Lyapunov method for the stability of fluid networks

Authors:
Heng Qing Ye;Hong Chen
Affiliations:
Faculty of Business Administration, National University of Singapore, Singapore;Faculty of Commerce and Business Administration, University of British Columbia, 2053 Main Mall Vancouver, BC, Canada V6T 1Z2
Venue:
Operations Research Letters
Year:
2001

Citing 7
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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.