The Probability Law of the Busy Period for Two Types of Queuing Processes

A simple combinatorial method is given for the determination of the joint distribution of the length of the busy period and the number of customers served during this period for two types of single-Berver queuing processes. (1) Customers arrive at a counter according to a Poisson process and the service times have a general distribution, (2) customers arrive at a counter according to a recurrent process and the service times have an exponential distribution.