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Sensitivity Analysis for Equilibrium Network Flow

Author

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  • Roger L. Tobin

    (GTE Laboratories Incorporated, Waltham, Massachusetts 02254)

  • Terry L. Friesz

    (University of Pennsylvania, Philadelphia, Pennsylvania 19104)

Abstract

Direct application of existing sensitivity analysis methods for nonlinear programming problems or for variational inequalities to nonlinear programming or variational inequality formulations of the equilibrium traffic assignment problem is not feasible, since, in general, the solution to the equilibrium traffic assignment problem does not satisfy the uniqueness conditions required by the sensitivity analysis methods. This paper presents an approach for sensitivity analysis of equilibrium traffic assignment problems in which an equivalent restricted problem is developed which has the desired uniqueness properties; the existing methods are applied to this restricted problem to calculate the derivatives of the equilibrium arc flows with respect to perturbations of the cost functions and of the trip table. These derivatives are then shown to be equivalent to the derivatives of the original unrestricted equilibrium traffic assignment problem; therefore, the method yields the desired sensitivity analysis results.

Suggested Citation

  • Roger L. Tobin & Terry L. Friesz, 1988. "Sensitivity Analysis for Equilibrium Network Flow," Transportation Science, INFORMS, vol. 22(4), pages 242-250, November.
    • Handle: RePEc:inm:ortrsc:v:22:y:1988:i:4:p:242-250
    DOI: 10.1287/trsc.22.4.242
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