Abstract
In this paper, we analyze a new discrete-time GeomX/G/1 queue model with multiple vacations. We obtain the Probability Generating Function (P.G.F.) of the queue length by using the method of an embedded Markov chain, and the mean of the queue length by using L'Hospital rule. We also derive the P.G.F. of the busy period and the probabilities for the system being in a busy state or in a vacation state. Moreover, we derive the P.G.F. of the waiting time based on the independence between the arrival process and the waiting time. Finally, we show some numerical results to compare the means of the queue length and the waiting time in special cases.
