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In this paper, we present a detailed analysis of a multi-server retrial queue with Bernoulli feedback, where the servers are subject to starting failures. Upon completion of a service, a customer would decide either to leave the system with probabilitypor to join the retrial orbit again for another service with complementary probability 1−p. We analyse this queueing system as a quasi-birth–death process. Specifically, the equilibrium condition of the system is given for the existence of the steady-state analysis. Applying the matrix-geometric method, the formulae for computing the rate matrix and stationary probabilities are obtained. We further develop the matrix-form expressions for various system performance measures. A cost model is constructed to determine the optimal number of servers, the optimal mean service rate and the optimal mean repair rate subject to the stability condition. Finally, we give a practical example to illustrate the potential applicability of this model. [ABSTRACT FROM PUBLISHER]

In this paper, we study a repairableK-out-of-(M+W) retrial system withMidentical primary components,Wstandby components and one repair facility. The time-to-failure and time-to-repair of the primary and standby components are assumed to be exponential and general distributions, respectively. The failed components are immediately for repair if the server is idle, otherwise the failed machines would enter an orbit. It is assumed that the retrial times are exponentially distributed. We present a recursive method using the supplementary variable technique and treating the supplementary variable as the remaining repair time to obtain the steady-state probabilities of down components at arbitrary epoch. Then, a unified and efficient algorithm is developed to compute the steady-state availability. The method is illustrated analytically for the exponential repair time distribution. Sensitivity analysis of the steady-state availability with respect to system parameters for a variety of repair time distributions is also investigated. [ABSTRACT FROM AUTHOR]