Non-convergence in dynamic assignment networks?

R Mounce*

*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

In the steady-state assignment model where each link has a non-decreasing cost flow curve we have monotonicity not just at the link level but also at the route level. In our dynamical system we assume that the users swap to cheaper routes. Monotonicity of the route cost function is enough to guarantee that the given function V, detailed later, is in fact a Lyapunov function and hence that the system converges to equilibrium.

In the dynamic assignment model, the route cost function is not a monotone function of route flow, as was shown in [1]. Therefore convergence does not immediately follow, as it does in the steady-state case. This paper essentially shows that the dynamic counterpart of the steady-state Lyapunov function is in fact not a Lyapunov function. This does not at all imply non-convergence of the dynamical system simulating a swap to cheaper routes, but it does raise the question of convergence. Obviously, if another function could be found that satisfies the criteria of being a Lyapunov function this would be sufficient for convergence.

Original languageEnglish
Title of host publication2001 IEEE Intelligent Transportation Systems - Proceedings
Place of PublicationNew York
PublisherIEEE Press
Pages569-572
Number of pages4
ISBN (Print)0-7803-7194-1
DOIs
Publication statusPublished - 2001
EventIEEE Intelligent Transportation Systems Conference (ITSC'01) - Oakland, Canada
Duration: 25 Aug 200129 Aug 2001

Conference

ConferenceIEEE Intelligent Transportation Systems Conference (ITSC'01)
CountryCanada
Period25/08/0129/08/01

Cite this

Mounce, R. (2001). Non-convergence in dynamic assignment networks? In 2001 IEEE Intelligent Transportation Systems - Proceedings (pp. 569-572). IEEE Press. https://doi.org/10.1109/ITSC.2001.948722