Stability conditions for queueing systems with regenerative flow of interruptions

This paper is focused on the multichannel queueing system with heterogeneous servers, regenerative input flow, and a regenerative process of interruptions. Two service disciplines are studied: preemptive-repeat-different service discipline and preemptive resume service discipline. We consider discrete as well as continuous-time cases. We introduce an auxiliary service flow, which does not depend on the input flow, and construct the common points of regeneration for these two flows. Using such a synchronization method, we establish necessary and sufficient conditions for stability of the system under some additional assumptions. Additionally, under weaker assumptions, we also find the conditions needed for the queue length process to be stochastically bounded.