A sufficient condition and a necessary condition for the diffusion approximations of multiclass queueing networks under priority service disciplines

Authors:
Hong Chen;Hanqin Zhang
Affiliations:
Faculty of Commerce and Business Administration, University of British Columbia, Vancouver, BC, Canada, and Department of Industrial Engineering and Engineering Management, Hong Kong University ...;Institute of Applied Mathematics, Academia Sinica, Beijing, China
Venue:
Queueing Systems: Theory and Applications
Year:
1999

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Abstract

We establish a sufficient condition for the existence of the (conventional) diffusion approximation for multiclass queueing networks under priority service disciplines. The sufficient condition relates to a sufficient condition for the weak stability of the fluid networks that correspond to the queueing networks under consideration. In addition, we establish a necessary condition for the network to have a continuous diffusion limit; the necessary condition is to require a reflection matrix (of dimension equal to the number of stations) to be completely-S. When applied to some examples, including generalized Jackson networks, single station multiclass queues, first-buffer-first-served re-entrant lines, a two-station Dai–Wang network and a three-station Dumas network, the sufficient condition coincides with the necessary condition.