A Convergent Algorithm for the Multimodal Traffic Equilibrium Problem

Abstract

The multimodal traffic equilibrium problem is in described in general by non-monotone, asymmetric, variational inequality problem. We show that in spite of the non-monotonicity of the cost operator, the problem may admit a different weaker property, which describes the hierarchical nature of the travel cost interactions. This property permits a natural decomposition approach, not otherwise available, which admits provably convergent algorithms- . We present one such algorithm, easily implementable using a solver for the single-class traffic equilibrium problem, and a convergence proof. This represents the first provably convergent method for solving the non-monot- one, asymmetric, traffic equilibrium problem.

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