Stability Region of a Three-Station Fluid Network

J. G. Dai, J. J. Hasenbein and J. H. Vande Vate
School of Industrial & Systems Engineering
Georgia Institute of Technology
Atlanta, GA 30332

This paper explores the global stability region of a three-station fluid network. We prove that
  1. A piecewise linear Lyapunov function characterizes the monotone global stability region of the three station network;
  2. The global stability region of fluid networks with more than two stations may not be monotone in terms of the service time vector;
  3. The linear program proposed by Bertsimas, Gamarnik and Tsitsiklis (1995) does not characterize the (monotone) global stability region of our three-station network;
  4. The global stability region of our three-station network is not the intersection of its stability regions under the static buffer priority disciplines.
Key words : stability, fluid models, multiclass queueing networks, piecewise linear Lyapunov functions, monotone global stability.