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This article aims to present the steady-state analysis in finite-buffer M/G/1 queues with starting failures under a randomized control of N-policy. When the system empties, the server is turned off. If the system size reaches the threshold N, the server is turned on with probability p or turned off with probability 1 − p. The server needs a startup time before providing service. If the server is started successfully (with probability θ), customers are served immediately. When the server is started unsuccessfully, he is started again. It is assumed that the restart is always successful. Using the supplementary variable method, we obtain the stationary distribution of the number of customers in the system. We develop a number of performance measures. A cost model is constructed, and we then determine numerical values of the optimal service rate to minimize the average cost per unit time. Finally, numerical examples are provided to show the effects of system parameters on performance measures and the optimal service rate. [ABSTRACT FROM AUTHOR]

In this paper, we propose a machine repair problem with constant retrial policy, wherein if a failed machine finds the repairman busy upon arrival, it enters into an orbit. The machines in the orbit form a single waiting line, and only the one at the head of the orbit repeats its request for repair. The failure times of operating machines and the repair times of failed machines follow exponential distributions. It is assumed that retrial times are generally distributed. We used the supplementary variable technique to obtain explicit expressions for the steady-state probabilities of the number of failed machines in the orbit. We performed sensitivity analysis of the machine availability and operative efficiency with respect to system parameters and the number of machines in operation. The analysis of the busy period and the waiting time were also presented. Finally, we developed a cost model and formulated a cost minimization problem. [ABSTRACT FROM AUTHOR]

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]