The definitive guide to queueing theory and its practical applications--features numerous real-world examples of scientific, engineering, and business applicationsThoroughly updated and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fifth Edition 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. 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.* Each chapter provides a self-contained presentation of key concepts and formulas, to allow readers to focus independently on topics relevant to their interests* 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* Examples from a range of disciplines highlight practical issues often encountered when applying the theory to real-world problems* A companion website features QtsPlus, an Excel-based software platform that provides computer-based solutions for most queueing models presented in the book.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--Fundamentals of Queueing Theory, Fifth Edition 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.

Acknowledgments 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 Qts Plus 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 NonJacksonNetworks 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 SemiMarkov 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