Stability of a Three-Station Fluid Network

Stability of a Three-Station Fluid Network (1999)

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by J. G. Dai , J. J. Hasenbein , J. H. Vande Vate

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@MISC{Dai99stabilityof,
    author = {J. G. Dai and J. J. Hasenbein and J. H. Vande Vate},
    title = {Stability of a Three-Station Fluid Network},
    year = {1999}
}

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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.

Citations

190	On positive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models,” Ann - Dai - 1995
94	Stability of queueing networks and scheduling policies - Kumar, Meyn - 1995
94	Distributed scheduling based on due dates and buffer priorities - Lu, Kumar - 1991
90	Dynamic instabilities and stabilization methods in distributed real-time scheduling of manufacturing systems - Kumar, Seidman - 1990
85	Ergodicity of stochastic processes describing the operations of open queueing networks. Problemy Pederachi Informatsii 28 - Rybko, Stolyar - 1992
74	Instability of FIFO queueing networks - Bramson - 1994
69	Stability and convergence of moments for multiclass queueing networks via fluid limit models - Dai, Meyn - 1995
59	Fluid approximations and stability of multiclass queueing networks I: Work-conserving disciplines - Chen - 1995
44	Duality and linear programs for stability and performance analysis of queueing networks and scheduling policies - Kumar, Meyn - 1996
43	Convergence to equilibria for fluid models of FIFO queueing networks - Bramson - 1996
43	Transience of multiclass queueing networks and their fluid models - Meyn - 1995
38	First come first serve can be unstable - Seidman - 1994
38	On Stability of Multiclass Queueing Networks: A Relaxed Sufficient Condition via Fluid Processes - Stolyar - 1995
34	Stability and instability of fluid models for reentrant lines - Dai, Weiss - 1996
33	Piecewise linear test functions for stability and instability of queueing networks - Down, Meyn - 1997
30	Stability of multiclass queueing networks under FIFO service discipline - Chen, Zhang - 1997
29	A fluid-limit model criterion for instability of multiclass queueing networks - Dai - 1996
27	Lyapounov functions for semimartingale reflecting Brownian motions - Dupuis, Williams - 1994
24	Instability of FIFO queueing networks with quick service times. The Annals of Applied Probability 4 - Bramson - 1993
18	Convergence to equilibria for fluid models of head-of-the-line proportional processor sharing queueing networks. Queueing Systems, Theory and Applications - Bramson - 1996
18	A multiclass network with non-linear, non-convex, non-monotonic stability conditions. Queueing Systems: Theory and Applications - Dumas - 1997
17	Stability of two families of queueing networks and a discussion of fluid limits. Queueing Systems: Theory and Applications - Bramson - 1998
17	Distributed scheduling based on due dates and bu er prioritization, tech - Lu, Kumar - 1990
16	Stability conditions for multiclass fluid queueing networks - Bertsimas, Gamarnik, et al. - 1996
15	Stability of open multiclass queueing networks via fluid models - Dai - 1995
14	Necessary conditions for global stability of multiclass queueing networks - Hasenbein - 1997
12	Ergodicity of conservative communication networks. Rapport de recherche 1772 - Botvich, Zamyatin - 1992
11	A stable queueing network with unstable fluid model - Bramson - 1999
11	Virtual stations and the capacity of two-station queueing networks - Dai, VandeVate - 1996
9	Global Stability of Two-Station Queueing Networks - Dai, Vate - 1996
8	The FCFS Service Discipline: Stable Network Topologies, Bounds on Traffic Burstiness and Delay, and Control by Regulators - Winograd, Kumar - 1996
7	Stability of multiclass Jackson-type networks - Foss, Rybko - 1995
7	Convergence to equilibria for models of FIFO queueing networks. Queueing Systems: Theory and Applications - Bramson - 1996
7	Convergence to equilibria for models of head-of-the-line proportional processor sharing queueing networks. Queueing Systems: Theory and Applications - Bramson - 1997
7	Stability and instability of models for re-entrant lines - Dai, Weiss - 1996
7	Vande Vate - Roth, H - 1990
5	On the stability of multiclass queueing networks - Stolyar - 1995
5	The stability of two-station multi-type networks - Dai, VandeVate - 2000
5	First come, served' can be unstable - Seidman - 1994
4	The stability of two-station fluid networks - Dai, VandeVate - 1997
4	Stability conditions for multiclass queueing networks - Bertsimas, Gamarnik, et al. - 1996
2	A regulator stabilization technique: Kumar-Seidman revisited - Jr, C - 1994
2	A stable queueing network with unstable network. Annals of Applied Probability - Bramson - 1998