Large deviations for performance analysis: queues, communications, and computing
This book consists of two synergistic parts. The first half develops the theory of large deviations from the beginning (i.i.d. random variables) through recent results on the theory for processes with boundaries, keeping to a very narrow path: continuous-time, discrete-state processes. By developing...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Chapman & Hall
1995
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Stochastic modeling series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | This book consists of two synergistic parts. The first half develops the theory of large deviations from the beginning (i.i.d. random variables) through recent results on the theory for processes with boundaries, keeping to a very narrow path: continuous-time, discrete-state processes. By developing only what is needed for the applications, the theory is kept to a manageable level, both in terms of length and in terms of difficulty. Within its scope, the treatment is detailed, comprehensive, and self-contained. As the book shows, there are sufficiently many interesting applications of jump Markov processes to warrant a special treatment The second half is a collection of applications developed at AT&T Bell Laboratories. The applications cover large areas of the theory of communication networks: circuit-switched transmission, packet transmission, multiple access channels, and the M/M/1 queue. Aspects of parallel computation are covered as well: basics of job allocation, rollback-based parallel simulation, assorted priority queuing models that may be used in performance models of various computer architectures, and asymptotic coupling of processors. These applications are thoroughly analyzed using the tools developed in the first half of the book. Advanced undergraduate and graduate students in engineering and applied mathematics will find this book to be an invaluable introduction to the theory and a compelling collection of real engineering applications. This book will also be an excellent resource for mathematicians, researchers, and engineers |
| Beschreibung: | Errata slip inserted. - Includes bibliographical references (p. 539-549) and index |
| Beschreibung: | viii, 556 p. ill. |
| ISBN: | 0412063115 |
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| 520 | 3 | |a This book consists of two synergistic parts. The first half develops the theory of large deviations from the beginning (i.i.d. random variables) through recent results on the theory for processes with boundaries, keeping to a very narrow path: continuous-time, discrete-state processes. By developing only what is needed for the applications, the theory is kept to a manageable level, both in terms of length and in terms of difficulty. Within its scope, the treatment is detailed, comprehensive, and self-contained. As the book shows, there are sufficiently many interesting applications of jump Markov processes to warrant a special treatment | |
| 520 | |a The second half is a collection of applications developed at AT&T Bell Laboratories. The applications cover large areas of the theory of communication networks: circuit-switched transmission, packet transmission, multiple access channels, and the M/M/1 queue. Aspects of parallel computation are covered as well: basics of job allocation, rollback-based parallel simulation, assorted priority queuing models that may be used in performance models of various computer architectures, and asymptotic coupling of processors. These applications are thoroughly analyzed using the tools developed in the first half of the book. Advanced undergraduate and graduate students in engineering and applied mathematics will find this book to be an invaluable introduction to the theory and a compelling collection of real engineering applications. This book will also be an excellent resource for mathematicians, researchers, and engineers | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | V
Table of contents
0. What this Book Is, and What It Is Not 1
0.1. What to Do with this Book 5
0.2. About the Format of the Book 5
0.3. Acknowledgments 6
1. Large Deviations of Random Variables 9
1.1. Heuristics and Motivation 9
1.2. I.I.D. Random Variables 14
1.3. Examples—I.I.D. Random Variables 19
1.4. I.I.D. Random Vectors 23
1.5. End Notes 25
2. General Principles 29
2.1. The Large Deviations Principle 29
2.2. Varadhan s Integral Lemma 33
2.3. The Contraction Principle 36
2.4. Empirical Measures: Sanov s Theorem 37
3. Random Walks, Branching Processes 45
3.1. The Ballot Theorem 46
3.2. Branching Random Walks 48
4. Poisson and Related Processes 53
4.1. The One Dimensional Case 53
4.2. Jump Markov Processes 56
4.3. Martingales and Markov Processes 61
5. Large Deviations for Processes 69
5.1. Kurtz s Theorem 75
5.2. Properties of the Rate Function 85
5.3. The Lower Bound 105
5.4. The Upper Bound: Orientation 114
5.5. Proof of the Upper Bound 117
6. Freidlin Wentzell Theory 129
6.1. The Exit Problem 132
6.2. Beyond the Exit Problem 157
6.3. Discontinuities 160
6.4. Convergence of Invariant Measures 164
vi
7. Applications and Extensions 169
7.1. Empirical Distributions of Finite Markov Processes 169
7.2. Simple Jump Processes 175
7.3. The Free M/M/l Process 179
7.4. Meaning of the Twisted Distribution 183
7.5. End Notes 189
8. Boundary Theory 191
8.1. The Rate Functions 195
8.2. Properties of the Rate Function 201
8.3. Proof of the Upper Bound 215
8.4. Constant Coefficient Processes 220
8.5. The Lower Bound 230
8.6. End Notes 242
Applications 243
9. Allocating Independent Subtasks 245
9.1. Useful Notions 246
9.2. Analysis 249
9.3. End Notes 253
10. Parallel Algorithms: Rollback 255
10.1. Rollback Algorithms 255
10.2. Analysis of a Rollback Tree 258
11. The M/M/l Queue 261
11.1. The Model 261
11.2. Heuristic Calculations 262
11.3. Most Probable Behavior 267
11.4. Reflection Map 272
11.5. The Exit Problem and Steady State 274
11.6. The Probability of Hitting a Point 277
11.7. Transient Behavior 279
11.8. Approach to Steady State 281
11.9. Further Extensions 283
11.10. End Notes 286
vii
12. Erlang s Model 289
12.1. Scaling and Preliminary Calculations 290
12.2. Starting with an Empty System 292
12.3. Starting with a Full System in Light Traffic 300
12.4. Justification 302
12.5. Erlang s Model: General Starting Point 305
12.6. Large Deviations Theory 308
12.7. Extensions to Erlang s Model 313
12.8. Transient Behavior of Trunk Reservation 318
12.9. End Notes 323
13. The Anick Mitra Sondhi Model 325
13.1. The Simple Source Model 328
13.2. Buffer Statistics 330
13.3. Small Buffer 341
13.4. Large Buffer 345
13.5. Consequences of the Solution 348
13.6. Justification 350
13.7. Control Schemes 361
13.8. Multiple Classes 378
13.9. EndNotes 386
14. Aloha 387
14.1. The I.D. Model and Heuristics 387
14.2. Related Models 394
14.3. Basic Analysis 397
14.4. Large Deviations of Aloha 398
14.5. Justification 400
14.6. A Paradox—Resolved 405
14.7. Slotted Aloha Models 409
14.8. End Notes 417
15. Priority Queues 419
15.1. Preemptive Priority Queue 421
15.2. MostProbableBehavior—PP 422
15.3. The Variational Problem—PP 423
15.4. Probabilistic Questions—PP 436
15.5. Justification—PP 438
15.6. Serve the Longest Queue 443
viii
15.7. Most Probable Behavior—SL 444
15.8. The Main Result—SL 445
15.9. Justification—SL 446
15.10. Join the Shortest Queue 454
15.11. EndNotes 458
16. The Flatto Hahn Wright model 459
16.1. Most Probable Behavior 462
16.2. Formal Large Deviations Calculations 463
16.3. Justification of the Calculation 467
16.4. End Notes 470
A. Analysis and Probability 471
A.l. Topology, Metric Spaces, and Functions 471
A.2. Ordinary Differential Equations 482
A.3. Probability and Integration 483
A.4. Radon Nikodym Derivatives 493
A.5. Stochastic Processes 495
B. Discrete Space Markov Processes 499
B.I. Generators and Transition Semigroups 499
B.2. The Markov Process 501
B.3. Birth Death Processes 503
B.4. Martingales 505
C. Calculus of Variations 515
C.I. Heuristics of the Calculus of Variations 515
C.2. Calculus of Variations and Large Deviations 518
C.3. One Dimensional Tricks 520
C.4. Results from the Calculus of Variations 525
D. Large Deviations Techniques 527
D.I. The Gartner Ellis Theorem 527
D.2. Subadditivity Arguments 533
D.3. Exponential Approximations 533
D.4. Level H 534
References 539
Index 551
|
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| language | English |
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| spelling | Shwartz, Adam Verfasser aut Large deviations for performance analysis queues, communications, and computing Adam Shwartz, Alan Weiss ; with an appendix by Robert J. Vanderbei 1. ed. London [u.a.] Chapman & Hall 1995 viii, 556 p. ill. txt rdacontent n rdamedia nc rdacarrier Stochastic modeling series Errata slip inserted. - Includes bibliographical references (p. 539-549) and index This book consists of two synergistic parts. The first half develops the theory of large deviations from the beginning (i.i.d. random variables) through recent results on the theory for processes with boundaries, keeping to a very narrow path: continuous-time, discrete-state processes. By developing only what is needed for the applications, the theory is kept to a manageable level, both in terms of length and in terms of difficulty. Within its scope, the treatment is detailed, comprehensive, and self-contained. As the book shows, there are sufficiently many interesting applications of jump Markov processes to warrant a special treatment The second half is a collection of applications developed at AT&T Bell Laboratories. The applications cover large areas of the theory of communication networks: circuit-switched transmission, packet transmission, multiple access channels, and the M/M/1 queue. Aspects of parallel computation are covered as well: basics of job allocation, rollback-based parallel simulation, assorted priority queuing models that may be used in performance models of various computer architectures, and asymptotic coupling of processors. These applications are thoroughly analyzed using the tools developed in the first half of the book. Advanced undergraduate and graduate students in engineering and applied mathematics will find this book to be an invaluable introduction to the theory and a compelling collection of real engineering applications. This book will also be an excellent resource for mathematicians, researchers, and engineers Grandes déviations ram Grote afwijkingen gtt Systeemanalyse gtt Systèmes, analyse de ram Large deviations System analysis Große Abweichung (DE-588)4330658-5 gnd rswk-swf Datennetz (DE-588)4011130-1 gnd rswk-swf Leistungsmessung (DE-588)4167290-2 gnd rswk-swf Große Abweichung (DE-588)4330658-5 s Datennetz (DE-588)4011130-1 s Leistungsmessung (DE-588)4167290-2 s DE-604 Weiss, Alan Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009976316&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shwartz, Adam Large deviations for performance analysis queues, communications, and computing Grandes déviations ram Grote afwijkingen gtt Systeemanalyse gtt Systèmes, analyse de ram Large deviations System analysis Große Abweichung (DE-588)4330658-5 gnd Datennetz (DE-588)4011130-1 gnd Leistungsmessung (DE-588)4167290-2 gnd |
| subject_GND | (DE-588)4330658-5 (DE-588)4011130-1 (DE-588)4167290-2 |
| title | Large deviations for performance analysis queues, communications, and computing |
| title_auth | Large deviations for performance analysis queues, communications, and computing |
| title_exact_search | Large deviations for performance analysis queues, communications, and computing |
| title_full | Large deviations for performance analysis queues, communications, and computing Adam Shwartz, Alan Weiss ; with an appendix by Robert J. Vanderbei |
| title_fullStr | Large deviations for performance analysis queues, communications, and computing Adam Shwartz, Alan Weiss ; with an appendix by Robert J. Vanderbei |
| title_full_unstemmed | Large deviations for performance analysis queues, communications, and computing Adam Shwartz, Alan Weiss ; with an appendix by Robert J. Vanderbei |
| title_short | Large deviations for performance analysis |
| title_sort | large deviations for performance analysis queues communications and computing |
| title_sub | queues, communications, and computing |
| topic | Grandes déviations ram Grote afwijkingen gtt Systeemanalyse gtt Systèmes, analyse de ram Large deviations System analysis Große Abweichung (DE-588)4330658-5 gnd Datennetz (DE-588)4011130-1 gnd Leistungsmessung (DE-588)4167290-2 gnd |
| topic_facet | Grandes déviations Grote afwijkingen Systeemanalyse Systèmes, analyse de Large deviations System analysis Große Abweichung Datennetz Leistungsmessung |
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