A single server queue with compulsory vacation has been considered. In addition the admission to queue is based on a Bernoulli process and also the server give two phase of essential services and an optional service. For this model the probability generating functions of number of customers in the queue for different server states are obtained using supplementary variable technique. Some performance measures are calculated. Particular models are deduced and some numerical examples are presented.
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Kalyanaraman et al. (2017) studied this question.
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