Vacation Queueing Models with Server Breakdowns

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An M[x]/G/1 retrial system with two phases of heterogeneous service, where the server is subjected to breakdown at each phase of service and operates under Bernoulli vacation policy is considered. In the proposed model, any arriving batch finding the server busy, breakdown or on vacation enters an orbit. Otherwise one customer from the arriving batch enters a service immediately while the rest join the orbit. After the completion of two phases of service, the server either goes for a vacation with probability p or may continue to serve the next customer with probability 1- p. At a vacation completion epoch, the server waits for the customers, if any in the orbit, or for new customers to arrive. While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. We have constructed the mathematical model and the steady-state probability distribution of number of customers in the system when it is idle, busy, on vacation and under repair are derived. Finally, some system performance measures and the effect of various parameters measures are discussed.