The Theory of Queuing Systems with Correlated Flows
This book is dedicated to the systematization and development of models, methods, and algorithms for queuing systems with correlated arrivals. After first setting up the basic tools needed for the study of queuing theory, the authors concentrate on compli
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Theory of Queuing Systems with Correlated Flows
The Theory of Queuing Systems with Correlated Flows
Alexander N. Dudin • Valentina I. Klimenok • Vladimir M. Vishnevsky
The Theory of Queuing Systems with Correlated Flows
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Alexander N. Dudin Dept. of Applied Mathematics and Informatics Belarusian State University Minsk, Belarus
Valentina I. Klimenok Dept. of Applied Mathematics and Informatics Belarusian State University Minsk, Belarus
Vladimir M. Vishnevsky V.A. Trapeznikov Institute of Control Sciences Russian Academy of Sciences Moscow, Russia
ISBN 978-3-030-32071-3 ISBN 978-3-030-32072-0 (eBook) https://doi.org/10.1007/978-3-030-32072-0 © Springer Nature Switzerland AG 2020 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, expressed 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
Foreword
It is my pleasure and honor to write this Foreword. As is known, every product or process we face in day-to-day activities involves either a manufacturing aspect or a service aspect (and possibly both). Queuing theory plays a major role in both these aspects. There are a number of excellent books written on queuing theory in the last many decades starting with the classical book by Takacs in 1960s to Kleinrock’s two volumes in the 1970s to Neuts’ ground-breaking ones on matrix-analytic methods in the 1980s. Along the way a number of notable books (undergraduate and graduate level) were published by Alfa, Bhat, Cohen, Gross and Harris, He, Latouche and Ramaswami, and Trivedi, et al., among others. This book, written by well-known researchers on queueing and related areas, is unique in the sense that the entire book is devoted to queues with correlated arrivals. Since the introduction of Markovian arrival processes by Neuts, possible correlation pres
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