Copyright (c) 2009 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW All Rights Reserved Library of Congress Cataloging-in-Publication Data Stewart, William J., 1946-- Probability, Markov chains, queues and simulation: the mathematical basis of performance modelling/William J. Stewart. - 1st ed. p. cm. ISBN 978-0-691-14062-9 (cloth : alk. paper) 1. Probability - Computer simulation. 2. Markov processes. 3. Queueing theory. I. Title. QA273.S7532 519.201'13--dc22 2008041122 British Library Cataloging-in-Publications dada is available This book has been composed in Times Printed on acid-free paper. press.princeton.edu Typeset by S R Nova Pvt Ltd, Bangalore, India Printed in the United States of America 10 9 8 7 6 5 4 3 2 1