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

Michael J. Smith, David P. Watling*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)132-141
Number of pages10
JournalTransportation Research Part B: Methodological
Publication statusPublished - 1 Mar 2016


  • Dynamical systems
  • Lyapunov function
  • Path-swapping
  • Stability
  • Stochastic user equilibrium

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