Note--On the Merits of an "Approximation" to the Busy Period of the GI/G/1 Queue

An approximation suggested by D. Gross and C. M. Harris in their book Fundamentals of Queueing Theory for computing the busy period characteristics in the single server queue with renewal input and general i.i.d. service times commonly denoted by GI/G/1 is shown to be lacking in accuracy, and therefore quite undesirable for practical use. Incidentally, we also demonstrate how for a wide subclass of such queues, computations can be done exactly using practical algorithmic methods.