Retrial queues with starting failure and service interruption

The purpose of this study is to investigate an M/M/R retrial queue with geometric loss and Bernoulli feedback, in which all servers are subject to breakdowns and starting failures. After the completion of service, unsatisfied customers can join the retrial group with probability p or depart from the system with probability 1 − p. All servers may breakdown at any time, and the failed server undergoes repair immediately when a breakdown occurs. An arriving customer finding all servers unavailable (busy or down), will either join the orbit with probability b or leave the system with probability 1 − b. For such a queuing model, the authors apply the matrix-geometric method to compute the stationary probabilities and develop system performance measures in the steady state. Moreover, they construct a cost model and formulate an optimisation problem of minimising the expected cost per unit time. Finally, numerical results are given for illustrative purposes.