Existence Condition for the Diffusion Approximations of Multiclass Priority Queueing Networks

Authors:
Hong Chen;Heng Qing Ye
Affiliations:
Faculty of Commerce and Business Administration, University of British Columbia, Vancouver, Canada;Department of Decision Sciences, Faculty of Business Administration, National University of Singapore, Singapore
Venue:
Queueing Systems: Theory and Applications
Year:
2001

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Abstract

In this paper, we extend the work of Chen and Zhang [12] 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.