Kronecker Modeling and Analysis of Multidimensional Markovian Systems
This work considers Kronecker-based models with finite as well as countably infinite state spaces for multidimensional Markovian systems by paying particular attention to those whose reachable state spaces are smaller than their product state spaces. Nume
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Tuğrul Dayar
Kronecker Modeling and Analysis of Multidimensional Markovian Systems
Springer Series in Operations Research and Financial Engineering Series Editors Thomas V. Mikosch Sidney I. Resnick Stephen M. Robinson
More information about this series at http://www.springer.com/series/3182
Tuˇgrul Dayar
Kronecker Modeling and Analysis of Multidimensional Markovian Systems
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Tuˇgrul Dayar Department of Computer Engineering Bilkent University Ankara, Turkey
ISSN 1431-8598 ISSN 2197-1773 (electronic) Springer Series in Operations Research and Financial Engineering ISBN 978-3-319-97128-5 ISBN 978-3-319-97129-2 (eBook) https://doi.org/10.1007/978-3-319-97129-2 Library of Congress Control Number: 2018951794 © Springer Nature Switzerland AG 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
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Preface
This book is about the Markovian modeling and analysis of systems with a discrete multidimensional state space in which various transitions take place. The models of interest are composed of submodels, each dimension corresponds to a submodel that represents a different subsystem, and submodels interact through possible transitions. Particular emphasis is on multidimensional models having unreachable states that appear in the product state space of submodels but can never be occupied in practice. The book shows step-by-step how the transition matrix of the model associated with the reachable state space can be represented compactly and exactly on computer using sums of Kronecker products of matrices associated with submodels. Then the analysis amounts to the numerical computation of steady-state or transient solutions of very large such
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