Stability of a dynamic model for traffic networks

R Mounce*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The dynamic assignment model assumes flow moves towards cheaper routes at each time at a rate proportional to the product of the flow along the more expensive route and the cost difference. Therefore it is important for the cost function to be monotone so that convergence to equilibrium will occur. Conditions on the bottleneck output function are given for the bottleneck delay function to be monotone, which will imply monotonicity of the route coat function in the single bottleneck per route case.

It is shown that for reasonable bottleneck output functions, we have monotonicity of the product of link cost with a decaying exponential. This decay-monotonicity transfers to the route cost in certain given circumstances. This will in turn imply convergence of the dynamical system by applying Lyapunov's theorem using the appropriate Lyapunov function. It is then important to note that monotonicity of the route coat function implies decay-monotonicity of the route cost function and hence the convergence result is valid for the single bottleneck per route case with monotone link cost functions.

Original languageEnglish
Title of host publicationIEEE 5TH INTERNATIONAL CONFERENCE ON INTELLIGENT TRANSPORTATION SYSTEMS, PROCEEDINGS
EditorsRL Cheu, D Srinivasan, DH Lee
Place of PublicationNew York
PublisherIEEE Press
Pages795-800
Number of pages6
ISBN (Print)0-7803-7389-8
DOIs
Publication statusPublished - 2002
EventIEEE 5th International Conference on Intelligent Transportation Systems - SINGAPORE, Singapore
Duration: 3 Sep 20026 Sep 2002

Conference

ConferenceIEEE 5th International Conference on Intelligent Transportation Systems
CountrySingapore
Period3/09/026/09/02

Keywords

  • convergence
  • cost function
  • mathematical model
  • mathematics
  • stability
  • telecommunication traffic
  • time measurement
  • traffic control
  • vehicle dynamics
  • vehicles

Cite this

Mounce, R. (2002). Stability of a dynamic model for traffic networks. In RL. Cheu, D. Srinivasan, & DH. Lee (Eds.), IEEE 5TH INTERNATIONAL CONFERENCE ON INTELLIGENT TRANSPORTATION SYSTEMS, PROCEEDINGS (pp. 795-800). IEEE Press. https://doi.org/10.1109/ITSC.2002.1041321