  User equilibrium is a central concept for studying transportation networks,
and one can view it as the result of a dynamical process of drivers' route
choice behavior. In this paper, based on a definition of O-D First-In-First-Out
violation, we propose a new dynamical system model of the route choice behavior
at the aggregate, route level for both static and dynamic transportation
networks. An equilibrium of such a dynamical system can be a user equilibrium
or a partial user equilibrium. We prove that, for static, symmetric traffic
assignment problem with fixed or variable demand, only user equilibria are
stable for the dynamical system, and the objective function in the mathematical
programming formulation (Beckmann, McGuire, and Winsten, 1956) can be
considered as the potential energy of the dynamical system. We then present an
Euler-based perturbation method for finding user equilibrium and solve two
examples for both static and dynamic traffic assignment problems. This new
model is simple in form and could be applied to analyze other properties of
transportation networks.
