M[x]/G/1 Retrial Queue with Two Phases of Service, Bernoulli Vacation and Server Break Down

A repairable batch arrival retrial queuing system with two phases of service, Bernoulli vacation and random server breakdown is considered. At the arrival epoch, if the server is busy the whole batch joins the orbit, whereas if the server is free, then one of the arriving customers starts its service immediately and the rest joins the orbit. For each customer the server provides two phases of service. After completion of each service, the server may take a vacation with probability θ or may continue in the system with complimentary probability. The steady state distribution of the server state and the number of customer in the orbit/system are obtained. While the server working with any phase of service, it may break down at any instant and the service channel will fail for a short interval of time and it is repaired immediately. Numerical example is presented to illustrate the influence of the parameters on several performance characteristics.

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