Abstract

In this paper we present a version of the (static) traffic equilibrium problem in which the cost incurred on each path is not simply the sum of the costs on the arcs that constitute that path. We motivate this nonadditive version of the problem by describing several situations in which the classic additivity assumption fails. We describe existence and uniqueness conditions for this problem and we also present convergence theory for a generic algorithm for solving nonadditive problems. INTRODUCTION Paraphrasing Wardrop [33], the (static) traffic equilibrium problem is to find a set of path flows that satisfy certain demand constraints and have the property that the costs on all used paths connecting an origin-destination pair are equal and less than or equal to the cost on all unused paths connecting that pair. In order to prove existence/uniqueness results and develop convergent algorithms, this problem has been formulated as a nonlinear program (NLP) [4], a nonlinear complementarity...

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