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|9th November 2009, 10:11||#1|
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Braess Paradox - adding roads can increase congestion
I read this as part of a study of crowd dynamics and control (as applicable to traffic)
Crowd Dynamics Ltd - G. Keith Still - PhD Thesis - Chapter 3
We have a solution where every car is careful to take the cheapest available route, and yet the total cost has increased. How can adding a road to a network slow everyone down?
The key is how the cost of using a road varies with the number of cars. Using our linear functions, we can imagine the constant term as representing the road's length, and the term in x an indication of how prone the road is to congestion. Note that this idea supposes that the `cost' of a journey is purely a matter of how long it takes. Then the new road allowed a shortcut between the two northwesterly roads, which are shorter than the alternatives, but suffer from substantially worse congestion.
The result is that each driver in turn takes this slightly quicker route, at a small saving for himself, but causing substantial extra delay to a number of other drivers. By the time everyone has decided whether to take the short cut, the total congestion gained by the system far outweighs the savings in distance.
The modified network is really a classic example of the Prisoner's Dilemma (PD), a paradox with many applications. Adding the extra road gave the commuters the opportunity to `defect', in PD terms. In this particular case it did not even have any compensating benefits.
When we consider the paradox with respect to egress systems we have many examples of Braess’s paradox in building design. Specifically, the assumption that adding addition exit routes it will increase the overall egress capacity. This also applies to the addition of ingress routes to a stadium. Simply adding more may not solve the problem of how to increase the ingress capacity.
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Last edited by Rudra Sen : 9th November 2009 at 10:19.
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