On Positive Harris Recurrence of Multiclass Queueing Networks: a Uniied Approach via Fluid Limit Models

It is now known that the usual traac condition (the nominal load being less than one at each station) is not suucient 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 uniied approach to this problem. In this paper, we prove that a queueing network is positive Harris recurrent if the corresponding uid limit model eventually reaches zero and stays there regardless of the initial system connguration. As an application of the result, we prove that single class networks, multiclass feedforward networks and rst-buuer-rst-served preemptive resume discipline in a re-entrant line are positive Harris recurrent under the usual traac condition.