| 一类休假排队平稳队长分布的无限位相表示 |
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| 引用本文： | 张宏波,王征.一类休假排队平稳队长分布的无限位相表示[J].高校应用数学学报(A辑),2019,34(3):287-294. |
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| 作者姓名： | 张宏波 王征 |
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| 作者单位： | 郑州西亚斯学院数学系,河南郑州451150;河南财政金融学院数学与统计学院,河南郑州450046;郑州西亚斯学院数学系,河南郑州,451150 |
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| 摘 要： | 讨论休假时间服从T-SPH分布的M/M/1单重休假模型,其中T-SPH表示可数状态吸收生灭过程吸收时间的分布.该排队模型可以用可数位相拟生灭过程(QBD过程)和算子几何解的方法进行建模分析.首先得到了QBD过程算子几何解的具体形式;其次在所得结果的基础上,进一步给出了排队模型平稳队长的随机分解结果,并说明附加队长服从离散时间无限位相分布.
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| 关 键 词： | M/M/1排队 QBD过程 率阵 随机分解 无限位相分布 |
Infinite phase type representation for queue length distribution of a vacation queue |
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| ZHANG Hong-bo,WANG Zheng.Infinite phase type representation for queue length distribution of a vacation queue[J].Applied Mathematics A Journal of Chinese Universities,2019,34(3):287-294. |
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| Authors: | ZHANG Hong-bo WANG Zheng |
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| Institution: | (Department of Mathematics, Sias University, Zhengzhou 451150, China;School of Mathematics and Statistics, Henan Finance University, Zhengzhou 450046, China) |
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| Abstract: | This paper considers an M/M/1 vacation queue with T-SPH vacation time,where T-SPH denotes the discrete-time phase type distribution defined on a birth and death process with countably many states.The queue model can be described by a quasi-birth-and-death(QBD)process with infinite phases.Firstly,the concrete forms of rate operator and operator-geometric solution of the QBD process are given.Secondly,the stochastic decomposition structure of the stationary queue length is presented.Finally,it is proved that the additional queue length follows discrete-time infinite phase type distribution. |
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| Keywords: | M/M/1 queue QBD process rate matrix stochastic decomposition infinite phase type distribution |
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