中文摘要：

本文首先证明当服务强度小于1时，GI／G／1排队系统的队长是一个特殊的马尔可夫骨架过程——正常返的Doob骨架过程，然后运用马尔可夫骨架过程的强大数定律和中心极限定理等重要结果，给出了队长的累积过程的期望和方差，并给出了该累积过程满足强大数定律和中心极限定理的充分条件。

英文摘要：

First, when service intensity is less than 1, the queue length in a GI/G/1 queueing system is proved to be a positive recurrent Doob skeleton process, which is a special ease of Markov skeleton processes. Second, the expectation and variance of the cumulative process of the queue length are obtained by using law of strong large numbers, central limit theorem and other important results of Markov skeleton processes. And finally, sufficient conditions for law of strong large numbers and central limit theorem of the accumulated process are given, respectively.