Fundamentals Of Queueing Theory

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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. Special Features New material and discussions on call centers, numerical techniques (such as TAM, TRM, and LC), and simulation have been added. Spreadsheet programs for Excel and Quattro are available on a companion WWW site while additional software programs are showcased and spread throughout the written text. Illustrative examples and exercises are employed to use with Excel, Quattro, and other popular software programs. Equations are boxed for easy reference and instant recall. Chapter problems are included and graded accordingly. An extensive Instructor's Manual is also available upon request. About The Author Donald Gross is a Distinguished Research Professor in the Systems Engineering and Operations Research Department at George Mason University in Fairfax, Virginia. John F. Shortle is Assistant Professor in the Systems Engineering and Operations Research Department at George Mason University. James M. Thompson is a senior financial analyst for the Freddie Mac Corporation of Maryland. Carl M. Harris, prior to his death in 2000, was BDM Professor of Operations Research and Associate Dean of the School of Information Technology and Engineering at George Mason University. All the authors have extensive backgrounds in the area of numerical solutions to stochastic operations research problems. Table Of Contents Introduction. Description of the Queueing Problem. Characteristics of Queueing Processes. Notation. Measuring System Performance. Some General Results. Simple Data Bookkeeping for Queues. Poisson Process and the Exponential Distribution. Markovian Property of the Exponential Distribution. Markovian Property of the Exponential Distribution. Stochastic Processes and Markov Chains. Problems. Simple Markovian Queueing Models. Birth Death Processes. Single-Server Queues (M/M/1). Multi-Server Queues (M/M/c). Choosing the Number of Servers. Queues with Truncation (M/M/c/K). Erlang's Loss Formula (M/M/c/c). Queues with Unlimited Service (M/M/1). Finite Source Queues. Finite Source Queues. State-Dependent Service. Queues with Impatience. Transient Behavior. Busy-Period Analysis. Problems. Advanced Markovian Queueing Models. Bulk Input (M[X]/M/1). Bulk Service (M/M[Y ]/1). Erlangian Models. Priority Queue Disciplines. Retrial Queues. Networks, Series, and Cyclic Queues. Series Queues. Open Jackson Networks. Closed Jackson Networks. Cyclic Queues. Extensions of Jackson Networks. Non-Jackson Networks. General Arrival or Service Patterns. General Service, Single Server (M/G/1). General Service, Single Server (M/G/1). General Service, Multi-Server (M/G/c/ú, M/G/1). General Input (G/M/1, G/M/c). More General Models and Theoretical Topics. G/Ek/1, G[k]/M/1, and G/PHk/1. General Input, General Service (G/G/1) . Multichannel Queues with Poisson Input and Constant Service (M/D/c). Semi-Markov and Markov Renewal Processes in Queueing. Other Queue Disciplines. Design and Control of Queues. Statistical Inference in Queueing. Bounds and Approximations. Bounds. Approximations. Network Approximations. Problems. Numerical Techniques and Simulation. Numerical Techniques. Numerical Inversion of Transforms. Discrete-Event Stochastic Simulation. Problems. Bibliography. Appendix 1. Symbols and Abbreviations. Appendix 2. Tables. Appendix 3. Transforms and Generating Functions. Appendix 4. Differential and Difference Equations. Appendix 5. QTSPlus Software.