An Introduction to Queueing Theory Modeling and Analysis in Applicat
This introductory textbook is designed for a one-semester course on queueing theory that does not require a course in stochastic processes as a prerequisite. By integrating the necessary background on stochastic processes with the analysis of models, the
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Series Editor N. Balakrishnan McMaster University Department of Mathematics and Statistics 1280 Main Street West Hamilton, Ontario L8S 4K1 Canada
Editorial Advisory Board Max Engelhardt EG&G Idaho, Inc. Idaho Falls, ID 83415 Harry F. Martz Group A-1 MS F600 Los Alamos National Laboratory Los Alamos, NM 87545 Gary C. McDonald NAO Research & Development Center 30500 Mound Road Box 9055 Warren, MI 48090-9055 Kazuyuki Suzuki Communication & Systems Engineering Department University of Electro Communications 1-5-1 Chofugaoka Chofu-shi Tokyo 182 Japan
U. Narayan Bhat
An Introduction to Queueing Theory Modeling and Analysis in Applications
Birkh¨auser Boston • Basel • Berlin
U. Narayan Bhat Professor Emeritus Statistical Science & Operations Research Southern Methodist University Dallas, TX 75275-0332 USA
ISBN: 978-0-8176-4724-7 DOI: 10.1007/978-0-8176-4725-4
e-ISBN: 978-0-8176-4725-4
Library of Congress Control Number: 2007941114 Mathematics Subject Classification (2000): 60J27, 60K25, 60K30, 68M20, 90B22, 90B36 c 2008 Birkh¨auser Boston All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkh¨auser Boston, c/o 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.
Cover design: Dutton and Sherman, Hamden, CT. Printed on acid-free paper. 9 8 7 6 5 4 3 2 1 www.birkhauser.com
In memory of my parents, Vaidya P. Ishwar and Parvati Bhat
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xi
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Basic System Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Problems in a Queueing System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 A Historical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Modeling Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2
System Element Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Probability Distributions as Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Deterministic Distribution (D) . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Exponential distribution; Poisson process (M) . . . . . . . . . . . . 2.2 Identification of Models . . . . . . . . . . . . . .
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