An examination is made of a queueing system M vertical G vertical 1 for which the intensity of servicing depends on the state of the system in the following way: if the queue length does not exceed N greater than equivalent to 1 immediately prior to the instant of beginning of servicing of an order, the distribution function of the service time of that order is B//1(x) and in the opposite case it is B//2(x). Limit theorems on the joint distribution of the busy period and the number of orders serviced during that period are proven.
Engineering Cybernetics (now Journal of Computer and System Sciences International),
Vol. 22, no. 4 (1984), pp. 18-22