THE k-BUSY PERIOD OF THE STOCHASTIC SERVICE SYSTEM GI/M/n

<正> For single-server systems, a number of authors have studied the probability law of the busy periods. But for many-server systems, there are only a few articles concerning the nonidle periods. The non-idle period characterizes only the state that the system is not idle. As for the design and management of the systems, however, it is more important to predict when all the servers in the system are going to be occupied and how long this state will last. For this purpose, we shall introduce the concept of k-busy period for many-server systems. This concept may be considered as an index characterizing and predicting to what degree the system is busy. For the system GI/M/n, we shall study the probability law of the k-busy period, and derive the explicit expressions.