Analysis of the busy period in threshold control system

Consideration was given to the controllable Markov queuing system with nonhomogeneous servers and threshold policy of server activation depending on the queue length. By the busy period is meant the time interval between the instant of customer arrival to the empty system and the instant of service completion when the system again becomes free. The system busy period and the number of serviced customers were analyzed. Recurrent relations for the distribution density in terms of the Laplace transform and generating function, as well as formulas for calculation of the corresponding arbitrary-order moments, were obtained.