中文摘要：

对Markov到达过程作了推广,即考虑在服从PH分布的随机时间间隔上的Markov到达过程,采用构造与之相关的潜在Markov过程的方法分析这一计数过程.讨论了这类计数过程的基本性质,并给出了更新次数的矩母函数.同时,证明了这一过程的更新总次数及最后更新时刻服从PH分布,并给出了具体表示式.

英文摘要：

In this paper,we generalized the Markovian arrival process.That is,we discussed the Markovian arrival process on a random interval,where the random interval time has a PH distribution.By means of constructing new underlying Markovian process,we transformed it into a new counting process.This process has the same distribution as the original one.We discussed the basic properties of this type of counting process and obtained the moment generating function in a finite interval.We proved that the total counting and the last renewal time satisfy the PH distribution,and also gave their formulas of these pH distributions.