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

Michael J. Smith; David P. Watling

doi:10.1016/j.trb.2015.12.015

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

Michael J. Smith, David P. Watling^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	132-141
Number of pages	10
Journal	Transportation Research Part B: Methodological
Volume	85
DOIs	https://doi.org/10.1016/j.trb.2015.12.015
Publication status	Published - 1 Mar 2016

Keywords

Dynamical systems
Lyapunov function
Path-swapping
Stability
Stochastic user equilibrium

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10.1016/j.trb.2015.12.015

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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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AU - Smith, Michael J.

AU - Watling, David P.

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N2 - 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.

AB - 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.

KW - Dynamical systems

KW - Lyapunov function

KW - Path-swapping

KW - Stability

KW - Stochastic user equilibrium

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DO - 10.1016/j.trb.2015.12.015

M3 - Article

AN - SCOPUS:84958959178

SN - 0191-2615

VL - 85

SP - 132

EP - 141

JO - Transportation Research Part B: Methodological

JF - Transportation Research Part B: Methodological

ER -

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

Abstract

Keywords

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