On the application of Rouche's theorem in queueing theory

摘要

The determination of the PGF of the queue length distfibution often requires the zeros on and within the unit circle of functions of the type z(s) - A(z), where A(z) is a PGF. We present an elementary proof of the existence of these zeros including series A(z) with a radius of convergence of one. (c) 2005 Elsevier B.V. All rights reserved.