Performance Analysis of GeomX /G/1 Queue with Exhaustive Service Rule and Multiple Vacations
نویسندگان
چکیده
Abstract In this paper, a new discrete-time GeomX /G/1 queue model with multiple vacations is analyzed. The Probability Generating Function (P.G.F.) of the queue length is obtained by using the method of an embedded Markov chain, and the mean of the queue length is obtained by using L’Hospital rule. Then the P.G.F. of the busy period is derived, and the probabilities for the system being in a busy state or in a vacation state are also derived. Moreover, the P.G.F. of the waiting time is derived based on the independence between the arrival process and the waiting time. Finally, some numerical results are shown to compare the means of the queue length and the waiting time in special cases.
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