Network Reliability and Resilience
This book is devoted to the probabilistic description of a network in the process of its destruction, i.e. removal of its components (links, nodes) appearing as a result of technical failures, natural disasters or intentional attacks . It is focused on a
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Ilya Gertsbakh Yoseph Shpungin •
Network Reliability and Resilience
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Prof. Dr. Ilya Gertsbakh Department of Mathematics Ben Gurion University 84105 Beer-Sheva Israel e-mail: [email protected]
ISSN 2191-8112 ISBN 978-3-642-22373-0 DOI 10.1007/978-3-642-22374-7
Dr. Yoseph Shpungin Department of Software Engineering Shamoon College of Engineering 84100 Beer-Sheva Israel e-mail: [email protected]
e-ISSN 2191-8120 e-ISBN 978-3-642-22374-7
Springer Heidelberg Dordrecht London New York Ó Ilya Gertsbakh 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm 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. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, 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 protective laws and regulations and therefore free for general use. Cover design: eStudio Calamar, Berlin/Figueres Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
This book is a result of our ongoing research on network reliability. Started in 1991 [1], it was first summarized in ‘‘Models of Network Reliability: Analysis, Combinatorics and Monte Carlo’’ [2]. Recently, we have widened our approach to include networks with many (more than two) states. In [2] we considered only networks with two states: UP and DOWN, mainly for the situation where DOWN meant loss of terminal connectivity. This was a relatively narrow approach and it becomes much more comprehensive when we assume that a network can have many states that reflect its degradation in the process of nodes or links failures. Such a comprehensive approach enables to describe probabilistically the process of network gradual disintegration into isolated clusters, which starts when all terminals are connected to each other and ends with partial or total isolation of all terminals. Another option that such an approach affords is to follow the size of the network’s largest connected component when network nodes are subject to random ‘‘attack’’. The main formal tools for our investigation are the so-called multidimensional D-spectrum and the marginal D-spectra. D-spectrum is an object of combinatorial nature and is completely determined by the system structure function. This allows to develop efficient Monte Carlo procedures for approximating system D-spectra and serves as a basis for numerical analysis and reliability calculations in the area of network reliability and
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