Iterative Methods for Queuing and Manufacturing Systems
Iterative Methods for Queuing and Manufacturing Systems introduces the recent advances and developments in iterative methods for solving Markovian queuing and manufacturing problems. Key highlights include: - an introduction to simulation and simulation s
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Springer-Verlag London Ltd.
Wai Ki Ching
Iterative Methods for Queuing and Manufacturing Systems With 17 Figures
~Springer
WaiKiChing Faculty of Mathematical Studies University of Southampton Highfield Southampton S017 lBJ
UK
Springer Monographs in Mathematics ISSN 1439-7382 ISBN 978-1-84996-870-6 British Library Cataloguing in Publication Data Ching, Wai Ki Iterative methods for queuing and manufacturing systems. (Springer monographs in mathematics) 1. Markov processes 2. Iterative methods (Mathematics) 3. Queuing Theory 4. System analysis 5. Flexible manufacturing systems- Mathernatical models I.Title 519 ISBN 978-1-84996-870~ Library of Congress Cataloging-in-Publication Data Ching, Wai Ki, 1969Iterative methods for queuing and rnanufacturing systems 1Wai Ki Ching. p. cm. -- (Springer monographs in rnathernatics) Includes bibliographical references. ISBN 978-1-4471-3905-8 (eBook) ISBN 978-1-84996-870-6 DOI 10.1007/978-1-4471-3905-8 !. Queuing Theory 2. Iterative methods (Mathernatics) 1. Title. Il. Series. T57.9.C48 2001 519.82-dc21 00-052659 Mathematics Subject Classification (1991): 65FIO, 60122, 90B05, 90B22
Apar! from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication rnay only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. © Springer-Verlag London 2001 Originally published by Springer-Verlag London Berlin Heidelberg in 2001 Softcover reprint of the hardcover 1st edition 2001 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Typesetting: Camera-ready by the author 12/3830-543210 Printedon acid-free paper SPIN 10790110
To Mandy Lee, Shun Tai Ching, and Kam Koo Wong
Preface
The aim of this book is to outline the recent development of iterative methods for solving Markovian queuing and manufacturing systems. Markov processes are widely used in the modeling of queuing systems, manufacturing systems, telecommunication systems, computer systems, and many other practical systems. Very often, in the system performance analysis, one faces the problem of solving the system steady-state probability distribution of a large number of states. Classical iterative methods such as Gauss-Seidel (GS) and Jacobi methods are the common iterative methods used to tackle the problem. However, their convergence rat
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