A route-swapping dynamical system and Lyapunov function for stochastic user equilibrium

An analysis of the continuous-time dynamics of a route-swap adjustment process is presented, which is a natural adaptation of that which was presented in Smith (1984) for deterministic choice problems, for a case in which drivers are assumed to make perceptual errors in their evaluations of travel cost, according to a Random Utility Model. We show that stationary points of this system are stochastic user equilibria. A Lyapnuov function is developed for this system under the assumption of monotone, continuously differentiable and bounded cost-flow functions and a logit-based decision rule, establishing convergence and stability of trajectories of such a dynamical system with respect to a stochastic user equilibrium solution.