Much has been done concerning the repairable M/G/1 queueing systems and many valuable results have been obtained. In this paper, by setting an N-threshold in the queueing we consider a repairable M/G(M/M)/1 queueing system whose service speed can be changed according to the number of the customers in the system. The discipline of speed change is that if the number exceeds the threshold N, the higher speed should be used to serve customers at once until there is no customer in queue. By the method of supplementary variables and L-transition, we obtain the distribution of the queue length and some reliability indexes.
