A hysteretic queueing system with random server capacity

We consider in this paper, an r-quorum queueing system with random server capacity under N-policy discipline (hysteretic system). We find a necessary and sufficient condition for ergodicity, the probability generating function of the steady state vector of probabilities for the embedded process and the continuous time parameter, and some system characteristics. The decomposition property is checked for both discrete and continuous time parameter processes. Special cases are considered and examples are provided.