Queueing Theory for Telecommunications Discrete Time Modelling of a
Queueing theory applications can be discovered in many walks of life including; transportation, manufacturing, telecommunications, computer systems and more. However, the most prevalent applications of queueing theory are in the telecommunications field.
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Attahiru Sule Alfa
Queueing Theory for Telecommunications Discrete Time Modelling of a Single Node System
1C
Attahiru Sule Alfa Dept. of Electrical & Computer Engineering University of Manitoba Winnipeg, Manitoba Canada R3T 5V6 [email protected]
ISBN 978-1-4419-7313-9 e-ISBN 978-1-4419-7314-6 DOI 10.1007/978-1-4419-7314-6 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010932011 © Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
This is dedicated to all my parents, my wife, my children and my grandchildren.
Preface
It is not as if there are not many books already on queueing theory! So, why this one – an additional book? Well, generally queueing models and their analyses can be presented in several different ways, ranging from the highly theoretical base to the very applied base. I have noticed that most queueing books are written based on the former approach, with mathematical rigour and as a result sometimes ignoring the application oriented reader who simply wants to apply the results to a real life problem. In other words, that reader who has a practical queueing problem in mind and needs an approach to use for modelling such a system and obtain numerical measures to assist in understanding the system behaviour. Other books that take the purely applied approach usually oversimplify queueing models and analyses to the extend that a reader is not able to find results useful enough for the major applications intended. For example, the models are limited to simple unrealistic arrival and service processes and rules of operation, in an attempt to obtain very simple analysis which may not capture the key behaviour of the system. One of the challenges is to present queueing models and clearly guide the reader on how to use available mathematical tools to help in analyzing the problems associated with the models. To this end the contents of this book are mainly presented in a form that makes their applications very easy to see, as such it is written to make queueing analysis easier to follow and also to make the new developments and results in the field more accessible to pragmatic user of the models. Nearly every queueing model can be set up as a Markov chain, even
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