# Closing Roads to Help Cut Traffic

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After looking at traffic routes in London, New York and Boston, three scientists have concluded that having more routing options can actually slow down the overall rate of travel.  More access routes results in Braess’s Paradox:

“For each point of a road network, let there be given the number of cars starting from it, and the destination of the cars. Under these conditions one wishes to estimate the distribution of traffic flow. Whether one street is preferable to another depends not only on the quality of the road, but also on the density of the flow. If every driver takes the path that looks most favorable to him, the resultant running times need not be minimal. Furthermore, it is indicated by an example that an extension of the road network may cause a redistribution of the traffic that results in longer individual running times.”

Eoin O’Carroll explains:

Imagine two routes to a destination, a short but narrow bridge and a longer but wider highway. Lets also imagine that the combined travel times of all the drivers is shortest if half take the bridge and half take the highway. But because each driver is selfishly trying to seek the shortest route for himself, this doesnt happen. At first, everyone will go for the bridge because its shorter. But then, as the bridge becomes backed up, more drivers start taking the highway, until the congestion on the bridge starts to clear up. At that point more drivers go back to the bridge, which then becomes backed up again. Eventually, the traffic flow settles into whats called the Nash equilibrium (named for the beautifully minded mathematician), in which each route takes the same amount of time. But in this equilibrium the travel time is actually longer than the average time it would take if half of the drivers took each route.

Networks of principal roads (both solid and dotted lines; the thickness represents the number of lanes). (a) Boston-Cambridge area, (b) London, UK, and (c) New York City. The color of each link indicates the additional travel time needed in the Nash equilibrium if that link is cut (blue: no change, red: more than 60 seconds additional delay). Black dotted lines denote links whose removal reduces the travel time, i.e., allowing drivers to use these streets in fact creates additional congestion. This counter-intuitive phenomenon is called ”Braess’s paradox.”