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An M/G/1 queue with optional deterministic server vacations. (English) Zbl 0997.60509
Summary: We investigate the steady state behaviour of a single server vacation queue with Poisson arrivals and arbitrary (general) service times. At the completion of each service, the server may take a vacation of a fixed (constant) duration with probability $$p$$ or may continue to be available in the system for next service with probability $$1-p$$. The supplementary variable technique is employed to find explicitly the probability generating function of the number in the system and the mean number in the system. Some particular cases of interest are discussed and some known results are derived as special cases.

##### MSC:
 60K25 Queueing theory (aspects of probability theory) 90B22 Queues and service in operations research