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 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 previously by the author (2001). 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.
Non-convergence in dynamic assignment networks?
2001-01-01
250279 byte
Aufsatz (Konferenz)
Elektronische Ressource
Englisch
Non-Convergence in Dynamic Assignment Networks?
British Library Conference Proceedings | 2001
|Convergence control in congested assignment
British Library Conference Proceedings | 1994
|Dynamic Traffic Assignment in Congested Networks
British Library Conference Proceedings | 1996
|Factors affecting convergence and stability in simulation-based dynamic traffic assignment
British Library Conference Proceedings | 2009
|