8/10/2019 [First Author] 2003 Stochastic Models in Queueing Theory (Second Edition)

1/4

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.

XV

8/10/2019 [First Author] 2003 Stochastic Models in Queueing Theory (Second Edition)

2/4

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

8/10/2019 [First Author] 2003 Stochastic Models in Queueing Theory (Second Edition)

3/4

8/10/2019 [First Author] 2003 Stochastic Models in Queueing Theory (Second Edition)

4/4

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