Fundamentals of Queueing Theory, 3rd Edition

by Donald Gross (George Mason University, Virginia); Carl M. Harris (George Mason University, Virginia)

• ISBN13: 9780471170839
• ISBN10: 0471170836
• Edition: 3rd
• Format: Hardcover
• Copyright: 1998-02-01
• Publisher: Wiley-Interscience

Summary

This look at queueing theory stresses the fundamentals of the analytic modeling of queues. It features Excel and Quattro software that allows greater flexibility in the understanding of the nature, sensitivities and responses of waiting- line systems to parameter and environmental changes."...this is one of the best books available for use as a textbook for a course and for an applied reference book. Its excellent organizational structure allows quick reference to specific models and its clear presentation coupled with the use of the QTS software solidifies the understanding of the concepts being presented. I highly recommend this book to educators and applied researchers."--IEE Transactions on Operations Engineering

Author Biography

DONALD GROSS is Research Professor in the Department of Operations Research and Engineering at George Mason University in Fairfax, Virginia. CARL M. HARRIS is BDM Professor of Operations Research and Associate Dean of the School of Information Technology and Engineering at George Mason University. Both authors have written extensively in the area of numerical solutions to stochastic operations research problems.

Table of Contents

Preface	ix
1. Introduction	1	(52)
1.1. Description of the Queueing Problem	1	(2)
1.2. Characteristics of Queueing Processes	3	(4)
1.3. Notation	7	(2)
1.4. Measuring System Performance	9	(1)
1.5. Some General Results	10	(3)
1.6. Simple Data Bookkeeping for Queues	13	(3)
1.7. Poisson Process and the Exponential Distribution	16	(6)
1.8. Markovian Property of the Exponential Distribution	22	(4)
1.9. Stochastic Processes and Markov Chains	26	(19)
1.10. Steady-State Birth-Death Processes	45	(2)
Problems	47	(6)
2. Simple Markovian Birth-Death Queueing Models	53	(63)
2.1. Steady-State Solution for the M/M/1 Model	53	(3)
2.2. Methods of Solving Steady-State Difference Equations	56	(13)
2.3. Queues with Parallel Channels (M/M/c)	69	(5)
2.4. Queues with Parallel Channels and Truncation (M/M/c/K)	74	(6)
2.5. Erlang's Formula (M/M/c/c)	80	(1)
2.6. Queues with Unlimited Service (M/M/XXX)	81	(1)
2.7. Finite Source Queues	82	(7)
2.8. State-Dependent Service	89	(4)
2.9. Queues with Impatience	93	(2)
2.10. Transient Behavior	95	(7)
2.11. Busy-Period Analyses for M/M/1 and M/M/c	102	(2)
Problems	104	(12)
3. Advanced Markovian Queueing Models	116	(49)
3.1. Bulk Input (M[x]/M/1)	116	(6)
3.2. Bulk Service (M/M[Y]/1)	122	(5)
3.3. Erlangian Models (M/E(k)/1, E(k)/M/1, E(j)/E(k)/1)	127	(14)
3.4. Priority Queue Disciplines	141	(18)
Problems	159	(6)
4. Networks, Series, and Cyclic Queues	165	(44)
4.1. Series Queues	167	(7)
4.2. Open Jackson Networks	174	(9)
4.3. Closed Jackson Networks	183	(16)
4.4. Cyclic Queues	199	(1)
4.5. Extensions of Jackson Networks	200	(2)
4.6. Non-Jackson Networks	202	(2)
Problems	204	(5)
5. Models with General Arrival or Service Patterns	209	(57)
5.1. Single-Server Queues with Poisson Input and General Service (M/G/1)	209	(33)
5.2. Multiserver Queues with Poisson Input and General Service	242	(6)
5.3. General Input and Exponential Service	248	(12)
Problems	260	(6)
6. More General Models and Theoretical Topics	266	(60)
6.1. G/E(k)/1, G[k]/M/1, and G/PH(k)/1	266	(8)
6.2. General Input, General Service (G/G/1)	274	(12)
6.3. Multichannel Queues with Poisson Input and Constant Service (M/D/c)	286	(2)
6.4. Semi-Markov and Markov Renewal Processes in Queueing	288	(6)
6.5. Other Queue Disciplines	294	(6)
6.6. Design and Control of Queues	300	(12)
6.7. Statistical Inference in Queueing	312	(9)
Problems	321	(5)
7. Bounds, Approximations, Numerical Techniques, and Simulation	326	(76)
7.1. Bounds and Inequalities	326	(14)
7.2. Approximations	340	(12)
7.3. Numerical Techniques	352	(18)
7.4. Discrete-Event Stochastic Simulation	370	(26)
Problems	396	(6)
References	402	(13)
Appendix 1. Symbols and Abbreviations	415	(8)
Appendix 2. Summary of Models Treated and Types of Results	423	(4)
Appendix 3. QTS Software	427	(6)
Index	433