Queueing Networks A Fundamental Approach
This handbook aims to highlight fundamental, methodological and computational aspects of networks of queues to provide insights and to unify results that can be applied in a more general manner. The handbook is organized into five parts:Part 1 consi
- PDF / 7,745,258 Bytes
- 814 Pages / 439.37 x 666.142 pts Page_size
- 52 Downloads / 214 Views
Volume 154
Series Editor: Frederick S. Hillier Stanford University, CA, USA Special Editorial Consultant: Camille C. Price Stephen F. Austin, State University, TX, USA
For further volumes: http://www.springer.com/series/6161
Richard J. Boucherie • Nico M. van Dijk Editors
Queueing Networks A Fundamental Approach
123
Editors Richard J. Boucherie Departement of Applied Mathematics University of Twente Stochastic OR Group PO Box 217 7500 AE Enschede The Netherlands [email protected]
Nico M. van Dijk Faculty of Economics and Business University of Amsterdam Roetersstraat 11 1018 WB Amsterdam The Netherlands [email protected]
ISSN 0884-8289 ISBN 978-1-4419-6471-7 e-ISBN 978-1-4419-6472-4 DOI 10.1007/978-1-4419-6472-4 Springer New York Dordrecht Heidelberg London © Springer Science+Business Media, LLC 2011 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 known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The origin of queueing theory and its application traces back to Erlang’s historical work for telephony networks as recently celebrated by the Erlang Centennial, 100 Years of Queueing, Copenhagen, recalling his first paper in 1909. Ever since, the simplicity and fundamental flavour of Erlang’s famous expressions, such as his loss formula for an incoming call in a circuit switched system to be lost, has remained intriguing. It has motivated the development of results with similar elegance and expression power for various systems modeling congestion and competition over resources. A second milestone was the step of queueing theory into queueing networks as motivated by the first so-called product form results for assembly type networks in manufacturing in the nineteen fifties (R.R.P. Jackson 1954, J.R. Jackson 1957, and E. Koenigsberg 1958, 1959). These results revealed that the queue lengths at nodes of a network, where customers route among the nodes upon service completion in equilibrium can be regarded as independent random variables, that is, the equilibrium distribution of the network of nodes factorizes over (is a product of) the marginal equilibrium distributions of the individual nodes as if in isolation. These networks are nowadays referred to as Jackson networks. A third milestone was inspired by the rapid development of computer systems and brought the attention fo
Data Loading...
