Abstract
We present a new discrete-time Geom/G/1 queueing model with multiple vacations. We obtain the Probability Generating Function (PGF) of the queue length by using the method of an embedded Markov chain, and give the mean of the queue length. Then we study the PGF of the waiting time based on the independence of the arrival process and the waiting time. And we derive the PGF of the busy period, and the probabilities for the system being in a busy state or in a vacation state. Moreover, we formulate a cost model in order to determine the optimal expected parameter of the system. Finally, we show some numerical results to compare the means of the queue length and the waiting time in special cases.
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