A retrial stochastic service system with balking and two-phase service

We consider an M/G/1 retrial stochastic service system with balking and two-phase service subject to the server breakdowns and delayed repairs. For an arbitrarily distributed retrial time distribution, the necessary and sufficient condition for the system stability is derived. In the steady state, the joint distribution of the server state and queue length is obtained along with some interesting and important performance measures. The stochastic decomposition property is investigated. Finally, numerical examples are provided.