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Brownian approximations of multiclass open-queueing networks. (English) Zbl 1163.90390

Summary: We study a multiclass open-queueing network with a set of single-server stations that operate under a combination of FIFO (first-in-first out) and priority service disciplines, and are subject to random breakdowns. Assuming that the primitive processes–in particular, external arrivals, service requirements, service capacities (up and down times), and the routing mechanism–follow two-moment approximations (based on functional central limit theorems), we develop a semi-martingale reflected Brownian motion (SRBM) approximation for the performance processes such as workload, queue lengths, and sojourn times. We illustrate through numerical examples in comparison against simulation that the SRBM approximation, while not always supported by a limit theorem, exhibits good accuracy in most cases. Through analyzing special networks, we also discuss the existence of the SRBM approximation in relation to the stability and the heavy traffic limits of the networks.

MSC:

90B15 Stochastic network models in operations research
90B18 Communication networks in operations research
90B22 Queues and service in operations research
90B35 Deterministic scheduling theory in operations research
90B36 Stochastic scheduling theory in operations research
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