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Abstract:

In 1968, Braess [1] demonstrated a remarkable and counterintuitive fact, now known as "Braess's Paradox ": in a network in which users selfishly and independentlychoose minimum-latency paths and the latency of an edge increases with the amount of edge congestion, deleting edges from the network can decrease the latency encountered by traffic. Our work here is primarily motivated by the paper of Roughgarden [3], which quantifies the maximumpossible severity of Braess's Paradox. Specifically, in [3] it was shown that there is a network with n vertices in which removing a set of edges decreases the latency encountered by the network traffic by a factor of #n/2#, and that no greater decrease is possible in any such network. The construction for n = 4 essentially gives Braess's original example. However, the "Braess graphs " of [3] differ from Braess's example in that #n/2 #-1 edges need to be removed to effect an #n/2#

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