The analysis of discrete time Geom/Geom/1 queue with single working vacation and multiple vacations (Geom/Geom/1/SWV+MV)

¹ School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, P.R. China
² School of Science, Nanjing University of Science and Technology, Nanjing, P.R. China

^* Corresponding author: yeqingzero@gmail.com

Received: 19 September 2017
Accepted: 13 October 2017

Abstract

In this article, we consider a discrete-time Geom/Geom/1 queue with two phase vacation policy that comprises single working vacation and multiple vacations, denoted by Geom/Geom/1/SWV+MV. For this model, we first derive the explicit expression for the stationary system size by the matrix-geometric solution method. Next, we obtain the stochastic decomposition structures of system size and the sojourn time of an arbitrary customer in steady state. Moreover, the regular busy period and busy cycle are analyzed by limiting theorem of alternative renewal process. Besides, some special cases are presented and the relationship between the Geom/Geom/1/SWV+MV queue and its continuous time counterpart is investigated. Finally, we perform several experiments to illustrate the effect of model parameters on some performance measures.