Sensitivity analysis of the perturbed utility stochastic traffic equilibrium

This paper develops a novel sensitivity analysis framework for the perturbed utility route choice (PURC) model and the accompanying stochastic traffic equilibrium model. We provide general results that determine the marginal change in link flows following a marginal change in link costs across the network in the cases of flow-independent and flow-dependent link costs. We derive analytical sensitivity expressions for the Jacobian of the individual optimal PURC flow and equilibrium link flows with respect to link cost parameters under mild differentiability assumptions. Numerical examples illustrate the robustness of our method, demonstrating its use for estimating equilibrium link flows after link cost shifts, identifying critical design parameters, and quantifying uncertainty in performance predictions. The findings have implications for network design, pricing strategies, and policy analysis in transportation planning and economics, providing a bridge between theoretical models and real-world applications.