A unified regenerative stability analysis of some non-conventional queueing models

Stepan Rogozin, Evsey Morozov
In this research we demonstrate how the regenerative methodology allows to deduce stability conditions in some particular queueing models by a unified way. We consider the retrial system with classical retrial discipline in which the retrial times becomes exponential when the orbit size exceeds a high threshold. Moreover we study the buffered system with state-dependent arrival rate, and finally, a buffered batch-arrival and batch-service system with random serving capacity and batch-size-dependent service. We present short transparent regenerative proofs of the stability conditions of these systems which have been obtained in previous works by various methods.