简介
Thoroughly updated to reflect current research and practice, this edition presents basic statistical principles necessary to analyze the probabilistic nature of queues. Gross (operations research and engineering, George Mason U., etc.) and his coauthors take a numerical approach to understanding how queues operate and making realistic estimations about how they will behave in real life. Using examples, they introduce Poisson processes, the Markovian property of the exponential distribution, stochastic processes and Markov chains. They cover simple and advanced Markovian queuing methods, networks, series, cyclic queues, general arrival or service patterns, general models and theoretical topics, bounds and approximations, and numerical techniques and simulation. They offer appendices covering transforms and generating functions as structures for downloading specialized software. The result is comprehensive, rigorous, and completely up-to-date. Annotation 漏2008 Book News, Inc., Portland, OR (booknews.com)
目录
Dedication p. v
Preface p. xi
Acknowledgments p. xiii
1 Introduction p. 1
1.1 Description of the Queueing Problem p. 2
1.2 Characteristics of Queueing Processes p. 3
1.3 Notation p. 7
1.4 Measuring System Performance p. 8
1.5 Some General Results p. 9
1.6 Simple Data Bookkeeping for Queues p. 12
1.7 Poisson Process and the Exponential Distribution p. 16
1.8 Markovian Property of the Exponential Distribution p. 20
1.9 Stochastic Processes and Markov Chains p. 24
1.10 Introduction to the QtsPlus Software p. 40
Problems p. 41
2 Simple Markovian Queueing Models p. 49
2.1 Birth-Death Processes p. 49
2.2 Single-Server Queues (M/M/1) p. 53
2.3 Multiserver Queues (M/M/c) p. 66
2.4 Choosing the Number of Servers p. 73
2.5 Queues with Truncation (M/M/c/K) p. 76
2.6 Erlang's Loss Formula (M/M/c/c) p. 81
2.7 Queues with Unlimited Service (M/M/[infinity]) p. 84
2.8 Finite-Source Queues p. 85
2.9 State-Dependent Service p. 91
2.10 Queues with Impatience p. 95
2.11 Transient Behavior p. 97
2.12 Busy-Period Analysis p. 102
Problems p. 103
3 Advanced Markovian Queueing Models p. 117
3.1 Bulk Input (M[superscript X]/M/1) p. 117
3.2 Bulk Service (M/M[superscript Y]/1) p. 123
3.3 Erlangian Models p. 128
3.4 Priority Queue Disciplines p. 141
3.5 Retrial Queues p. 157
Problems p. 171
4 Networks, Series, and Cyclic Queues p. 179
4.1 Series Queues p. 181
4.2 Open Jackson Networks p. 187
4.3 Closed Jackson Networks p. 195
4.4 Cyclic Queues p. 209
4.5 Extensions of Jackson Networks p. 210
4.6 Non-Jackson Networks p. 212
Problems p. 214
5 General Arrival or Service Patterns p. 219
5.1 General Service, Single Server (M/G/1) p. 219
5.2 General Service, Multiserver (M/G/c/[infinity], M/G/[infinity]) p. 254
5.3 General Input (G/M/1, G/M/c) p. 259
Problems p. 270
6 General Models and Theoretical Topics p. 277
6.1 G/E[subscript k]/1, G[superscript k]/M/1, and G/PH[subscript k]/1 p. 277
6.2 General Input, General Service (G/G/1) p. 284
6.3 Poisson Input, Constant Service, Multiserver (M/D/c) p. 294
6.4 Semi-Markov and Markov Renewal Processes in Queueing p. 296
6.5 Other Queue Disciplines p. 301
6.6 Design and Control of Queues p. 306
6.7 Statistical Inference in Queueing p. 317
Problems p. 325
7 Bounds and Approximations p. 329
7.1 Bounds p. 330
7.2 Approximations p. 343
7.3 Network Approximations p. 356
Problems p. 367
8 Numerical Techniques and Simulation p. 369
8.1 Numerical Techniques p. 369
8.2 Numerical Inversion of Transforms p. 385
8.3 Discrete-Event Stochastic Simulation p. 398
Problems p. 421
References p. 427
Appendix A Symbols and Abbreviations p. 439
Appendix B Tables p. 447
Appendix C Transforms and Generating Functions p. 455
C.1 Laplace Transforms p. 455
C.2 Generating Functions p. 462
Appendix D Differential and Difference Equations p. 467
D.1 Ordinary Differential Equations p. 467
D.2 Difference Equations p. 483
Appendix E QtsPlus Software p. 489
E.1 Instructions for Downloading p. 493
Index p. 495
Preface p. xi
Acknowledgments p. xiii
1 Introduction p. 1
1.1 Description of the Queueing Problem p. 2
1.2 Characteristics of Queueing Processes p. 3
1.3 Notation p. 7
1.4 Measuring System Performance p. 8
1.5 Some General Results p. 9
1.6 Simple Data Bookkeeping for Queues p. 12
1.7 Poisson Process and the Exponential Distribution p. 16
1.8 Markovian Property of the Exponential Distribution p. 20
1.9 Stochastic Processes and Markov Chains p. 24
1.10 Introduction to the QtsPlus Software p. 40
Problems p. 41
2 Simple Markovian Queueing Models p. 49
2.1 Birth-Death Processes p. 49
2.2 Single-Server Queues (M/M/1) p. 53
2.3 Multiserver Queues (M/M/c) p. 66
2.4 Choosing the Number of Servers p. 73
2.5 Queues with Truncation (M/M/c/K) p. 76
2.6 Erlang's Loss Formula (M/M/c/c) p. 81
2.7 Queues with Unlimited Service (M/M/[infinity]) p. 84
2.8 Finite-Source Queues p. 85
2.9 State-Dependent Service p. 91
2.10 Queues with Impatience p. 95
2.11 Transient Behavior p. 97
2.12 Busy-Period Analysis p. 102
Problems p. 103
3 Advanced Markovian Queueing Models p. 117
3.1 Bulk Input (M[superscript X]/M/1) p. 117
3.2 Bulk Service (M/M[superscript Y]/1) p. 123
3.3 Erlangian Models p. 128
3.4 Priority Queue Disciplines p. 141
3.5 Retrial Queues p. 157
Problems p. 171
4 Networks, Series, and Cyclic Queues p. 179
4.1 Series Queues p. 181
4.2 Open Jackson Networks p. 187
4.3 Closed Jackson Networks p. 195
4.4 Cyclic Queues p. 209
4.5 Extensions of Jackson Networks p. 210
4.6 Non-Jackson Networks p. 212
Problems p. 214
5 General Arrival or Service Patterns p. 219
5.1 General Service, Single Server (M/G/1) p. 219
5.2 General Service, Multiserver (M/G/c/[infinity], M/G/[infinity]) p. 254
5.3 General Input (G/M/1, G/M/c) p. 259
Problems p. 270
6 General Models and Theoretical Topics p. 277
6.1 G/E[subscript k]/1, G[superscript k]/M/1, and G/PH[subscript k]/1 p. 277
6.2 General Input, General Service (G/G/1) p. 284
6.3 Poisson Input, Constant Service, Multiserver (M/D/c) p. 294
6.4 Semi-Markov and Markov Renewal Processes in Queueing p. 296
6.5 Other Queue Disciplines p. 301
6.6 Design and Control of Queues p. 306
6.7 Statistical Inference in Queueing p. 317
Problems p. 325
7 Bounds and Approximations p. 329
7.1 Bounds p. 330
7.2 Approximations p. 343
7.3 Network Approximations p. 356
Problems p. 367
8 Numerical Techniques and Simulation p. 369
8.1 Numerical Techniques p. 369
8.2 Numerical Inversion of Transforms p. 385
8.3 Discrete-Event Stochastic Simulation p. 398
Problems p. 421
References p. 427
Appendix A Symbols and Abbreviations p. 439
Appendix B Tables p. 447
Appendix C Transforms and Generating Functions p. 455
C.1 Laplace Transforms p. 455
C.2 Generating Functions p. 462
Appendix D Differential and Difference Equations p. 467
D.1 Ordinary Differential Equations p. 467
D.2 Difference Equations p. 483
Appendix E QtsPlus Software p. 489
E.1 Instructions for Downloading p. 493
Index p. 495
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