Optimal sub-networks in traffic assignment problem and the Braess paradox

This paper is related to the Braess paradox. For a given transportation network, we are interested in the origin-destination (OD) travel costs in its sub-networks. Speaking about the performance of a network in terms of its equilibrium travel costs, we try to select the best sub-network of the original one. In a one OD pair network, by removing arcs, the equilibrium travel cost can decrease. Thus we ask for a sub-network for which the travel cost at equilibrium is minimum. In the case of multiple OD pairs, a multi-criteria comparison concept (Pareto optimality) is used to compare equilibria in sub-networks. The problem is formulated as an optimization problem. Only the fixed demand case is dealt with.