不可约非周期马尔可夫链状态分类定理及其在排队过程中的应用

本文给出了不可约非周期Markov链常返性的一个充分条件和非常返性的一个充要条件,并将F·G·Foster中的定理4和定理5作为特例。从而,使我们可以在除去P的有限行之后进行状态分类研究,最后将结果应用于排队过程的嵌入Markov链,使Bailey研究的M/G/1成批服务排队过程的状态分类问题得到解决。

THE CLASSIFICATION THEOREM OF THE STATES FOR AN IRREDUCIBLE APERIODIC MARKOV.CHAIN AND ITS APPLICATION ON CERTAIN QUEUEING PROCESS

A sufficient condition of the recurrence and a sufficient and ne-cessary condition of the transience for an irreducible and aperiodic Markvo chain are given in this paper. The theorem 4 and- theorem 5 proved by F, G. Foster [1] are just the particular cases of them. Finally, these results are applied to the embedded Markov chain associated with queueing process so as to resolve the problem of the state classification for M/G/1 queueing process with bulk service studied by Bailey [2].