Introduction. Exponential Interarrival and Service Times:
Closed-Form Expressions.
Exponential Interarrival and Service Times: Numerical Techniques
and Approximations. General Interarrival and/or Service Times:
Closed-Form Expressions and Approximations. Multiclass Queues under
Various Service Disciplines. Exact Results in Network of Queues:
Product Form. Approximations for General Queueing Networks. Fluid
Models for Stability, Approximations, and Analysis of Time-Varying
Queues. Stochastic Fluid-Flow Queues: Characteristics and Exact
Analysis. Stochastic Fluid-Flow Queues: Bounds and Tail
Asymptotics. Appendix A: Random Variables. Appendix B: Stochastic
Processes. References. Index.
Natarajan Gautam
"The breadth and scope of topics in this book surpass the books
currently on the market. For most graduate engineering or business
courses on this topic the selection is perfect. … presented in
sufficient depth for any graduate class. I like in particular the
"problems" presented at regular intervals, along with detailed
solutions. … excellent coverage of both classical and modern
techniques in queueing theory. Compelling applications and case
studies are sprinkled throughout the text. For many of us who teach
graduate courses in queueing theory, this is the text we have been
waiting for!"
—John J. Hasenbein, The University of Texas at Austin"Dr. Gautam
has an obvious passion for queueing theory. His delight in
presenting queueing paradoxes beams through the pages of the book.
His relaxed conversational style makes reading the book a pleasure.
His introductory comments about having to account for a large
variety of educational backgrounds among students taking graduate
courses indicate that he takes education very seriously. It shows
throughout the book. He has made an excellent choice of topics and
presented them in his own special style. I highly recommend this
queueing text by an expert who clearly loves his field."
—Dr. Myron Hlynka, University of Windsor, Ontario, Canada"… will be
a good addition to my collection of books on queueing theory."
—Attahiru S. Alfa, University of Manitoba, Canada"Queueing systems
are widely used to provide stochastic modelling of many problems
arising in computer, communication and transportation networks,
manufacturing, and waiting lines in daily life. This book presents
a survey of results and methods of queueing theory, and a basic
exposition of the most commonly used stochastic processes such as
discrete-time Markov chains (DTMCs), continuous-time Markov chains
(CTMCs), semi-Markov and Markov regenerative processes, Brownian
motion and Itˆo calculus; still, some topics, e.g. simulation and
parameter fitting in queueing models, are barely mentioned. The book
was conceived by its author as a book written for students, and
thus an important feature of the presentation is the systematic use
of solved examples.The book is divided into ten chapters and two
appendices, which could be used by instructors in two courses: a
basic course, covering the appendices and Chapters 1 through 4; and
an advanced course, covering Chapters 5 through 10. Each chapter is
concluded by bibliographical comments and a list of exercises. The
prerequisite for the book is an undergraduate course on
probability. Almost all material in Chapters 1 through 6 can be
found in many excellent texts, such as Queueing methods. For
services and manufacturing by R. W. Hall [Prentice Hall, Englewood
Cliffs, NJ, 1991], Modelling and analysis of stochastic systems by
V. G. Kulkarni [Texts Statist. Sci. Ser., Chapman and Hall, London,
1995; MR1357414] and Fundamentals of queueing theory by D. Gross et
al. [fourth edition, Wiley Ser. Probab. Stat., Wiley, Hoboken, NJ,
2008; MR2446330], among others. Chapters 7 through 10 are closely
related to some selected papers and a few texts, including the
excellent monographs Large deviations for performance analysis by
A. Shwartz and A. Weiss [Stochastic Model. Ser., Chapman & Hall,
London, 1995; MR1335456], Fundamentals of queueing networks by H.
Chen and D. D. W. Yao [Appl. Math. (N. Y.), 46, Springer, New York,
2001; MR1835969] and Stochastic-process limits by W. Whitt
[Springer Ser. Oper. Res., Springer, New York, 2002; MR1876437].To
start with, Chapter 1 presents introductory remarks about the
analysis of queues, by addressing three questions: Where has
analysis of queues been successfully used?What do we need as inputs
to do the analysis and what can we expect as outputs?How do we plan
to go about analysing queues? Chapter 1 also presents key results
and fundamental queueing notations. In Chapter 2, the interest is
in the use of CTMCs in the analysis of classical queueing models,
and how to solve balance equations by using generating functions
and reversibility principles. Unlike Chapter 2 where the focus is
on exact/closed algebraic expressions, Chapter 3 explains some
numerical techniques, mostly based on matrix analysis, followed by
some approximations. In this setting, a fundamental structure is
the quasi-birth-death (QBD) Markov chain, the matrix geometric
solution of a QBD process and the computational treatment of
finite-state Markov chains. Chapter 4 focusses on how to analyse
queues where inter-arrival and/or service times are generally
distributed. To that end, the author first describes the
fundamentals involved in DTMCs and uses them in two classical
systems, the M/G/1 and GI/M/1 queues, via embedded Markov chains.
The mean value analysis (MVA) approach is then used to obtain
approximations when the queueing system cannot easily be modelled
as a suitably defined stochastic process. MVA is combined with other
techniques to derive bounds and approximations for average
performance measures in G/G/s queues, and exact results for various
different models (M/G/∞, processor sharing service discipline,
M/G/s/s) are derived by using more specific methods. For multiclass
systems, Chapter 5 addresses how to evaluate performance measures
of various service disciplines (for example, exhaustive polling,
gated policy, limited service in polling systems; and shortest
processing time, preemptive shortest job first and shortest
remaining processing time schemes in the M/G/1 queue), and how to
decide the order of service in terms of optimal policies. Chapter 6
explains how to deal with networks of queues by using product-form
solutions for the joint distribution for the number of customers in
each node, under a variety of distributional assumptions such as
Jackson networks, Jackson-like networks with deterministic routing,
multiclass networks and loss networks. Material in Chapters 7
through 10 can be seen as advanced and results are mainly derived
from the use of more complex stochastic processes than Markov
chains. In that spirit, Chapter 7 presents approximations based on
reflected Brownian motions, which make it possible to model using
the mean and variance of the inter-arrival time as well as service
time at each queue of a general queueing network, hence making
these techniques easy to implement. The notion of fluid queue is
analysed in Chapters 8 through 10, but there is very little
commonality between what are called fluid queues in Chapter 8 and
what are called fluid queues in Chapters 9 and 10. More
particularly, Chapter 8 considers deterministic fluid queues where
the flow rates are mostly constant or vary deterministically over
time, whereas the emphasis in Chapters 9 and 10 is on stochastic
fluid queues where flow rates, from a countable set, are piecewise
constant and vary stochastically over time. Two appendices act as a
refresher on the topic of random variables and stochastic
processes, as well as a point of clarification for notation.Analysis
of queues is written to teach students and professionals how to use
basic concepts of queueing theory to solve queuing problems from
the stochastic perspective, but without going into detail on the
underlying stochastic processes. The book is written in simple
language, the techniques are comprehensible for the reader and all
important questions are illustrated with examples or a few case
studies, such as staffing and work-assignment in call centres
(Chapter 4), hospital emergency ward planning (Chapter 5),
automobile service station (Chapter 6), and network interface card
in cluster computing (Chapter 7). Understanding the contents of
this book does not require a background in advanced concepts of
probability, and the exercises at the end of each chapter can help
the reader master queueing techniques."{For the 2012 original see
[N. Gautam, Analysis of queues: methods and applications, CRC
Press, Boca Raton, FL, 2012].} - Antonio G´omez-Corral -
Mathematical Reviews Clippings - November 2018
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