The Annals of Applied Probability

On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models

J. G. Dai

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 5, Number 1 (1995), 49-77.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177004828

Digital Object Identifier
doi:10.1214/aoap/1177004828

Mathematical Reviews number (MathSciNet)
MR1325041

Zentralblatt MATH identifier
0822.60083

JSTOR
links.jstor.org

Subjects
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]

Keywords
Multiclass queueing networks Harris positive recurrent stability fluid approximation

Citation

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


Export citation