An Efficiency Improvement of the Equilibrium Solution Search on the Selfish Routing Game by Removing Redundant Paths

The selfish routing game is a mathematical model to represent the behavior of selfish players who select a path in a congested network. In the equilibrium solution search on the selfish routing game, the amount of flow passing through each path is designated as the decision variable. Therefore, it is difficult to obtain the equilibrium solution of the selfish routing game in large-scale networks with a vast number of paths in a realistic time. In many cases, flows pass through a few part of the paths only and no flow passes through the other paths in the equilibrium solution of the selfish routing game in large-scale networks. If some of the paths which are zero-flow paths in the equilibrium solution can be removed from the decision variables in advance, the efficiency of the equilibrium solution search is expected to be improve. This paper proposes a new solution search method to improve the efficiency of the equilibrium solution search by removing redundant paths which can be detected in advance by considering a condition with respect to the equilibrium solution. The effectiveness of the proposed method is confirmed through numerical experiments.

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