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
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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.Abstract: In this paper we study a discrete-time Geo/T-IPH/1 queue model, where T-IPH 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 countably many phases. Using operator-geometric solution method, we first 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.