The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 6, Number 3 (1996), 751-757.
A fluid limit model criterion for instability of multiclass queueing networks
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.
Ann. Appl. Probab., Volume 6, Number 3 (1996), 751-757.
First available in Project Euclid: 18 October 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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