On the application of Rouché's theorem in queueing theory

Authors:
I. J. B. F. Adan;J. S. H. Van Leeuwaarden;E. M. M. Winands
Affiliations:
EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlands and Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;EURANDOM, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands and Department of Technology Management, Eindhoven University o ...
Venue:
Operations Research Letters
Year:
2006

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Abstract

The determination of the PGF of the queue length distribution 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.