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Two bulk queueing models with vacation periods. (English) Zbl 0634.60091
Summary: This paper discusses two queueing models with server’s vacation in which arrivals occur in batches of variable size and service occurs in batches of maximum capacity. On completion of a service if the server finds none waiting for service it leaves the system immediately and goes for a vacation of random duration.
In Model I, on termination of the vacation, it returns to the system and begins to serve units, if any, that have arrived during the vacation. If no units have arrived, the server waits for a batch to arrive when an ordinary busy period is initiated.
In Model II, if the server finds the system empty at the end of a vacation another independent vacation will start immediately. The server resumes service at the end of the cumulative period of a random number of successive vacations called the vacation period.
Probability generating functions of queue size at epochs of departure and vacation termination for both the models have been obtained using the imbedded Markov chain technique. Corresponding results have been derived explicitly when service time has a phase-type distribution.
60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems