An Introduction to Queueing Theory - Modeling and Analysis in Applications
by U. Narayan Bhat


Book Description
This introductory textbook is designed for a one-semester course on queueing theory that does not require a course in stochastic processes as a prerequisite. Oftentimes students in applied disciplines such as computer science, operations research, and engineering do not take a course on queueing theory because it requires a prerequisite course on stochastic processes; or they take a course without the necessary background and learn as one would use a cookbook. By integrating the necessary background on stochastic processes with the analysis of models, this book provides a sound foundational introduction to the modeling and analysis of queueing systems for a broad interdisciplinary audience.
Key features:
* An introductory chapter including a historical account of the growth of queueing theory in the last 100 years.
* A modeling-based approach with emphasis on identification of models using topics such as collection of data and tests for stationarity and independence of observations.
* Rigorous treatment of the foundations of basic models commonly used in applications with appropriate references for advanced topics.
* A chapter on modeling and analysis using computational tools.
* A comprehensive treatment of statistical inference for queueing systems.
* A discussion of operational and decision problems.
* Modeling exercises as a motivational tool, and review exercises covering background material on statistical distributions.
* Minimal prerequisites: calculus with some differential equations and an undergraduate course in probability and statistics.
* Appendices containing essential background material.
From the reviews:

"This is a new addition to the literature in Queueing Theory, which has been a subject area of intense interest because of its theoretical [richness] and wide applicability. This book has brought a freshness and novelty as it deals mainly with modeling and analysis in applications as well as with statistical inference for queueing problems. The book includes basics of stochastic processes and some mathematical topics, in addition to a chapter written by two computer scientists on modeling and analysis using computational tools, with useful simulation programs...With his 40 years of valuable experience in teaching and high level research in this subject area, Professor Bhat has been able to achieve what he aimed: to make [the work] somewhat different in content and approach from other books."—Assam Statistical Review

“The huge range of applications makes queueing theory an interesting object of study for students of mathematics, computer science, operations research and engineering. This book is an introduction to queueing theory. … The book also contains 3 appendices about Poisson and Markov processes and other background material … . the extensive bibliography of the queueing literature (202 references) which is given at the end of the book … help readers to further their research.” (Slobodanka S. Mitrović, Mathematical Reviews, Issue 2010 a)

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Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Basic System Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Problems in a Queueing System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 A Historical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Modeling Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 System Element Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1 Probability Distributions as Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 Deterministic Distribution (D) . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.2 Exponential distribution; Poisson process (M) . . . . . . . . . . . . 14
2.2 Identification of Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.1 Collection of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2 Tests for Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.3 Tests for Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.4 Distribution Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Review Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Basic Concepts in Stochastic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1 Stochastic Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Point, Regenerative, and Renewal Processes . . . . . . . . . . . . . . . . . . . . 23
3.3 Markov Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4 Simple Markovian Queueing Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.1 A General Birth-and-Death Queueing Model . . . . . . . . . . . . . . . . . . . . 29
4.2 The Queue M/M/1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2.1 Departure Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.3 The Queue M/M/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.4 The Finite Queue M/M/s/K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.5 The Infinite-Server Queue M/M/∞. . . . . . . . . . . . . . . . . . . . . . . . . . . 58
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12 Modeling and Analysis Using Computational Tools . . . . . . . . . . . . . . . . 207
12.1 Mean Value Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
12.2 The Convolution Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
12.2.1 Computing Other Performance Measures . . . . . . . . . . . . . . . . 213
12.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
12.4 MATLAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
12.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223