, and the data and assumptions that they use, including Google Maps for road length, classification, and capacity, BPR (Bureau of Public Roads) function for delays, makes the development of a Google Maps mashup for this algorithm relatively straightforward.
Any takers? If you work in a city that would consider reducing congestion and saving millions in capital expenses, drop me a line.