A single-server queuing system with infinite capacity and a recurrent input flow is considered. Service times of the customer units have an exponential distribution with random parameter. The current value of the parameter is chosen from a finite set with given probabilities at the time the service of a certain customer is completed. Sequential values of the parameters form a special kind of Markov chain. The nonstationary behavior of the queue length is studied.

中文翻译：

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服务时间相关的排队系统中的队列长度

考虑具有无限容量和循环输入流的单服务器排队系统。客户单元的服务时间具有随机参数的指数分布。在某个客户的服务完成时，从具有给定概率的有限集合中选择参数的当前值。参数的顺序值形成一种特殊的马尔可夫链。研究了队列长度的非平稳行为。