[First Author] 2003 Stochastic Models in Queueing Theory (Second Edition)
Transcript of [First Author] 2003 Stochastic Models in Queueing Theory (Second Edition)
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Preface
Overview
The study of queueing models has been of considerable active interest ever
since the birth of queueing theo ry at the beginn ing of the last century. Q ueu e
ing theory continues to be one of the most extensive theories of stochastic
models. Its progress and development, both in methodology and in applica
t ions, are ever growing. Innovative analytic treatments toward its theoretical
developm ent are being advanced, an d newer areas of application are emerging .
There is a large and growing audience interested in the study of queueing
models. The level of background and preparation among them varies a great
deal, along with their requirements for depth of coverage. The audience is
composed of advanced undergraduate and graduate students from a number
of disciplines. In addition to students of standard graduate courses, there are
ma ny researchers, professionals, and in dus try analysts who require an in-de pth
know ledge of the subject.
The re are, of course, som e excellent advan cedworks ,mon ogra phs, and texts
on the subject as well. The rap id dev elopm ent of the subject dem and s upd ated
texts,
especially for the type of audience aimed at. Furthermore, the style of
presentation and the appro ach of individual auth ors appeal to different sections
of this large and varied aud ience .
The author feels that there is sufficient scope and material to warrant ad
ditional texts, especially at the graduate level, in this ever-growing subject
area. This bo ok has grown ou t of the au thor's long experience of teaching and
research in India, the U nited States, an d C ana da. A reviewer's glowing c om pli
m e n t
{in Am erican Mathema tical M onthly
on the au thor's first bo ok
Stochastic
rocesses(Wiley Eastern, and Halsted Wiley 1982) inspired th e auth or to un de r
take prep aration of
a
book on queueing models in a similar readable style.
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xvi Preface
Organization of the book
The bookisdivided into eight chapters . Cha pter is a sum m ary of basic results
in stochastic processes. This shou ld be helpful to users in eliminating the need
to refer frequently to other books on stochastic processes just for basic results.
Ch apte r 2, which is devoted to general con cepts, con tains som e discussions on
conc epts such as PASTA, sup erpo sition of arrival processes, and custom er and
time averages. Chapters 3 and 4 deal with birth-and-death queueing models
and non-birth-and-death systems, respectively. Transient behavior and busy
period analysis have been discussed at some length, and a uniformity of ap
proach is emphasized. Some models of bulk queues have also been included
because of their importance in transportation science. Chapter 5 is devoted
to network s of queues and C hapter 6 to certain no n-M arkov ian queueing sys
tems.
In Chapter 7, systems with both general arrival and service patterns are
discussed. Chapter 8 covers miscellaneous topics such as asymptotic methods
and queues with vacations, with a brief excursion into the design and control
of que ues. Diffusion app rox ima tions , which have eme rged as powerful tools,
have been discussed in some detail. We believe this chapter will be especially
useful to researchers and professionals w ho w ish to have a bro ad, general idea
of the diffusion appro ximation me thod s.
Each of the chapters (except Ch apte r 2) contains a nu m be r of worked e xam
ples and p roble ms , and all the cha pters includ e extensive and recent references.
The problems contain some materials that have been discussed, keeping in
m in d researchers and tho se wh o wish to pu rsue the subject further.
hanges to the new edition
In o rd er to facilitate use of the seco nd e ditio n by those wh o are already familiar
w ith th e first edition, a drastic change in the basic structur e has been avoided.
The number of chapters has been kept at eight, with considerable additions in
the broad topics mainly based on recent developments d urin g the intervening
years.
Ap art from inclusion of new topics (including some em erging durin g the
pa st few
years),
new examp les, and new pro blem s, topical discussions have been
expanded through notes, remarks, and so on. References have been updated.
These have been su pple me nted by related works of interest for further reading.
Ch apte rs 3, 6, and 8, in particular, conta in ma ny new topics. Some of the new
m atter s address finite inp ut sou rce and finite buffer mo dels, advanced vacation
models, retrial queueing systems, and a newly emerging trend in teletraffic
processes and their analyses. My sincere hope is that the book will be found
useful as a graduate text and also as a reference book by professionals and
researchers in this subject area.
In add ition to m athem atics and statistics, the book could be used for a one-
or two-semester course at the advanced undergraduate or graduate level in
operations research, computer science, systems science, industrial (and other
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xviii Preface
(reviewer of the first edition in
Mathematical Reviews
took great pains to
look into the first edition carefiiUy and was kind enough to offer concrete
suggestions for imp rov em ent. I am im men sely grateful to him . I would like to
tha nk Professors Sheldo n Ross, Svetlozar Rachev, Don ald Miller, Ch un Jin, and
Morteza Shafii-Mousavi, as well as Dr. Patrick L. Reilly (then with Motorola)
for their man y helpful co mm ents. I than kDr A. Borthakur, Dr. G. Chou dhu ry,
andDr K. K.
Das,
who helped m e with proo freading. My very special thank s are
du e to Dr. Das who alon g with M itra also manag ed m uc h of the typesetting in
LaTex with great efficiency. D eepa nkar prov ided m e with interesting ma terial
and references. Our grandson Riddhiman was a source of inspiration.
Last bu t no t least, I than k m y
wife,
Prity, wh o bore w ith m e patiently th roug h
the long hours that kept me engaged for m on ths an d m on ths and who seldom
complained of (or was tired of) waiting
Assistance from th e De pa rtm en t of Science and Technology, Go vernm ent of
India, is gratefully a cknow ledged. Th ank s are also due to M s. Barbara Ho lland,
M s.
Nancy Zachor, Mr. Tom Singer and other concerned individuals of
Academic Press for their care and cooperation.
July 1, 2002 Jyotiprasad M edh i