The Annals of Applied Probability

A fluid limit model criterion for instability of multiclass queueing networks

J. G. Dai

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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

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1034968225

Digital Object Identifier
doi:10.1214/aoap/1034968225

Mathematical Reviews number (MathSciNet)
MR1410113

Zentralblatt MATH identifier
0860.60075

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22] 90B22: Queues and service [See also 60K25, 68M20]
Secondary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) [See also 90Bxx] 90B35: Scheduling theory, deterministic [See also 68M20]

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

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


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References

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