Article ID: | iaor20013042 |
Country: | Netherlands |
Volume: | 33 |
Issue: | 4 |
Start Page Number: | 293 |
End Page Number: | 325 |
Publication Date: | Jan 1999 |
Journal: | Queueing Systems |
Authors: | Dai J.G., Hasenbein J.J., Vate J.H. Vande |
Keywords: | networks: path, programming: linear |
This paper studies the stability of a three-station fluid network. We show that, unlike the two-station networks in Dai and Vande Vate, the global stability region of our three-station network is not the intersection of its stability regions under static buffer priority disciplines. Thus, the ‘worst’ or extremal disciplines are not static buffer priority disciples. We also 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. We also show that the LP proposed by Bertsimas