Stability of a Three-Station Fluid Network

Abstract

This paper studies the stability of a three-station fluid network. We prove that the global stability region of our three-station network is not monotone in the service times and so, we may move a service time vector out of the global stability region by reducing the service time for a class. We introduce the monotone global stability region and show that a linear program (LP) related to a piecewise linear Lyapunov function characterizes this largest monotone subset of the global stability region for our three-station network. The linear program proposed by Bertsimas, Gamarnik and Tsitsiklis [1] does not characterize either the global stability region or even the monotone global stability region of our three-station network. We also show that the global stability region of our three-station network is not the intersection of its stability regions under the static buffer priority disciplines and that the LP related to the linear Lyapunov function proposed by Chen and Zhang [11] does not..