The Annals of Applied Probability

A fluid limit model criterion for instability of multiclass queueing networks

J. G. Dai

Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 6, Number 3 (1996), 751-757.

Dates
First available in Project Euclid: 18 October 2002

https://projecteuclid.org/euclid.aoap/1034968225

Digital Object Identifier
doi:10.1214/aoap/1034968225

Mathematical Reviews number (MathSciNet)
MR1410113

Zentralblatt MATH identifier
0860.60075

Citation

Dai, J. G. A fluid limit model criterion for instability of multiclass queueing networks. Ann. Appl. Probab. 6 (1996), no. 3, 751--757. doi:10.1214/aoap/1034968225. https://projecteuclid.org/euclid.aoap/1034968225

References

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