Sensitivity analysis of logit-based stochastic user equilibrium network flows with entry-exit toll schemes

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. © 2008 Computer-Aided Civil and Infrastructure Engineering.