Nikolaos Limnios - Queueing Theory 2

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SCIENCES

Mathematics , Field Director – Nikolaos Limnios

Queuing Theory and Applications , Subject Head – Vladimir Anisimov

Coordinated by

Vladimir Anisimov

Nikolaos Limnios

First published 2020 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd

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John Wiley & Sons, Inc.

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© ISTE Ltd 2020

The rights of Vladimir Anisimov and Nikolaos Limnios to be identified as the author of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2019957522

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN 978-1-78945-004-0

ERC code:

PE1 Mathematics

PE1_21 Application of mathematics in industry and society

Vladimir ANISIMOV1 and Nikolaos LIMNIOS2

1Amgen Inc., London, United Kingdom

2University of Technology of Compiègne, France

Queueing theory is a huge and very rapidly developing branch of science belonging to probability theory and stochastic modelling that originated a long time ago from the pioneering works by Erlang (1909) on the analysis of the models for telephone communication using Poisson processes. Later on, these results were extended further in different directions in the works of such famous mathematicians as Pollaczek, Khinchin, Kendall, Kleinrock and many others.

Nowadays, queueing theory is rapidly growing in various areas including a theoretical analysis of queueing models and networks of rather complicated structure using rather sophisticated mathematical models and various types of stochastic processes. It also includes very wide areas of modern applications: computing and telecommunication networks, traffic engineering, mobile telecommunications, etc.

The aim of this second volume, together with Volume 1, is to reflect the current cutting-edge thinking and established practices in the analysis and applications of queueing models.

This volume includes 8 chapters written by experts well-known in their areas.

Two chapters, Chapters 1and 7, are devoted to investigating a stability analysis of some types of multiserver regenerative queueing systems with heterogeneous servers and a regenerative input flow using synchronization of the input and majorizing output flows; and a stability analysis of regenerative queueing systems based on a renewal analysis technique, which is illustrated on classical GI/G/ 1 and GI/G/m queueing systems.

Chapter 2considers a few selected queueing models that are useful in service sectors using both analytical and simulation approaches; and highlights the significant role played by the correlated arrivals, which may occur due to the fact that customers/jobs arrive from different sources. Some interesting observations based on the analytical models of some well-known queueing systems are also reported.

Chapter 3is devoted to the discussion of similarity between probability distributions and random processes related to queueing and reliability models and their use in economics, industry, demography, environmental studies. Some open and challenging new problems for further research directions are marked, as well as various possible areas of practical applications.

Chapter 4is devoted to an important problem of how a social planner or a monopolist should act to incite customers to adopt a desirable behaviour, that is, to increase the social welfare or the monopolist’s revenue/profit, respectively, using the concepts of free market. Several techniques for the control of information in queueing systems and their impact on strategic customer behaviour using different mechanisms, e.g. pricing structures, priority systems and non-standard queueing disciplines, are considered and illustrated using various examples.

Chapter 5is devoted to applications of Renyi’s and Tsallis’s non-extensive maximum entropy methods of inductive inference for the analysis of state probabilities of the stable M/G/ 1 queue with long-range interactions (heavy tails) of order q (0.5 < q > 1). Consequently, novel q-dependent state probabilities of the M/G/ 1 queue with heavy tails are derived by maximising the respective non-extensive maximum entropy functionals. Some numerical examples are considered.