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A New Look at the Multiclass Network Equilibrium Problem

DIRO, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, Canada H3C 3J7
IBM Research, P.O. Box 704, Yorktown Heights, New York 10598
patrice.marcotte{at}umontreal.ca
lwynter{at}us.ibm.com

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.

Key Words: multiclass traffic network equilibrium; nested monotonicity; variational inequalities
History: Received: June 2002; revised: November 2002; accepted: January 2003.

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