Nikolaos Limnios - Queueing Theory 1

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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:

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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: 2019955378

British Library Cataloguing-in-Publication Data

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

ISBN 978-1-78945-001-9

ERC code:

PE1 Mathematics

PE1_21 Application of mathematics in industry and society

Vladimir ANISIMOV 1and Nikolaos LIMNIOS 2

1Amgen Inc., London, United Kingdom

2University of Technology of Compiègne, France

Queueing theory is a huge and very rapidly developing branch of science that originated a long time ago from the pioneering works by Erlang (1909) on the analysis of the models for telephone communication.

Now, it is growing in various directions 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 applications: computing and telecommunication networks, traffic engineering, mobile telecommunications, etc.

The aim of this book is to reflect the current state-of-the-art and some contemporary directions of the analysis of queueing models and networks including some applications.

The first volume of the book consists of 10 chapters written by world-known experts in these areas. These chapters cover a large spectrum of theoretical and asymptotic results for various types of queueing models, including different applications.

Chapter 1is devoted to the investigation of some theoretical problems for non-classical queueing models including the analysis of queues with inter-dependent arrival and service times.

Chapter 2deals with the analysis of some characteristics of fluid queues including busy period, congestion analysis and loss probability.

Some contemporary tendencies in the asymptotic analysis of queues are reflected in the following three survey Chapters 3, 7and 10.

Chapter 3includes the results on the average and diffusion approximation of Markov queueing systems and networks with a small series parameter ε including applications to some Markov state-dependent queueing models and some other type of models, in particular, repairman problem, superposition of Markov processes and semi-Markov type queueing systems.

Diffusion and Gaussian limits for multi-channel queueing networks with rather general time-dependent input flow and under heavy traffic conditions including some applications to networks with semi-Markov or renewal type input and Markov service are considered in Chapter 7.

Chapter 10is devoted to the asymptotic analysis of time-varying queues using the large deviations principle for two-time-scale non-homogeneous Markov chains including the analysis of the queue length process and some characterizations of the quality and the efficiency of the system.

The analysis of so-called retrial queueing models is reflected in two Chapters – 4and 8.

In Chapter 4, two models that provide some modifications of “First-Come First- Served” retrial queueing system introduced by Laszlo Lakatos are investigated.

Chapter 8gives a review of recent results on single server finite-source retrial queueing systems with random breakdowns and repairs and collisions of the customers.

The analysis of transient behavior of the infinite-server queueing models with a mixed arrival process and Coxian service times and of the Markov-modulated infinite¬server queue with general service times is considered in Chapter 5.

Chapter 6deals with the applications of fast simulation methods used in queueing theory to solve some high-dimension combinatorial problems in case the other approaches fail.