Geo/G/1 discrete-time queue with multiple server vacations and Min(N, V)-policy

In this paper, we consider a discrete-time Geo/G/1 queueing system in which the server takes multiple vacations and the system adopts min(N, V)-policy. By using the total probability decomposition technique and renewal process theory, we study the transient and steady distributions of the queue length and obtain both the expression of the z-transformation of the transient distribution and the recursion expression of the steady distribution at arbitrary time epoch n+. Furthermore, we obtain the steady distribution of the queue length at time epoch n, n-, and outside observer's time epoch, respectively. Especially, some corresponding results under special cases are directly given by our results obtained in this paper. Finally, by numerical examples we illustrate the important application value of the expression of the steady state queue-length distribution for calculating conveniently in the system capacity design. ©, 2015, Systems Engineering Society of China. All right reserved.