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带有Bernoulli反馈的多级适应性休假的Geo/G/1排队系统分析
引用本文:魏瑛源,唐应辉,顾建雄.带有Bernoulli反馈的多级适应性休假的Geo/G/1排队系统分析[J].高校应用数学学报(A辑),2010,25(1).
作者姓名:魏瑛源  唐应辉  顾建雄
作者单位:1. 河西学院数学系,甘肃张掖,734000
2. 四川师范大学数学与软件科学学院,四川成都,610066
基金项目:国家自然科学基金,教育部高校博士点专项研究基金 
摘    要:考虑带有Bernoulli反馈的多级适应性休假的Geo/G/1离散时间排队系统.通过引入服务员忙期和使用一种简洁的分解方法,讨论了队长的瞬时分布,得到了在任意时刻n队长为j的概率关于时刻n的z-变换的递推式,及队长平稳分布的递推式,且证明了稳态队长的随机分解性质.最后,给出了在特殊情形下相应的一些结果和数值计算实例.

关 键 词:离散时间排队  多级适应性休假  Bernoulli反馈  队长分布  随机分解

Analysis of Geo/G/1 queueing system with multiple adaptive vacations and Bernoulli feedback
WEI Ying-yuan,TANG Ying-hui,GU Jian-xiong.Analysis of Geo/G/1 queueing system with multiple adaptive vacations and Bernoulli feedback[J].Applied Mathematics A Journal of Chinese Universities,2010,25(1).
Authors:WEI Ying-yuan  TANG Ying-hui  GU Jian-xiong
Abstract:This paper considers a discrete-time Geo/G/1 queue with multiple adaptive vacations and Bernoulli feedback. By introducing the server busy period and using a concise decomposition method, the transient distribution of the queue length is studied. Both the recursion expression of the z-transform about epoch n of the probability that the queueing length equals to j at any epoch n and the recursion formulae of the stationary distribution for the queue length are obtained. The stochastic decomposition property of steady-state queue length has been proved. Finally, some corresponding results and numerical examples under special cases are also given.
Keywords:discrete-time queue  multiple adaptive vacation  Bernoulli feedback  queue-length distribution  stochastic decomposition
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