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Sensitivity Analysis of Combined Distribution–Assignment Model with Applications

The equilibrium trip distribution–assignment model with variable destination costs (ETDA-VDC) is critical for the modeling of evacuation strategies that consider transportation network capacity. The model is an improvement over the combined distribution–assignment model because it integrates the destination cost function. With mild requirements, a rectified restriction approach was developed to generate a restricted equilibrium problem, in which the applicability of the implicit function theorem was proved. Explicit expressions of the derivatives of model variables for perturbations of input variables and parameters of the ETDA-VDC model were derived. The results of a simple numerical example were used to demonstrate four applications: sensitivity-based algorithm for the bilevel network capacity model, analysis of paradox, identification of critical parameters, and access control. The usefulness and importance of the sensitivity expressions were also demonstrated.