带启动期的单重工作休假GI/Geom/1排队

The discrete-time GI/Geom/1 queue with single working vacation and setup times

详细分析了带启动期的单重工作休假GI/Geom/1排队.首先在顾客到达时刻嵌入二维Markov链,把状态转移概率矩阵表示成Block-Jocabi形式.然后用矩阵几何解方法导出了稳态队长的分布及其随机分解结构,得到等待时间的母函数及其随机分解结构,同时给出了平均队长和平均等待时间.最后,用Matlab软件验证了一个数值例子.

The GI/Geom/1 queue with single working vacation and setup times is considerd in this paper.With the two-dimensional Markov chain embedded in the time that the customers arrive the system,its transition probability matrix is expressed in Block-Jocabi form.And with the matrix-geometric solution method,probability distribution of the stationary queue length and the highly complicated PGF of the stationary waiting time are firstly derived.Meanwhile,the mean queue length and the mean waiting time are given.Finally,the numerical results with Matlab are presented.