Fundamentals of Queueing Theory

Fundamentals of Queueing Theory


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Product Details

ISBN-13: 9781118943526
Publisher: Wiley
Publication date: 04/10/2018
Series: Wiley Series in Probability and Statistics Series , #399
Pages: 576
Product dimensions: 6.20(w) x 9.10(h) x 1.30(d)

About the Author

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.

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Table of Contents

Dedication     v
Preface     xi
Acknowledgments     xiii
Introduction     1
Description of the Queueing Problem     2
Characteristics of Queueing Processes     3
Notation     7
Measuring System Performance     8
Some General Results     9
Simple Data Bookkeeping for Queues     12
Poisson Process and the Exponential Distribution     16
Markovian Property of the Exponential Distribution     20
Stochastic Processes and Markov Chains     24
Introduction to the QtsPlus Software     40
Problems     41
Simple Markovian Queueing Models     49
Birth-Death Processes     49
Single-Server Queues (M/M/1)     53
Multiserver Queues (M/M/c)     66
Choosing the Number of Servers     73
Queues with Truncation (M/M/c/K)     76
Erlang's Loss Formula (M/M/c/c)     81
Queues with Unlimited Service (M/M/[infinity])     84
Finite-Source Queues     85
State-Dependent Service     91
Queues with Impatience     95
Transient Behavior     97
Busy-Period Analysis     102
Problems     103
Advanced Markovian Queueing Models     117
Bulk Input (M[superscript X]/M/1)     117
Bulk Service (M/M[superscript Y]/1)     123
Erlangian Models     128
Priority Queue Disciplines     141
Retrial Queues     157
Problems     171
Networks, Series, and Cyclic Queues     179
Series Queues     181
Open Jackson Networks     187
Closed Jackson Networks     195
Cyclic Queues     209
Extensions of Jackson Networks     210
Non-Jackson Networks     212
Problems     214
General Arrival or Service Patterns     219
General Service, Single Server (M/G/1)     219
General Service, Multiserver (M/G/c/[infinity], M/G/[infinity])     254
General Input (G/M/1, G/M/c)     259
Problems     270
General Models and Theoretical Topics     277
G/E[subscript k]/1, G[superscript k]/M/1, and G/PH[subscript k]/1     277
General Input, General Service (G/G/1)     284
Poisson Input, Constant Service, Multiserver (M/D/c)     294
Semi-Markov and Markov Renewal Processes in Queueing      296
Other Queue Disciplines     301
Design and Control of Queues     306
Statistical Inference in Queueing     317
Problems     325
Bounds and Approximations     329
Bounds     330
Approximations     343
Network Approximations     356
Problems     367
Numerical Techniques and Simulation     369
Numerical Techniques     369
Numerical Inversion of Transforms     385
Discrete-Event Stochastic Simulation     398
Problems     421
References     427
Symbols and Abbreviations     439
Tables     447
Transforms and Generating Functions     455
Laplace Transforms     455
Generating Functions     462
Differential and Difference Equations     467
Ordinary Differential Equations     467
Difference Equations     483
QtsPlus Software     489
Instructions for Downloading     493
Index     495

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From the Publisher

"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

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