Sensitivity analysis of the perturbed utility stochastic traffic equilibrium

TL;DR

This paper introduces a sensitivity analysis framework for the perturbed utility stochastic traffic equilibrium model, enabling the assessment of how link flow changes respond to cost variations in transportation networks.

Contribution

It derives analytical sensitivity expressions for the PURC model, facilitating efficient computation of flow responses to link cost changes under general assumptions.

Findings

Analytical Jacobian expressions for PURC flows are derived.

The method efficiently estimates equilibrium flows after link cost shifts.

Demonstrated application in large-scale network example.

Abstract

This paper develops a sensitivity analysis framework for the perturbed utility route choice (PURC) model and the accompanying stochastic traffic equilibrium model. 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 general assumptions. This allows us to determine the marginal change in link flows following a marginal change in link costs across the network. We show how to implement these results while exploiting the sparsity generated by the PURC model. Numerical examples illustrate the use of our method for estimating equilibrium link flows after link cost shifts, identifying critical design parameters, and quantifying uncertainty in performance predictions. Finally, we demonstrate the method in a large-scale example. 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.