基于单重工作休假的离散时间排队稳态分析

STATIONARY ANALYSIS OF THE DISCRETE TIME QUEUE BASED ON THE SINGLE WORKING VACATION

详细地分析了一个单重工作休假的离散时间Geom/G/1排队系统.首先,构造二维嵌入马尔可夫链,得到其M/G/1型转移概率矩阵.其次,利用矩阵分析的方法,导出了稳态队长的概率分布,进一步得到稳态队长的随机分解结果和平均队长公式.最后,给出稳态等待时间的随机分解结构及其平均等待时间公式.

This paper is concerned with a discrete time Geom/G/1 queue with single working vacation.Firstly,a two-dimensional embedded Markov chain is established and its transition probability matrix is obtained.By using the matrix analysis method,the probability distribution of the stationary queue size is derived.Furthermore,the stochastic decomposition structure of the stationary queue size and the expression of mean queue size are given.Finally, the PGF of the stationary waiting time and mean waiting time are obtained.