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On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models (1995)
| Venue: | Annals of Applied Probability |
| Citations: | 353 - 28 self |
BibTeX
@ARTICLE{Dai95onpositive,
author = {J. G. Dai},
title = {On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models},
journal = {Annals of Applied Probability},
year = {1995},
volume = {5},
pages = {49--77}
}
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Abstract
It is now known that the usual traffic condition (the nominal load being less than one 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 re-entrant line are positive Harris recurrent under the usual traffic condition. AMS 1991 subject classification: Primary 60K25, 90B22; Secondary 60K20, 90B35. Key words and phrases: multiclass queueing networks, Harris positive recurrent, stability, fluid approximation Running title: Stability of mu...
Keyphrases
positive harris recurrence multiclass queueing network positive harris recurrent usual traffic condition queueing network multiclass feedforward network fluid approximation subject classification single class network re-entrant line first-buffer-first-served preemptive resume discipline multiclass network key word nominal load stability condition initial system configuration corresponding fluid limit model unified approach harris positive recurrent
