Long term behavior of dynamic equilibria in fluid queuing networks

Roberto Cominetti, José Correa, Neil Olver

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

21 Scopus citations

Abstract

A fluid queuing network constitutes one of the simplest models in which to study flow dynamics over a network. In this model we have a single source-sink pair and each link has a per-time-unit capacity and a transit time. A dynamic equilibrium (or equilibrium flow over time) is a flow pattern over time such that no flow particle has incentives to unilaterally change its path. Although the model has been around for almost fifty years, only recently results regarding existence and characterization of equilibria have been obtained. In particular the long term behavior remains poorly understood. Our main result in this paper is to show that, under a natural (and obviously necessary) condition on the queuing capacity, a dynamic equilibrium reaches a steady state (after which queue lengths remain constant) in finite time. Previously, it was not even known that queue lengths would remain bounded. The proof is based on the analysis of a rather non-obvious potential function that turns out to be monotone along the evolution of the equilibrium. Furthermore, we show that the steady state is characterized as an optimal solution of a certain linear program. When this program has a unique solution, which occurs generically, the long term behavior is completely predictable. On the contrary, if the linear program has multiple solutions the steady state is more difficult to identify as it depends on the whole temporal evolution of the equilibrium.

Original languageEnglish
Title of host publicationInteger Programming and Combinatorial Optimization - 19th International Conference, IPCO 2017, Proceedings
EditorsFriedrich Eisenbrand, Jochen Koenemann
PublisherSpringer Verlag
Pages161-172
Number of pages12
ISBN (Print)9783319592497
DOIs
StatePublished - 2017
Event19th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2017 - Waterloo, Canada
Duration: 26 Jun 201728 Jun 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10328 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference19th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2017
Country/TerritoryCanada
CityWaterloo
Period26/06/1728/06/17

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