Abstract
This paper considers an M/M/1 unreliable retrial queueing system with geometric loss and feedback under the threshold-based policy. After the customer is served completely, he may decide either to leave the system or to join the retrial orbit again for another service. If the server is found busy, the customer may either leave the system or join the retrial orbit. The server may be broken down at any time during the server is operating. When the server is broken down, it cannot be repaired immediately until the number of customers in the system reaches a specified threshold value. This system is modelled by a quasi-birth-and-death process, and some system performance measures are derived. The formulae for computing the rate matrix and stationary probabilities are derived by means of matrix-analytical approach. We obtain the optimal threshold value and the optimal service rate simultaneously to minimise the cost function of the system.
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