Bernoulli反馈排队的N策略Geom/G/1排队系统的队长分布

The Distributions of Queue-length for Geom/G/1 under N-policy with Bernoulli Feedback Queue

考虑具有Bernoulli反馈排队和N策略休假的离散时间Geom/G/1排队系统,采用一种直观、简洁的全概率分解方法以及U-变换技术,研究了该排队系统队长的瞬态性质,得到队长瞬态分布的U-变换形式的递推表达式;进一步导出队长稳态分布的递推表达以及平稳队长分布的随机分解;最后,计算出稳态队长分布,并且考察了其统计性质。

This paper considers the discrete-time Geom/G/1 queue under N-policy vacation with Bernoulli feedback queue in which service time follows arbitrary discrete distribution. By using an intuitive and concise total probability decomposition method and U-tansformation technique, we study the recursion expression of the U-transformation of the transient queue- length distribution at any time, and obtain the expressions of the distribution and stochastic decomposition of the queue- length at a random point in equilibrium. Finally, the stationary queue-length distribution is calculated, and furthermore, its nature of statistics is also investigated.