This paper deals with a retrial queuing system with a finite number of sources and collision of the customers, where the server is subject to random breakdowns and repairs depending on whether it is idle or busy. A significant difference of this system from the previous ones is that the service time is assumed to follow a general distribution while the server’s lifetime and repair time is supposed to be exponentially distributed. The considered system is investigated by the method of asymptotic analysis under the condition of an unlimited growing number of sources. As a result, it is proved that the limiting probability distribution of the number of customers in the system follows a Gaussian distribution with given parameters. The Gaussian approximation and the estimations obtained by stochastic simulations of the prelimit probability distribution are compared to each other and measured by the Kolmogorov distance. Several examples are treated and figures show the accuracy and area of applicability of the proposed asymptotic method.

本文讨论了一种具有有限数量的源和客户冲突的重试排队系统，其中服务器根据其空闲还是忙碌而遭受随机故障和维修。该系统与以前的系统的显着区别是，假定服务时间遵循一般分布，而服务器的寿命和维修时间则呈指数分布。在源数量不受限制的情况下，通过渐近分析的方法对所考虑的系统进行了研究。结果证明，系统中用户数量的极限概率分布遵循具有给定参数的高斯分布。高斯近似和通过随机模拟极限概率分布获得的估计值相互比较，并通过Kolmogorov距离进行测量。处理了几个示例，图显示了所提出的渐近方法的准确性和适用范围。