A RepairableM/G/l Retrial Queue with Bernoulli Vacation and Two-Phase Service

A repairable M/G/1 retrial queue with general retrial times, Bernoulli vacation, setup times and two-phase service is investigated in this paper. Customers are allowed to balk and renege at particular times. We assume that the customers who find the server busy or down are queued in the orbit in accordance with a first-come-first-served (FCFS) discipline. All customers demand the first "essential" service, whereas only some of them demand the second multiple “optional” service. We assume that the retrial time, the service time, the repair time, the vacation time and the setup time of the server are all arbitrarily distributed. By using the supplementary variables method, we obtain the steady-state solutions for both queueing and reliability measures of interest.