Unreliable M/G/1 retrial queue with geometric loss and random reserved time

We consider an M/G/1 retrial queue with breakdowns, repairs and geometric loss. The customer whose service is interrupted can stay at the server waiting for repair or enter into service orbit. After repair, the server is required to search for the customer in service orbit. We concentrate on the main aspects of the study of retrial queues: stability condition, joint generating function of the number of customers in the orbit and the state of the server, waiting times and busy period. We also give the first three probabilities of the number of customers served during the busy period.