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 cos...

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Bibliographic Details
Published in:Transportation science 2004-08, Vol.38 (3), p.282-292
Main Authors: Marcotte, Patrice, Wynter, Laura
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Cost functions
Equilibrium
Exact sciences and technology
Ground, air and sea transportation, marine construction
Inequality
Logistics
Mathematical analysis
Mathematical functions
Mathematical inequalities
Mathematical monotonicity
Mathematical vectors
multiclass traffic network equilibrium
nested monotonicity
Networks
Operating costs
Studies
Traffic
Transport
Transportation
Transportation planning, management and economics
Travel expenses
Variational inequalities
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Summary: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.
ISSN:0041-1655
1526-5447
DOI:10.1287/trsc.1030.0039