An M/G/1M/G/1 retrial queue with an unreliable server and general repair times

An M/G/1M/G/1 type queueing system with an unreliable server is considered. If the server fails during the service of a customer, the customer leaves the server, joins a retrial group and in random intervals repeats the attempts to get service. We find the joint distribution of the server state, the number of customers in the queue and the number of customers in the retrial group in a steady state when both the service time and repair time have general distributions.