How harmful the paradox can be in the Braess/Cohen-Kelly-Jeffries networks

Consider networks in Wardrop equilibria, i.e., situations where each user in a network strives to optimize its own cost noncooperatively but has only an infinitesimal impact on other users. In computer networking, some shortest-path routing protocols that reflect link queueing delays may bring about situations close to Wardrop equilibria. The Braess (1968) paradox is a famous example of paradoxical cases where adding capacity to a network degrades the costs for all users. This paper investigates, in particular, networks generalized from what were studied by Cohen (1990, 1997), Kelly (1990), and Jeffries (1997) in comparison with the networks of the same topology as the original Braess network. The measure of cost degradation considered is the ratio of the cost for each user of a network after adding capacity (a link) to that before adding capacity. It has been shown that a value of the measure is less than 2 for every general Braess network. The results of this paper show that the measure of paradoxical cost degradation is also less than 2 for all of the networks considered in this paper.