本文给出了GI/M/1型马氏过程正常返的等价条件. 在第一部分, 介绍了基本概念, 并利用禁忌概率定义速率矩阵 R. 在第二部分, 证明了 R 的一些性质,同时得到了计算 R 的一种迭代算法, R 为一方程的最小非负解. 另外, 在 R 的所有特征值均在单位圆中时, 用 R 表示出了马氏过程的平稳分布. 在第三部分,进一步讨论了矩阵 A 不可约的情形下, R 的所有特征值在单位圆中的等价条件. 在最后一部分, 通过对连续时间马氏过程 Q 矩阵进行变换, 将离散时间情形的结论推广到了连续时间的情形.

In this thesis, we give the equivalent condition of the positive recurrence of the GI/M/1 type Markov chain. In the first chapter, we introduce some basic concepts. We also use the taboo probability to define the rate matrix R. In the second chapter, we prove some properties of the matrix R, and we obtain a iterated algorithm to compute the matrix R. Besides, we use R to show the stationary distribution of the Markov chain, while R has all its eigenvalues lies inside the unit disk. In the third chapter, we discuss the equivalent condition of R having all its eigenvalues lies inside the unit disk, while the matrix A is irreducible. In the last chapter, we transform the Q matrix of the continuous parameter Markov chain to generalize conclusions of the discrete time situation.