T-IPH分布的若干性质及其在排队论中的应用

Some Properties of T-IPH Distribution,with Applications to Queueing Systems

本文讨论T-IPH分布的一些重要性质,其中T-IPH表示可数状态离散时间吸收生灭链吸收时间的分布.对该分布,首先给出了其概率生成函数（PGF）,在此基础上,进一步给出了计算分布概率分布律以及阶乘矩数值结果的迭代公式.另外,还讨论了T-IPH分布在排队论中的一个应用.

In this paper, we discuss some important properties of T-IPH distribution, where T-IPH denotes the infinite phase type distribution defined on a discrete-time birth and death process with countably many states. For the distribution, we firstly give the probability generating function （PGF）, then the obtained results enable us to further give the recursive formula to calculating numerical results of distributional law and factorial moment for the distribution. Finally, we also give an application of T-IPH distribution in queueing systems.