×

On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models. (English) Zbl 0822.60083

Summary: It is now known that the usual traffic condition (the nominal load being less than 1 at each station) is not sufficient for stability for a multiclass open queueing network. Although there has been some progress in establishing the stability conditions for a multiclass network, there is no unified approach to this problem. We prove that a queueing network is positive Harris recurrent if the corresponding fluid limit model eventually reaches zero and stays there regardless of the initial system configuration. As an application of the results, we prove that single class networks, multiclass feedforward networks and first-buffer-first- served preemptive resume discipline in a reentrant line are positive Harris recurrent under the usual traffic condition.

MSC:

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
90B35 Deterministic scheduling theory in operations research
PDFBibTeX XMLCite
Full Text: DOI