Lyapunov method for the stability of fluid networks

Hengqing Ye, Hong Chen

Research output: Journal article publicationJournal articleAcademic researchpeer-review

9 Citations (Scopus)

Abstract

One of the primary tools in establishing the stability of a fluid network is to construct a Lyapunov function. In this paper, we establish the sufficiency in the use of a Lyapunov function. Specifically, we show that a necessary and sufficient condition for the stability of a generic fluid network is the existence of a Lyapunov function for its fluid level process. Then by applying this result to various specific fluid networks, including a fluid network under all work-conserving service disciplines, a fluid network under a priority service discipline, and a fluid network under a first-in-first-out service discipline, we establish the existence of a Lyapunov function for their fluid level processes is a necessary and sufficient condition for their stabilities. The result is also applied to various fluid limit models and a linear Skorohod problem.
Original languageEnglish
Pages (from-to)125-136
Number of pages12
JournalOperations Research Letters
Volume28
Issue number3
DOIs
Publication statusPublished - 1 Jan 2001
Externally publishedYes

Keywords

  • Fluid network
  • Linear Skorohod problem
  • Lyapunov method
  • Queueing network
  • Stability

ASJC Scopus subject areas

  • Software
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics

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