Stability and bifurcations in transportation networks with heterogeneous users

TL;DR

This paper investigates how heterogeneity among users in transportation networks affects the stability of equilibria, revealing bifurcations and conditions for stability under logit dynamics.

Contribution

It introduces an analysis of stability and bifurcations in heterogeneous routing games using logit dynamics, extending understanding beyond homogeneous models.

Findings

Logit dynamics can cause bifurcations as noise varies.

Provided conditions ensure stability of user equilibria.

Heterogeneity introduces complex stability behaviors.

Abstract

A critical aspect in strategic modeling of transportation systems is user heterogeneity. In many real-world scenarios, e.g., when tolls are charged and drivers have different trade-offs between time and money, or when they get informed about current congestion by different routing apps, modeling users as rational decision makers with homogeneous utility functions becomes too restrictive. While global asymptotic stability of user equilibria in homogeneous routing games is known to hold for a broad class of evolutionary dynamics, the stability analysis of user equilibria in heterogeneous routing games is a largely open problem. In this work we study the logit dynamics in heterogeneous routing games on arbitrary network topologies. We show that the dynamics may exhibit bifurcations as the noise level of the dynamics varies, and provide sufficient conditions for asymptotic stability of user equilibria.