Fundamentals of Queueing Theory (eBook)

DONALD GROSS, PhD, is Distinguished Research Professor ofOperations Research and Engineering at George Mason University andProfessor Emeritus of Operations Research at The GeorgeWashingtonUniversity. With over forty years of experience inacademia and consulting, Dr. Gross has published extensively in thearea of queueing applications to repairable item inventory control,air traffic control, and Internet congestion. JOHN F. SHORTLE, PhD, is Associate Professor in theDepartment of Systems Engineering and Operations Research at GeorgeMason University. He has authored or coauthored over thirtypublished articles on the application of simulation and queueingtheory in telecommunications and aviation. JAMES M. THOMPSON is an Enterprise Architect at theFederal Home Loan Mortgage Corporation. His current areas ofresearch interest include computer system performance modeling,system capacity studies and benchmarking, information architecture,and computational finance. The Late CARL M. HARRIS, PhD, was BDM InternationalProfessor and the founding chair of the Systems Engineering andOperations Research Department at George Mason University. For hisresearch contributions to the areas of applied probability andstatistics, queueing theory, simulation, and public systemsanalysis, Dr. Harris was awarded the George E. Kimball Medal by theInstitute for Operations Research and the Management Sciences(INFORMS) in 1999.

Dedication.

Preface.

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.

Problems.

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.

Problems.

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.

Problems.

8. Numerical Techniques and Simulation.

8.1 Numerical Techniques.

8.2 Numerical Inversion of Transforms.

8.3 Discrete-Event Stochastic Simulation.

Problems.

Bibliography.

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.

"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)"This exceptional book is a most welcome text for advanceduniversity undergraduate and/or graduate students. It is built onthe solid foundation of the three previous widely acclaimededitions since 1975 that have been among the few cornerstones oftexts in the field. The new edition contains a superb blend oftheoretical and contemporary real-world examples."
-Dr. Percy Brill, Department of Management Science andDepartment of Mathematics and Statistics, University of Windsor