Abstract
In the present paper, non-Markovian queue with bulk arrival, server breakdown, and randomized vacation policy is studied. It is considered that the balking phenomenon may arise in the units while joining the system in distinct server’s states. The units who find the service unsatisfactory may rejoin the queue as feedback customer. There is a provision of essential/optional service to all arriving units joining the system. Moreover, the server may fail while providing essential or optional service. The broken-down server can be recovered with the aid of repair facility, but delay in repair may occur due to any unforeseen circumstance. The server is permitted to avail at most l vacations under randomized vacation policy. Supplementary variable technique is employed for evaluating the various performance characteristics of the system. Cost function is developed and numerical illustrations are presented for sensitivity analysis of concerned model.
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