A new look at the multiclass network equilibrium problem

The multiclass network equilibrium problem is expressed in general as a nonmonotone, asymmetric, variational inequality problem. We show that in spite of the nonmonotonicity of the cost operator, the problem may actually satisfy a weaker property, induced by the hierarchical nature of the travel cost interactions. This property allows a natural decomposition approach, not otherwise available, that admits provably convergent algorithms. We present one such algorithm, easily implementable using a solver for the single-class network equilibrium problem, together with a convergence proof.