Mathematical Methods in Queueing Theory
Volume 98 of the series Lecture Notes in Economics and Mathematical Systems pp 8190
WienerHopf Techniques in Queueing Theory
 N. U. PrabhuAffiliated withCornell University
Abstract
In queueing theory WienerHopf techniques were first used in a nonprobabilistic context by W. L. Smith, and later in a probabilistic context by F. Spitzer. The specific problem considered by these authors was the solution of the Lindley integral equation for the limit d.f. of waiting times. The more general role played by these techniques in the theory of random walks (sums of independent and identically distributed random variables) is now well known; it has led to considerable simplification of queueing theory.
Now the queueing phenomenon is essentially one that occurs in continuous time, and the basic processes that it gives rise to are continuous time processes, specifically those with stationary independent increments. It is therefore natural to seek an extension of some of the WienerHopf techniques in continuous time. Recent work has yielded several results which can be used to simplify existing theory and generate new results. In the present paper we illustrate this by considering the special case of the compound Poisson process X(t) with a countable statespace. Using the WienerHopf factorization for this process, we shall derive in a simple manner all of the properties of a singleserver queue for which X(t) represents the net input.
 Title
 WienerHopf Techniques in Queueing Theory
 Book Title
 Mathematical Methods in Queueing Theory
 Book Subtitle
 Proceedings of a Conference at Western Michigan University, May 10–12, 1973
 Pages
 pp 8190
 Copyright
 1974
 DOI
 10.1007/9783642808388_5
 Print ISBN
 9783540067634
 Online ISBN
 9783642808388
 Series Title
 Lecture Notes in Economics and Mathematical Systems
 Series Volume
 98
 Series Subtitle
 Operations Research
 Series ISSN
 00758442
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin · Heidelberg
 Additional Links
 Topics
 Industry Sectors
 Editors

 Dr. A. Bruce Clarke ^{(3)}
 Editor Affiliations

 3. Department of Mathematics, Western Michigan University
 Authors

 N. U. Prabhu ^{(4)}
 Author Affiliations

 4. Cornell University, USA
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