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<p>Preface ix</p> <p>Acknowledgments xi</p> <p>About the Companion Website xiii</p> <p><b>1 Introduction 1</b></p> <p>1.1 Measures of System Performance 2</p> <p>1.2 Characteristics of Queueing Systems 4</p> <p>1.3 The Experience of Waiting 9</p> <p>1.4 Little’s Law 10</p> <p>1.5 General Results 19</p> <p>1.6 Simple Bookkeeping for Queues 22</p> <p>1.7 Introduction to the QtsPlus Software 26</p> <p>Problems 27</p> <p><b>2 Review of Stochastic Processes 35</b></p> <p>2.1 The Exponential Distribution 35</p> <p>2.2 The Poisson Process 39</p> <p>2.3 Discrete-Time Markov Chains 49</p> <p>2.4 Continuous-Time Markov Chains 62</p> <p>Problems 69</p> <p><b>3 Simple Markovian Queueing Models 73</b></p> <p>3.1 Birth-Death Processes 73</p> <p>3.2 Single-Server Queues <i>(M=M=1)</i> 77</p> <p>3.3 Multiserver Queues <i>(M=M=c)</i> 90</p> <p>3.4 Choosing the Number of Servers 97</p> <p>3.5 Queues with Truncation <i>(M=M=c=K)</i> 100</p> <p>3.6 Erlang’s Loss Formula <i>(M=M=c=c)</i> 105</p> <p>3.7 Queues with Unlimited Service <i>(M=M=1)</i> 108</p> <p>3.8 Finite-Source Queues 109</p> <p>3.9 State-Dependent Service 115</p> <p>3.10 Queues with Impatience 119</p> <p>3.11 Transient Behavior 121</p> <p>3.12 Busy-Period Analysis 126</p> <p>Problems 127</p> <p><b>4 Advanced Markovian Queueing Models 147</b></p> <p>4.1 Bulk Input <i>(M^[X]=M=1)</i> 147</p> <p>4.2 Bulk Service <i>(M=M_{[Y ]}=1)</i> 153</p> <p>4.3 Erlang Models 158</p> <p>4.4 Priority Queue Disciplines 172</p> <p>4.5 Retrial Queues 191</p> <p>Problems 204</p> <p><b>5 Networks, Series, and Cyclic Queues 213</b></p> <p>5.1 Series Queues 215</p> <p>5.2 Open Jackson Networks 221</p> <p>5.3 Closed Jackson Networks 229</p> <p>5.4 Cyclic Queues 243</p> <p>5.5 Extensions of Jackson Networks 244</p> <p>5.6 NonJackson Networks 246</p> <p>Problems 248</p> <p><b>6 General Arrival or Service Patterns 255</b></p> <p>6.1 General Service, Single Server <i>(M=G=1)</i> 255</p> <p>6.2 General Service, Multiserver <i>(M=G=c=_,M=G=1)</i> 290</p> <p>6.3 General Input <i>(G=M=1, G=M=c)</i> 295</p> <p>Problems 306</p> <p><b>7 General Models and Theoretical Topics 313</b></p> <p>7.1 <i>G=E_k=1, G^[k]=M=1, and G=PH_k=1</i> 313</p> <p>7.2 General Input, General Service <i>(G=G=1)</i> 320</p> <p>7.3 Poisson Input, Constant Service, Multiserver <i>(M=D=c)</i> 330</p> <p>7.4 Semi-Markov and Markov Renewal Processes in Queueing 332</p> <p>7.5 Other Queue Disciplines 337</p> <p>7.6 Design and Control of Queues 342</p> <p>7.7 Statistical Inference in Queueing 353</p> <p>Problems 361</p> <p><b>8 Bounds and Approximations 365</b></p> <p>8.1 Bounds 366</p> <p>8.2 Approximations 378</p> <p>8.3 Deterministic Fluid Queues 392</p> <p>8.4 Network Approximations 400</p> <p>Problems 411</p> <p><b>9 Numerical Techniques and Simulation 417</b></p> <p>9.1 Numerical Techniques 417</p> <p>9.2 Numerical Inversion of Transforms 433</p> <p>9.3 Discrete-Event Stochastic Simulation 446</p> <p>Problems 469</p> <p>References 475</p> <p><b>Appendix A: Symbols and Abbreviations 487</b></p> <p><b>Appendix B: Tables 495</b></p> <p><b>Appendix C: Transforms and Generating Functions 503</b></p> <p>C.1 Laplace Transforms 503</p> <p>C.2 Generating Functions 510</p> <p><b>Appendix D: Differential and Difference Equations 515</b></p> <p>D.1 Ordinary Differential Equations 515</p> <p>D.2 Difference Equations 531</p> <p><b>Appendix E: QtsPlus Software 537</b></p> <p>E.1 Instructions for Downloading 540</p> <p>Index 541</p>

<p> <strong>John F. Shortle, PhD,</strong> is Professor in the Department of Systems Engineering and Operations Research at George Mason University. <p> <strong>James M. Thompson</strong> is an Enterprise Architect at the Federal Home Loan Mortgage Corporation. <p> <strong>Donald Gross, PhD,</strong> is Professor emeritus, The George Washington University, and was Distinguished Research Professor of Operations Research and Engineering at George Mason University. <p> The late <strong>Carl M. Harris, PhD,</strong> was BDM International Professor and the founding chair of the Systems Engineering and Operations Research Department at George Mason University.

<p> <strong>The definitive guide to queueing theory and its practical applications—features numerous real-world examples of scientific, engineering, and business applications</strong> <p> Thoroughly updated and expanded to reflect the latest developments in the field, <em>Fundamentals of Queueing Theory, Fifth Edition</em> presents the statistical principles and processes involved in the analysis of the probabilistic nature of queues. Rather than focus narrowly on a particular application area, the authors illustrate the theory in practice across a range of fields, from computer science and various engineering disciplines to business and operations research. Critically, the text also provides a numerical approach to understanding and making estimations with queueing theory and provides comprehensive coverage of both simple and advanced queueing models. <p> As with all preceding editions, this latest update of the classic text features a unique blend of the theoretical and timely real-world applications. The introductory section has been reorganized with expanded coverage of qualitative/non-mathematical approaches to queueing theory, including a high-level description of queues in everyday life. New sections on non-stationary fluid queues, fairness in queueing, and Little's Law have been added, as has expanded coverage of stochastic processes, including the Poisson process and Markov chains. <ul> <li>Each chapter provides a self-contained presentation of key concepts and formulas, to allow readers to focus independently on topics relevant to their interests</li> <li>A summary table at the end of the book outlines the queues that have been discussed and the types of results that have been obtained for each queue</li> <li>Examples from a range of disciplines highlight practical issues often encountered when applying the theory to real-world problems</li> <li>A companion website features QtsPlus, an Excel-based software platform that provides computer-based solutions for most queueing models presented in the book.</li> </ul> <br> <p> Featuring chapter-end exercises and problems—all of which have been classroom-tested and refined by the authors in advanced undergraduate and graduate-level courses—<em>Fundamentals of Queueing Theory, Fifth Edition</em> is an ideal textbook for courses in applied mathematics, queueing theory, probability and statistics, and stochastic processes. This book is also a valuable reference for practitioners in applied mathematics, operations research, engineering, and industrial engineering.

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