The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 5, Number 1 (1995), 49-77.
On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models
It is now known that the usual traffic condition (the nominal load being less than 1 at each station) is not sufficient for stability for a multiclass open queueing network. Although there has been some progress in establishing the stability conditions for a multiclass network, there is no unified approach to this problem. In this paper, we prove that a queueing network is positive Harris recurrent if the corresponding fluid limit model eventually reaches zero and stays there regardless of the initial system configuration. As an application of the result, we prove that single class networks, multiclass feedforward networks and first-buffer-first-served preemptive resume discipline in a reentrant line are positive Harris recurrent under the usual traffic condition.
Ann. Appl. Probab., Volume 5, Number 1 (1995), 49-77.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 90B22: Queues and service [See also 60K25, 68M20] 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) [See also 90Bxx] 90B35: Scheduling theory, deterministic [See also 68M20]
Dai, J. G. On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models. Ann. Appl. Probab. 5 (1995), no. 1, 49--77. doi:10.1214/aoap/1177004828. https://projecteuclid.org/euclid.aoap/1177004828