A network efficiency measure for congested networks

In this paper, we propose a network efficiency measure for congested networks, that captures demands, costs, flows, and behavior. The network efficiency/ performance measure can identify which network components, that is, nodes and links, have the greatest impact in terms of their removal, due to, for example, natural disasters, structural failures, terrorist attacks, etc., and, hence, are important from both vulnerability as well as security standpoints. The new measure is applied to the Braess paradox network in which the demands are varied over the horizon and explicit formulae are derived for the importance values of the network nodes and links. This measure is applicable to such congested networks as urban transportation networks and the Internet.