Sensitivity Analysis of Logit‐Based Stochastic User Equilibrium Network Flows with Entry–Exit Toll Schemes

Abstract

Abstract: This article addresses sensitivity analysis of logit-based stochastic user equilibrium (SUE) network flows on transportation networks with entry–exit toll schemes. These schemes have a technical challenge that the generalized travel time including tolls on a path is nonadditive. First, it shows that the perturbed logit-based network flows—link and entry–exit flows—are implicit but continuously differentiable functions with respect to the perturbation parameters arising from link travel time functions, origin–destination demands, and entry–exit tolls. Second, this article derives elegant analytical expressions of gradients of perturbed logit-based SUE network flows, and elaborates that these gradients can be calculated by the two-stage stochastic network loading algorithm, which obviates the need for path enumeration. Finally, two numerical examples are presented to demonstrate the calculation process and computational capability.

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