Abstract
In the present study, we investigate a bulk arrival queue with Bernoulli feedback, service interruption and having the facility of multi-phases essential/optional services. If units present in the system are accumulated to $$ N, $$ the server is switched on so that it may start service with probability $$ p, $$ or it remains switched off with probability $$ 1 - p $$ . There is a provision to avail the vacation schedule by the server as soon as the system becomes empty. After returning from vacation if the system size is more than $$ N, $$ the server immediately starts serving the units waiting in the queue. During one of the stages of the service, the server may become inoperative due to some fault; in such a scenario it will undergo for repair with a probable situation leading to delayed repair due to unforeseen reasons. Supplementary variable technique (SVT) is employed for queueing analysis and to derive various performance measures characterizing the delay and service interruption. Some reliability indices and cost function are established for the concerned model. SVT is exhibited by taking numerical illustration.
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