Abstract
A variant of an M/ G/1 queuing model with finite waiting room is studied in this paper. In this system, every busy period of the server at the queue is followed by the execution of additional tasks. The time spent by the server to perform these tasks is called a vacation time away from the queue. The server will begin a vacation from the queue if either the queue has been emptied or M customers have been served during the visit. The embedded Markov chain approach is used to obtain the steady state queue length distribution. The Laplace-Stieltjes transforms of the busy period and cycle time distributions are given. Using a combination of the supplementary variables and sample biasing techniques, the waiting time distribution, blocking probability and general queue length distribution are derived. Finally the results for the case of infinite waiting places are provided.
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