Braess' paradox

Braess' paradox, credited to the mathematician Dietrich Braess, states that sometimes adding extra capacity to a network can reduce overall performance. This is because the equilibrium of such a system is not necessarily optimal.

Related Topics:
Dietrich Braess - Network

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According to A. D. Irvine, Braess' paradox can be shown to be equivalent to Newcomb's problem.

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Oversimplified, imagine there are two routes to a destination with no way to switch between them and each route has 100% of the cars it can carry before a traffic jam occurs. If enough additional cars are added to either route, a traffic jam will occur on that route. So if one route starts with 110% of capacity and the other has 90%, there will be a jam on the route with 110% capacity. But if you add a crossroad that connects the two routes, drivers can now start out on one route, take the crossroad, and finish their journey on the other route.

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If then enough drivers (about 20%) on the jammed route decide to switch to the other route, the remainder of the route they are on will have 90%, and the OTHER route will become jammed at 110%. In fact, as traffic tends to back up, the second route will be jammed at, after and a bit before where drivers merge in.

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Hence half of the first route and most of the second route become jammed, because too many drivers took the crossover route! Adding capacity has reduced overall performance (more traffic jams).

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Of course, if only enough drivers switch over so that both routes are at 100%, it works fine. Hence a sociological issue is that when too many drivers take the crossover to try to avoid jammed traffic, very few benefit. Only the first few drivers switching routes will benefit. Some drivers would have to avoid trying to improve traffic for themselves in order for everyone to benefit.

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