Fundamentals of Queueing Theory

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  • Edition: 4th
  • Format: Hardcover
  • Copyright: 2008-08-11
  • Publisher: Wiley-Interscience

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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

Dedicationp. v
Prefacep. xi
Acknowledgmentsp. xiii
Introductionp. 1
Description of the Queueing Problemp. 2
Characteristics of Queueing Processesp. 3
Notationp. 7
Measuring System Performancep. 8
Some General Resultsp. 9
Simple Data Bookkeeping for Queuesp. 12
Poisson Process and the Exponential Distributionp. 16
Markovian Property of the Exponential Distributionp. 20
Stochastic Processes and Markov Chainsp. 24
Introduction to the QtsPlus Softwarep. 40
Problemsp. 41
Simple Markovian Queueing Modelsp. 49
Birth-Death Processesp. 49
Single-Server Queues (M/M/1)p. 53
Multiserver Queues (M/M/c)p. 66
Choosing the Number of Serversp. 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 Queuesp. 85
State-Dependent Servicep. 91
Queues with Impatiencep. 95
Transient Behaviorp. 97
Busy-Period Analysisp. 102
Problemsp. 103
Advanced Markovian Queueing Modelsp. 117
Bulk Input (M[superscript X]/M/1)p. 117
Bulk Service (M/M[superscript Y]/1)p. 123
Erlangian Modelsp. 128
Priority Queue Disciplinesp. 141
Retrial Queuesp. 157
Problemsp. 171
Networks, Series, and Cyclic Queuesp. 179
Series Queuesp. 181
Open Jackson Networksp. 187
Closed Jackson Networksp. 195
Cyclic Queuesp. 209
Extensions of Jackson Networksp. 210
Non-Jackson Networksp. 212
Problemsp. 214
General Arrival or Service Patternsp. 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
Problemsp. 270
General Models and Theoretical Topicsp. 277
G/E[subscript k]/1, G[superscript k]/M/1, and G/PH[subscript k]/1p. 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 Queueingp. 296
Other Queue Disciplinesp. 301
Design and Control of Queuesp. 306
Statistical Inference in Queueingp. 317
Problemsp. 325
Bounds and Approximationsp. 329
Boundsp. 330
Approximationsp. 343
Network Approximationsp. 356
Problemsp. 367
Numerical Techniques and Simulationp. 369
Numerical Techniquesp. 369
Numerical Inversion of Transformsp. 385
Discrete-Event Stochastic Simulationp. 398
Problemsp. 421
Referencesp. 427
Symbols and Abbreviationsp. 439
Tablesp. 447
Transforms and Generating Functionsp. 455
Laplace Transformsp. 455
Generating Functionsp. 462
Differential and Difference Equationsp. 467
Ordinary Differential Equationsp. 467
Difference Equationsp. 483
QtsPlus Softwarep. 489
Instructions for Downloadingp. 493
Indexp. 495
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