Fundamentals of Queueing Theory

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

• ISBN13: 9780471791270
• ISBN10: 047179127X
• Edition: 4th
• Format: Hardcover
• Copyright: 2008-08-11
• Publisher: Wiley-Interscience

Summary

This revised and expanded edition of Fundamentals of Queueing Theory presents the analytic modeling of queues using up-to-date examples. Though the detailed coverage of the fundamentals of analytic modeling remains virtually the same, this new edition contains additional material (call centers and simulation), discussions (Transform Approximation Method and Level Crossing Analysis), and exercises. A fresh emphasis on the telecommunications boom enlivens the text, and spreadsheet programs for Excel and Quattro on the book's related Web site aids in understanding the sensitivity of waiting-line systems to parameter and environmental changes. Software programs for additional systems are spread throughout the text. In the treatment of the advanced material, the authors have commingled mathematical details with numerical results and intuitive arguments. Related website http://mason.gmu.edu/~jshortle/fqt4th.html

Author Biography

Donald Gross, PhD, is Distinguished Research Professor of Operations Research and Engineering at George Mason University and Professor Emeritus of Operations Research at The George WashingtonUniversity. With over forty years of experience in academia and consulting, Dr. Gross has published extensively in the area of queueing applications to repairable item inventory control, air traffic control, and Internet congestion. JOHN F. SHORTLE, PhD, is?Associate Professor in the Department of Systems Engineering and Operations Research at George Mason University. He has authored or coauthored over thirty published articles on the application of simulation and queueing theory in telecommunications and aviation. JAMES M. THOMPSON is an Enterprise Architect at the Federal Home Loan Mortgage Corporation. His current areas of research interest include computer system performance modeling, system capacity studies and benchmarking, information architecture, and computational finance. The Late CARL M. HARRIS, PhD, was BDM International Professor and the founding chair of the Systems Engineering and Operations Research Department at George Mason University. For his research contributions to the areas of applied probability and statistics, queueing theory, simulation, and public systems analysis, Dr. Harris was awarded the George E. Kimball Medal by the Institute for Operations Research and the Management Sciences (INFORMS) in 1999.

Table of Contents

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