Sensitivity of Static Traffic User Equilibria with Perturbations in Arc Cost Function and Travel Demand

Abstract

This paper deals with sensitivity analysis of static traffic user equilibrium problems. We apply some recently developed sensitivity analysis techniques for generalized equations to analyze the behavior of the equilibrium arc flow of such a problem when both the arc cost function and the travel demand vary. Our methods permit calculation of semiderivatives under general conditions and of derivatives under more restrictive conditions; we calculate the semiderivatives by solving a linear traffic user equilibrium problem and the derivatives by matrix multiplication together with the solution of a linear equation the dimension of which is at most the number of arcs. Three numerical examples show how to use these results in practice.

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