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.