Pursuing robust decisions in uncertain traffic equilibrium problems

TL;DR

This paper investigates the robustness of traffic equilibria under demand uncertainty, using scenario approach theory to provide distribution-free guarantees without requiring explicit demand distribution knowledge.

Contribution

It extends the hose model to uncertain demands within a polyhedral set and applies scenario approach theory for robust equilibrium analysis.

Findings

Distribution-free feasibility guarantees established

Scenario approach effectively handles demand uncertainty

Numerical example confirms theoretical results

Abstract

We evaluate the robustness of agents' traffic equilibria in randomized routing games characterized by an uncertain network demand with a possibly unknown probability distribution. Specifically, we extend the so-called hose model by considering a traffic equilibrium model where the uncertain network demand configuration belongs to a polyhedral set, whose shape is itself a-priori unknown. By exploiting available data, we apply the scenario approach theory to establish distribution-free feasibility guarantees for agents' traffic equilibria of the uncertain routing game without the need to know an explicit characterization of such set. A numerical example on a traffic network testbed corroborates the proposed theoretical results.