The regenerative stability analysis of some vacation models

Stepan Rogozin
In this research we consider two different vacation model. First, we study the stability of a multi-server vacation model with self-sustained servers and some general distribution of service time. Also we consider a single-server vacation model, when there are consecutive periods of attachment (glue), service and vacation. We present the stability conditions of these systems which have been obtained in previous works by various methods. The purpose of this note is to show how the regenerative methodology allows to deduce these stability conditions of these systems by a unified way.