A route-swapping dynamical system and Lyapunov function for stochastic user equilibrium |
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| Institution: | 1. Department of Mathematics, University of York, York, United Kingdom\n;2. Institute for Transport Studies, University of Leeds, Leeds, United Kingdom\n;1. University of Salerno, Dept of Civil Engineering, via Giovanni Paolo II, 132, 84084 Fisciano, SA, Italy;2. University of Leeds, UK;1. School of Computer Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia;2. Research Centre for Integrated Transport Innovation, School of Civil and Environmental Engineering, University of New South Wales, Sydney, NSW 2052, Australia;3. School of Engineering, University of Glasgow, Glasgow G12 8QQ, United Kingdom;4. Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong |
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| Abstract: | 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. |
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