Geo/T-IPH/1排队平稳队长分布的精确解  

Explicit Solution for Stationary Queue Length Distribution of Geo/T-IPH/1 Queue

作　　者：郑群珍 封平华 张宏波 ZHENG Qunzhen;FENG Pinghua;ZHANG Hongbo(School of Statistics and Mathematics,Henan Finance University,Zhengzhou,450046,China)

机构地区：[1]河南财政金融学院统计与数学学院,郑州450046

出　　处：《应用概率统计》2023年第4期506-516,共11页Chinese Journal of Applied Probability and Statistics

基　　金：河南省高等学校重点科研项目(批准号:22B110002)资助。

摘　　要：本文讨论离散时间Geo/T-IPH/1排队,其中T-IPH表示可数状态吸收生灭链吸收时间的分布.首先对排队系统建立无限位相拟生灭过程(QBD)模型,然后通过算子几何解方法,得到了过程联合平稳分布的解.在此基础上,进一步得到了所研究排队系统平稳队长分布的精确解.最后,还通过数值例子说明了分析方法的有效性.In this paper we study a discrete-time Geo/T-IPH/1 queue model,where T-IPH denotes the discrete-time phase type distribution de ned 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 countably many phases.Using operator-geometric solution method,we rst give the expression of the joint stationary distribution.Then we obtain the explicit stationary queue length distribution of the queue we considered.Finally,a numerical example is also presented to illustrate the computational procedure.

关 键 词：Geo/T-IPH/1排队 QBD过程 无限位相 平稳队长 

分 类 号：O226[理学—运筹学与控制论]