Fundamentals of Queueing Theory

John F. Shortle, PhD, is Professor in the Department of Systems Engineering and Operations Research at George Mason University. James M. Thompson is an Enterprise Architect at the Federal Home Loan Mortgage Corporation. Donald Gross, PhD, is Professor emeritus, The George Washington University, and was Distinguished Research Professor of Operations Research and Engineering at George Mason University. 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.

• Preface ixAcknowledgments xiAbout the Companion Website xiii1 Introduction 11.1 Measures of System Performance 21.2 Characteristics of Queueing Systems 41.3 The Experience of Waiting 91.4 Little’s Law 101.5 General Results 191.6 Simple Bookkeeping for Queues 221.7 Introduction to the QtsPlus Software 26Problems 272 Review of Stochastic Processes 352.1 The Exponential Distribution 352.2 The Poisson Process 392.3 Discrete-Time Markov Chains 492.4 Continuous-Time Markov Chains 62Problems 693 Simple Markovian Queueing Models 733.1 Birth-Death Processes 733.2 Single-Server Queues (M=M=1) 773.3 Multiserver Queues (M=M=c) 903.4 Choosing the Number of Servers 973.5 Queues with Truncation (M=M=c=K) 1003.6 Erlang’s Loss Formula (M=M=c=c) 1053.7 Queues with Unlimited Service (M=M=1) 1083.8 Finite-Source Queues 1093.9 State-Dependent Service 1153.10 Queues with Impatience 1193.11 Transient Behavior 1213.12 Busy-Period Analysis 126Problems 1274 Advanced Markovian Queueing Models 1474.1 Bulk Input (M[X]=M=1) 1474.2 Bulk Service (M=M[Y ]=1) 1534.3 Erlang Models 1584.4 Priority Queue Disciplines 1724.5 Retrial Queues 191Problems 2045 Networks, Series, and Cyclic Queues 2135.1 Series Queues 2155.2 Open Jackson Networks 2215.3 Closed Jackson Networks 2295.4 Cyclic Queues 2435.5 Extensions of Jackson Networks 2445.6 NonJackson Networks 246Problems 2486 General Arrival or Service Patterns 2556.1 General Service, Single Server (M=G=1) 2556.2 General Service, Multiserver (M=G=c=_,M=G=1) 2906.3 General Input (G=M=1, G=M=c) 295Problems 3067 General Models and Theoretical Topics 3137.1 G=Ek=1, G[k]=M=1, and G=PHk=1 3137.2 General Input, General Service (G=G=1) 3207.3 Poisson Input, Constant Service, Multiserver (M=D=c) 3307.4 Semi-Markov and Markov Renewal Processes in Queueing 3327.5 Other Queue Disciplines 3377.6 Design and Control of Queues 3427.7 Statistical Inference in Queueing 353Problems 3618 Bounds and Approximations 3658.1 Bounds 3668.2 Approximations 3788.3 Deterministic Fluid Queues 3928.4 Network Approximations 400Problems 4119 Numerical Techniques and Simulation 4179.1 Numerical Techniques 4179.2 Numerical Inversion of Transforms 4339.3 Discrete-Event Stochastic Simulation 446Problems 469References 475Appendix A: Symbols and Abbreviations 487Appendix B: Tables 495Appendix C: Transforms and Generating Functions 503C.1 Laplace Transforms 503C.2 Generating Functions 510Appendix D: Differential and Difference Equations 515D.1 Ordinary Differential Equations 515D.2 Difference Equations 531Appendix E: QtsPlus Software 537E.1 Instructions for Downloading 540Index 541

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