Discrete-Event Control of Stochastic Networks: Multimodularity and Regularity
Opening new directions in research in both discrete event dynamic systems as well as in stochastic control, this volume focuses on a wide class of control and of optimization problems over sequences of integer numbers. This is a counterpart of convex opti
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Eitan Altman Bruno Gaujal Arie Hordijk
Discrete-Event Control of Stochastic Networks: Multimodularity and Regularity
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Authors Eitan Altman INRIA 2004 Route des Lucioles 06902 Sophia-Antipolis Cedex, France e-mail: [email protected] Bruno Gaujal ENS Lyon, LIP 46 All´ee d’Italie 69364 Lyon Cedex 07, France e-mail: [email protected] Arie Hordijk Mathematical Institute Leiden University P.O. Box 9512 2300 RA Leiden, The Netherlands e-mail: [email protected]
Cataloging-in-Publication Data applied for Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de
Mathematics Subject Classification (2000): 60-XX, 60C05, 49-XX, 93-XX ISSN 0075-8434 ISBN 3-540-20358-3 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag is a part of Springer Science+Business Media springeronline.com c Springer-Verlag Berlin Heidelberg 2003 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the authors SPIN: 10964620
41/3142/du - 543210 - Printed on acid-free paper
To our families
Preface
This work has been made possible largely thanks to the kind support of the Van Gogh project N. 98001 “Multimodularity and Control” (French-Dutch scientific cooperation project) and of INRIA Action de Recherche Coop´erative Maddes. The work of Arie Hordijk on this book was initiated while he was on sabbatical leave at INRIA, Sophia-Antipolis; partially supported by the ´ Minist`ere Fran¸cais de l’Education Nationale et de l’Enseignement Sup´erieur et de la Recherche. We wish to thank colleagues with whom we have had stimulating discussions and who helped us with different theoretical points presented here. In particular, we wish to thank Fran¸cois Baccelli, Sandjay Bhulai, Jerome Galtier, Alex Heinis, Emmanuel Hyon, Alain Jean-Marie, Ger Koole, Zhen Liu, Rob Tijdeman and Dinard van der Laan. This book summarizes several years of research work of its authors. Part of the material in the book was obtained jointly with other researcher
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