Stability Analysis of Transportation Networks with Multiscale Driver Decisions

TL;DR

This paper investigates the stability of Wardrop equilibria in transportation networks considering multiscale driver decisions influenced by both local and global information, demonstrating conditions under which the network approaches equilibrium.

Contribution

It introduces a novel coupled differential equation model capturing multiscale driver decision-making and proves stability results showing convergence to Wardrop equilibrium under certain update frequency conditions.

Findings

Network state approaches Wardrop equilibrium when preference updates are infrequent.

The model demonstrates robustness of Wardrop's postulate against non-persistent perturbations.

Combines techniques from singular perturbation, game theory, and dynamical systems.

Abstract

Stability of Wardrop equilibria is analyzed for dynamical transportation networks in which the drivers' route choices are influenced by information at multiple temporal and spatial scales. The considered model involves a continuum of indistinguishable drivers commuting between a common origin/destination pair in an acyclic transportation network. The drivers' route choices are affected by their, relatively infrequent, perturbed best responses to global information about the current network congestion levels, as well as their instantaneous local observation of the immediate surroundings as they transit through the network. A novel model is proposed for the drivers' route choice behavior, exhibiting local consistency with their preference toward globally less congested paths as well as myopic decisions in favor of locally less congested paths. The simultaneous evolution of the traffic congestion on the network and of the aggregate path preference is modeled by a system of coupled ordinary differential equations. The main result shows that, if the frequency of updates of path preferences is sufficiently small as compared to the frequency of the traffic flow dynamics, then the state of the transportation network ultimately approaches a neighborhood of the Wardrop equilibrium. The presented results may be read as a further evidence in support of Wardrop's postulate of equilibrium, showing robustness of it with respect to non-persistent perturbations. The proposed analysis combines techniques from singular perturbation theory, evolutionary game theory, and cooperative dynamical systems.