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

•Proposal of a new, smooth, path-swapping dynamical system based on the logit random utility model.•Proof that stationary points of this system are SUE solutions.•Lyapunov function and stability results for this dynamical system, establishing convergence to SUE.•Generalisation to SUE of the result in Smith (1984) for the case of DUE.

An analysis of the continuous-time dynamics of a route-swap adjustment process is presented, which is a natural adaptation of that 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.