ANALYSIS BASED ON DISCRETE TIME BULK INPUT QUEUE WITH MULTIPLE WORKING VACATIONS
基于多重工作休假的成批到达离散时间排队的性能分析

This paper is concerned with a bulk input Geom$^{X]}$/Geom/1 queue with multiple working vacations. Firstly a two-dimensional Markov chain model is established, and with the matrix analysis method, highly complicated PGF of thestationary queue size is derived, from which the stochastic decompositionresult for the PGF of the stationary queue size is obtained, which indicates the evident relationship with that of the classical Geom$^{X]}$/Geom/1 queue without vacation. The biparameter addition theorems for the conditional negative binomial distribution is established, with which the upper bound and the lower bound of the stationary waiting time is given in the moment generating function order. Furthermore, the mean queue size, the upper bound and the lower bound of the mean waiting time are obtained. Finally, some numerical examples are presented.