Analysis of Queues: Methods and Applications (Hardback) book cover

Analysis of Queues

Methods and Applications

By Natarajan Gautam

© 2012 – CRC Press

802 pages | 141 B/W Illus.

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About the Book

Written with students and professors in mind, Analysis of Queues: Methods and Applications combines coverage of classical queueing theory with recent advances in studying stochastic networks. Exploring a broad range of applications, the book contains plenty of solved problems, exercises, case studies, paradoxes, and numerical examples.

In addition to the standard single-station and single class discrete queues, the book discusses models for multi-class queues and queueing networks as well as methods based on fluid scaling, stochastic fluid flows, continuous parameter Markov processes, and quasi-birth-and-death processes, to name a few. It describes a variety of applications including computer-communication networks, information systems, production operations, transportation, and service systems such as healthcare, call centers and restaurants.


"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

Table of Contents


Analysis of Queues: Where, What, and How?

Systems Analysis: Key Results

Queueing Fundamentals and Notations

Psychology in Queueing

Reference Notes


Exponential Interarrival and Service Times: Closed-Form Expressions

Solving Balance Equations via Arc Cuts

Solving Balance Equations Using Generating Functions

Solving Balance Equations Using Reversibility

Reference Notes


Exponential Interarrival and Service Times: Numerical Techniques and Approximations

Multidimensional Birth and Death Chains

Multidimensional Markov Chains

Finite-State Markov Chains

Reference Notes


General Interarrival and/or Service Times: Closed-Form Expressions and Approximations

Analyzing Queues Using Discrete Time Markov Chains

Mean Value Analysis

Bounds and Approximations for General Queues

Matrix Geometric Methods for G/G/s Queues

Other General Queues but with Exact Results

Reference Notes


Multiclass Queues under Various Service Disciplines


Evaluating Policies for Classification Based on Types: Priorities

Evaluating Policies for Classification Based on Location: Polling Models

Evaluating Policies for Classification Based on Knowledge of Service Times

Optimal Service-Scheduling Policies

Reference Notes


Exact Results in Network of Queues: Product Form

Acyclic Queueing Networks with Poisson Flows

Open Jackson Networks

Closed Jackson Networks

Other Product-Form Networks

Reference Notes


Approximations for General Queueing Networks

Single-Server and Single-Class General Queueing Networks

Multiclass and Multiserver Open Queueing Networks with FCFS

Multiclass and Single-Server Open Queueing Networks with Priorities

Reference Notes


Fluid Models for Stability, Approximations, and Analysis of Time-Varying Queues

Deterministic Fluid Queues: An Introduction

Fluid Models for Stability Analysis of Queueing Networks

Diffusion Approximations for Performance Analysis

Fluid Models for Queues with Time-Varying Parameters

Reference Notes


Stochastic Fluid-Flow Queues: Characteristics and Exact Analysis


Single Buffer with Markov Modulated Fluid Source

First Passage Times

Reference Notes


Stochastic Fluid-Flow Queues: Bounds and Tail Asymptotics

Introduction and Preliminaries

Performance Analysis of a Single Queue

Multiclass Fluid Queues

Reference Notes


Appendix A: Random Variables

Appendix B: Stochastic Processes



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Subject Categories

BISAC Subject Codes/Headings:
BUSINESS & ECONOMICS / Operations Research
MATHEMATICS / Probability & Statistics / Bayesian Analysis