Skip to main content

Fundamentals of Queueing Theory, 4th Edition

Donald Gross, John F. Shortle, James M. Thompson, Carl M. Harris

ISBN: 978-1-118-62565-1 May 2013 528 Pages



Praise for the Third Edition

"This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."
IIE Transactions on Operations Engineering

Thoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.

This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:

  • Retrial queues

  • Approximations for queueing networks

  • Numerical inversion of transforms

  • Determining the appropriate number of servers to balance quality and cost of service

Each chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.

With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Related Resources


View Instructor Companion Site

Contact your Rep for all inquiries



1. Introduction.

1.1 Description of the Queueing Problem.

1.2 Characteristics of Queueing Processes.

1.3 Notation.

1.4 Measuring System Performance.

1.5 Some General Results.

1.6 Simple Data Bookkeeping for Queues.

1.7 Poisson Process and the Exponential Distribution.

1.8 Markovian Property of the Exponential Distribution.

1.9 Stochastic Processes and Markov Chains.


2. Simple Markovian Queueing Models.

2.1 Birth Death Processes.

2.2 Single-Server Queues (M/M/1).

2.3 Multi-Server Queues (M/M/c).

2.4 Choosing the Number of Servers.

2.5 Queues with Truncation (M/M/c/K).

2.6 Erlang?s Loss Formula (M/M/c/c).

2.7 Queues with Unlimited Service (M/M/1).

2.8 Finite Source Queues.

2.9 State-Dependent Service.

2.10 Queues with Impatience.

2.11 Transient Behavior.

2.12 Busy-Period Analysis.


3. Advanced Markovian Queueing Models.

3.1 Bulk Input (M[X]/M/1).

3.2 Bulk Service (M/M[Y ]/1).

3.3 Erlangian Models.

3.4 Priority Queue Disciplines.

3.5 Retrial Queues.

4. Networks, Series, and Cyclic Queues.

4.1 Series Queues.

4.2 Open Jackson Networks.

4.3 Closed Jackson Networks.

4.4 Cyclic Queues.

4.5 Extensions of Jackson Networks.

4.6 Non-Jackson Networks.

5. General Arrival or Service Patterns.

5.1 General Service, Single Server (M/G/1).

5.2 General Service, Multi-Server (M/G/c/ú, M/G/1).

5.3 General Input (G/M/1, G/M/c).

6. More General Models and Theoretical Topics.

6.1 G/Ek/1, G[k]/M/1, and G/PHk/1.

6.2 General Input, General Service (G/G/1) .

6.3 Multichannel Queues with Poisson Input and Constant Service (M/D/c).

6.4 Semi-Markov and Markov Renewal Processes in Queueing.

6.5 Other Queue Disciplines.

6.6 Design and Control of Queues.

6.7 Statistical Inference in Queueing.

7. Bounds and Approximations.

7.1 Bounds.

7.2 Approximations.

7.3 Network Approximations.


8. Numerical Techniques and Simulation.

8.1 Numerical Techniques.

8.2 Numerical Inversion of Transforms.

8.3 Discrete-Event Stochastic Simulation.



Appendix 1. Symbols and Abbreviations.

Appendix 2. Tables.

Appendix 3. Transforms and Generating Functions.

A3.1 Laplace Transforms.

A3.2 Generating Functions.

Appendix 4. Differential and Difference Equations.

A4.1 Ordinary Differential Equations.

A4.2 Difference Equations.

Appendix 5. QTSPlus Software.

A5.1 Instructions for Downloading.

  • New material and discussions on call centers, numerical techniques (such as TAM, TRM, and LC), and simulation have been added. 
  • Spreadsheet programs for Excel and Quattro are available on a companion WWW site while additional software programs are showcased and spread throughout the written text
"Despite its title, the book is rather advanced, so it is appropriate for practitioners, those in academia, and upper-class students. However, any reader will benefit from the concise introductions to the problems, the detailed descriptions supported with step-by-step formulas, the solutions provided by the manual, and the QtsPlus software." (Computing Reviews, 1 December 2011)

"This is an accessible and attractive book with good writing all the way through. It has the advantage of years of classroom testing. The exercises are extensive and creative." (MAA Reviews, March 19, 2009)

  • Illustrative examples and exercises are employed to use with Excel, Quattro, and other popular software programs. 
  • Equations are boxed for easy reference and instant recall. 
  • Chapter problems are included and graded accordingly. 
  • An accompanying Student Solutions Manual is available for purchase, and an extensive Instructor's Manual is also available upon request.