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

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

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Article ID: iaor20013056
Country: Netherlands
Volume: 34
Issue: 1/4
Start Page Number: 237
End Page Number: 268
Publication Date: Jan 2000
Journal: Queueing Systems
Authors: ,
Keywords: networks: path
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 wear 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.

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