中文摘要：

本文运用齐次可列半马尔可夫过程的向后方程和向前方程,分别研究了GI/M/1和M/G/1排队系统队长的瞬时分布.首先得到了GI/M/1队长的转移概率的拉普拉斯变换满足的向后方程组,然后得到了M/G/1队长的转移概率的拉普拉斯变换满足的向前方程组,所得方程组的系数矩阵都是拟下三角矩阵,都可以通过迭代法进行求解.

英文摘要：

In this paper,the backward equations and forward equations of homogeneous denumerable semi-Markov processes are used to study the instantaneous distribution of queue lengths of GI/M/1 and M/G/1 queuing systems,respectively.For the GI/M/1 queuing system,the backward equations of the Laplace transform of the transition probability of its queue length are obtained.For the M/GI/1 queuing system,the forward equations of the Laplace transform of the transition probability of its queue length are obtained.These backward equations and forward equations,whose coefficient matrices are quasi-triangular matrices,can be easily solved by using the iterative method.