Publication | Open Access
On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models
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1995
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Mathematical ProgrammingEngineeringNetwork AnalysisEducationPositive Harris RecurrentUsual Traffic ConditionQueueing TheoryStabilityOperations ResearchStochastic NetworkNetwork CalculusSystems EngineeringDiscrete MathematicsCombinatorial OptimizationStochastic SystemProbability TheoryComputer ScienceMulticlass NetworkQueueing SystemsMulticlass Queueing NetworksNetwork Traffic ControlPositive Harris RecurrenceFluid QueueCongestion Control
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. In this paper, 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 result, 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.