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August 1996 A fluid limit model criterion for instability of multiclass queueing networks
J. G. Dai
Ann. Appl. Probab. 6(3): 751-757 (August 1996). DOI: 10.1214/aoap/1034968225


This paper studies the instability of multiclass queueing networks. We prove that if a fluid limit model of the queueing network is weakly unstable, then the queueing network is unstable in the sense that the total number of customers in the queueing network diverges to infinity with probability 1 as time $t \to \infty$. Our result provides a converse to a recent result of Dai which states that a queueing network is positive Harris recurrent if a corresponding fluid limit model is stable. Examples are provided to illustrate the usage of the result.


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J. G. Dai. "A fluid limit model criterion for instability of multiclass queueing networks." Ann. Appl. Probab. 6 (3) 751 - 757, August 1996.


Published: August 1996
First available in Project Euclid: 18 October 2002

zbMATH: 0860.60075
MathSciNet: MR1410113
Digital Object Identifier: 10.1214/aoap/1034968225

Primary: 60K25 , 90B22
Secondary: 60K20 , 90B35

Keywords: fluid approximation , fluid model , Harris positive recurrent , instability , Multiclass queueing networks , transience

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.6 • No. 3 • August 1996
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