On the Stability of User Equilibria in Static Transportation Networks

Abstract

The stability of a user equilibrium determines whether it could be realized or sustained in a transportation network, when subject to perturbations in traffic conditions and drivers' route choice behaviors. In this paper, with a simple deterministic dynamical system model of the traffic assignment problem, we first develop a systematic approach to analyzing asymptotic stability and instability of user equilibria in static transportation networks with fixed demand. We then discuss two examples of non-monotone traffic assignment problem. Compared with existing approaches, the new approach is simpler to use and leads to results consistent with the former. This study could be helpful for analysis and design of real transportation networks.

Wardrop’s First Principle: Extension for Capacitated Networks

“…His analysis is valid when there are no explicit capacity restrictions, and exploits the concept of swapping flow from the more expensive route of an O/D pair to a less costly alternative route of that O/D. Jin [15], briefly mentioning the evolution of the traffic assignment problem from early 1950's to 2005, analyzes the asymptotic stability of the fixed demand UE in static transportation networks for two non-monotone traffic assignment models of Smith [14] and Jin [16] representing day-to-day user behavior, and shows that both models present consistent results, with the latter being simpler than the former, particularly when dealing with road network traffic dynamics and capacity constraints. (A discussion of the conventional Dynamic Traffic Assignment (DTA) models and the existence and uniqueness of their solutions, particularly, in regard to Wardropian solution, may be found in Szeto and Lo [17].…”