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Library of Congress Control Number: 2019955378
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ISBN 978-1-78945-001-9
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PE1 Mathematics
PE1_21 Application of mathematics in industry and society
Preface
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 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 1 is 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 2 deals 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, 7 and 10.
Chapter 3 includes 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 10 is 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 – 4 and 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 8 gives 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 6 deals with the applications of fast simulation methods used in queueing theory to solve some high-dimension combinatorial problems in case the other approaches fail.
A survey on the analysis of a strong stability method and its applications to queueing systems and networks and some perspectives are considered in Chapter 9.
The second volume of the book will include the additional chapters devoted to some other contemporary directions of the analysis of queueing models.
The volumes will be useful for graduate and PhD students, lecturers, and also the researchers and developers working in mathematical and stochastic modelling and various applications in computer and communication networks, science and engineering in the departments of Mathematics & Applied Mathematics, Statistics, or Operations Research at universities and in various research and applied centres.
Dedication to Igor Mykolayovych Kovalenko who died shortly after
