本文由PH分布与马氏过程相联系的思想出发,将有限状态马氏链吸收时间的分布理论推广到可列状态马氏链,由此得到一类新分布-NPH分布. 文章主体部分包括: 给出NPH分布的定义, 用半群-生成元理论,最小非负解理论等, 研究此类分布的性质, 包括数字特征, 封闭性质,渐进性质等. 并且将分布性质与过程的遍历理论相联系,得到一组有关可积性的充要判据. 在讨论一般性质的过程中, 将此类分布的讨论与排队论忙期的概念相联系.得到有关$M/M/1$,\ $M/M/\infty$排队模型的忙期的有关结论.

Based on the idea of attaching PH distribution and Markov chain together, we get a new type of distribution-NPH distribution, which relates to numerable absorbing Markov chains. In the main chapter of this article, I define this new distribution, and study the properties including numerical characteristic, closureproperty, asymptotic property by way of Group-generator theory, the theory of minimum non-negative solution and so on. Also, there is a close relation between the ergodicity of the chain and the integralproperty of the distribution, here I will get three couples of results. During the course of deduction, I try to get some results concerning the busy period of $M/M/1$, $M/M/\infty$ queueing systems, which is in fact a kind of NPH distribution.