The repairable M/G/(M/G)/1 queueing systems with variable service speed under an N-threshold

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 queue, 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, speed-two should be used to serve the next customer; otherwise, speed-one is used. By the method of supplementary variable and L-transition, we obtain the distribution of the queue length and some reliability indexes.