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.
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Chen, H., Zhang, H. A sufficient condition and a necessary condition for the diffusion approximations of multiclass queueing networks under priority service disciplines. Queueing Systems 34, 237–268 (2000). https://doi.org/10.1023/A:1019113204634
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DOI: https://doi.org/10.1023/A:1019113204634