Existence condition for the diffusion approximations of multiclass priority queueing networks

In this paper, we extend the work of Chen and Zhang and establish a new sufficient condition for the existence of the (conventional) diffusion approximation for multiclass queueing networks under priority service disciplines. This sufficient condition relates to the weak stability of the fluid netwo...

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Bibliographic Details
Published inQueueing systems Vol. 38; no. 4; pp. 435 - 470
Main Authors Chen, Hong, Ye, Heng Qing
Format Journal Article
LanguageEnglish
Published Dordrecht Kluwer 01.01.2001
Springer Nature B.V
Subjects
Applied sciences
Approximation
Brownian motion
Central limit theorem
Communications networks
Employment
Exact sciences and technology
Mathematical models
Operational research and scientific management
Operational research. Management science
Queuing
Queuing theory. Traffic theory
Random variables
Servers
Studies
Brownian motion
Existence condition
Sufficient condition
Stability
Priority
Heavy traffic
Fluid model
Buffer system
Queueing network
Semimartingale
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Summary:In this paper, we extend the work of Chen and Zhang and establish a new sufficient condition for the existence of the (conventional) diffusion approximation for multiclass queueing networks under priority service disciplines. This sufficient condition relates to the weak stability of the fluid networks and the stability of the high priority classes of the fluid networks that correspond to the queueing networks under consideration. Using this sufficient condition, we prove the existence of the diffusion approximation for the last-buffer-first-served reentrant lines. We also study a three-station network example, and observe that the diffusion approximation may not exist, even if the "proposed" limiting semimartingale reflected Brownian motion (SRBM) exists. [PUBLICATION ABSTRACT]
ISSN:0257-0130
1572-9443
DOI:10.1023/A:1010952012771