Max-Plus Linear Stochastic Systems and Perturbation Analysis

During the last decade, the area of stochastic max-plus linear systems has witnessed a rapid development, which created a growing interest in this area. This book provides a thorough treatment of the theory of stochastic max-plus linear systems. Max-plus

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THE INTERNATIONAL SERIES ON DISCRETE EVENT DYNAMIC SYSTEMS Series Editor Yu-Chi Ho Harvard University SUPERVISION OF PETRI NETS Geert Stremersch ISBN: 0-7923-7486-X ANALYSIS OF MANUFACTURING ENTERPRISES: An Approach to Leveraging Value Delivery Processes for Competitive Advantage N. Viswanadham ISBN: 0-7923-8671-X INTRODUCTION TO DISCRETE EVENT SYSTEMS Christos G. Cassandras, St6phane Lafortune ISBN: 0-7923-86094 OBJECT-ORIENTED COMPUTER SIMULATION OF DISCRETE-EVENT SYSTEMS Jerzy Tyszer ISBN: 0-7923-8506-3 TIMED PETRI NETS: Theory and Application Jiacun Wang ISBN: 0-7923-8270-6 SUPERVISORY CONTROL OF DISCRETE EVENT SYSTEMS USING PETRI NETS John O. Moody and Panos J. Antsaklis ISBN: 0-7923-8199-8 GRADIENT ESTIMATION VIA PERTURBATION ANALYSIS P. Glasserman ISBN: 0-7923-90954 PERTURBATION ANALYSIS OF DISCRETE EVENT DYNAMIC SYSTEMS Yu-Chi Ho and Xi-Ren Cao ISBN: 0-7923-9174-8 PETRI NET SYNTHESIS FOR DISCRETE EVENT CONTROL OF MANUFACTURING SYSTEMS MengChu Zhou and Frank DiCesare ISBN: 0-7923-9289-2 MODELING AND CONTROL OF LOGICAL DISCRETE EVENT SYSTEMS Ratnesh Kumar and Vijay K. Garg ISBN: 0-7923-9538-7 UNIFORM RANDOM NUMBERS: THEORY AND PRACTICE Shu Tezuka ISBN: 0-7923-9572-7 OPTIMIZATION OF STOCHASTIC MODELS: THE INTERFACE BETWEEN SIMULATION AND OPTIMIZATION Georg Ch. Pflug ISBN: 0-7923-9780-0 CONDITIONAL MONTE CARLO: GRADIENT ESTIMATION AND OPTIMIZATION APPLICATIONS Michael FU and Jian-Qiang HU ISBN: 0-7923-98734

MAX-PLUS LINEAR STOCHASTIC SYSTEMS AND PERTURBATION ANALYSIS

by

Bernd Heidergott Vrije Universiteit, Amsterdam, The Netherlands

^ Springer

Bernd Heidergott Vrije Universiteit Faculty of Economics and Business Administration Department of Econometrics and Operations Research DeBoelelaanllOS 1081 HV Amsterdam Email: [email protected]

Library of Congress Control Number: 2006931638 Max-Plus Linear Stochastic Systems and Perturbation Analysis by Bernd Heidergott ISBN-13: 978-0-387-35206-0 ISBN-10: 0-387-35206-6 e-ISBN-13: 978-0-387-38995-0 e-ISBN-10: 0-387-38995-4 Printed on acid-free paper.

Parts of this manuscript [in Chapter 3] were reprinted by permission, [Heidergott, B. 2001. A differential calculus for random matrices with applications to (max, +)-linear stochastic systems. Math. Oper. Res. 26 679-699]. Copyright 2006, the Institute for Operations Research and the Management Sciences, 7240 Parkway Drive, Suite 310, Hanover, MD 21076 USA. © 2006 Springer Science+Business Media, LLC 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 know or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if the are not identified as such, is