服务速度依门限N波动的可修M/G(M/G)/1排队系统

The Repairable M/G(M/G)/1 Queueing Systems with Fluctuant Service Speed under an N-threshold

有关可修M G 1排队系统已有很多成功的研究成果 ,笔者作了进一步的推广 ,通过对排队系统中的顾客数设置一个门限 -N值 ,考虑研究了在服务台对某顾客服务结束时刻如果此时系统中的顾客数超过预先设定的门限N值则以服务强度 2服务下一个顾客 ,反之 ,则以强度 1服务的可修M G(M G) 1排队系统模型 通过L -变换、母函数以及补充变量法得到了瞬态队长分布。

Much has been done concerning repairable M/G/1 queueing systems and many important results have been obtained. In this paper, by setting an N -threshold in the queueing, we consider a repairable M/G(M/G)/1 queueing systems model whose service speed can be changed according to the following disciplines. At the moment of customers leaving the system, if the number of customers exceeds the threshold N , the speed two should be used to serve the next customer; otherwise, the speed one be used. By the method of supplementary variable and L -transition, we obtain the distribution of the queue length and some reliability indexes.