AIMD dynamics and distributed resource allocation:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
Society for Industrial and Applied Mathematics
[2016]
|
| Schriftenreihe: | Advances in design and control
29 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 235 Seiten Diagramme |
| ISBN: | 9781611974218 |
Internformat
MARC
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| 245 | 1 | 0 | |a AIMD dynamics and distributed resource allocation |c M. Corless, Purdue University, West Lafayette, Indiana, C. King, Northeastern University, Boston, Massachusetts, R. Shorten, University College Dublin, Dublin, Ireland, F. Wirth, University of Passau, Passau, Germany |
| 264 | 1 | |a Philadelphia |b Society for Industrial and Applied Mathematics |c [2016] | |
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| 650 | 4 | |a Queuing theory |x Mathematics | |
| 650 | 4 | |a Stochastic systems |x Mathematical models | |
| 650 | 4 | |a AIMD algorithms | |
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Datensatz im Suchindex
| _version_ | 1804175941201559552 |
|---|---|
| adam_text | Contents
List of Figures ix
Notation xi
Preface xiii
1 ORIGINS AND APPLICATIONS OF AIMD 1
1.1 Background and description....................................... 1
1.2 Mathematical formulation . ...................................... 2
1.3 Nonsynchronized and nonhomogeneous AIMD.......................... 6
1.4 Research questions concerning AIMD and its variants.............. 8
1.5 Further reading.................................................. 9
1.6 Why write this book now?...................................... 10
1.7 Outline of the book.......................................... 10
1 LINEAR AIMD 13
2 SYNCHRONIZED HOMOGENEOUS AIMD 15
2.1 Convergence .................................................. 15
2.2 The spectrum of AIMD matrices................................... 21
2.3 Symmetric matrices, consensus, and a standard form ............. 24
2.4 Further reading................................................. 27
3 NONSYNCHRONIZED NONHOMOGENEOUS AIMD 29
3.1 AIMD matrices are contractive (nonexpansive).................... 32
3.2 Left products of AIMD matrices and the “memoryless” property . . 35
3.3 Right products of AIMD matrices................................. 38
3.4 A glaring omission: Multiple constraints........................ 38
3.5 Further reading................................................. 42
4 THE IID AIMD MODEL 45
4.1 The IID AIMD model............................................. 46
4.2 Convergence of the mean................................. . 47
4.3 Convergence of second-order moments ........................... 52
4.4 Further reading................................................. 58
v
VI
Contents
5 MATHEMATICAL BACKGROUND FOR PART I 61
5.1 Eigenvalues and eigenvectors.............................. 62
5.2 Positive, nonnegative, and stochastic matrices........... 64
5.3 Probability and expected values........................... 65
5.4 Proof of AIMD contraction properties ..................... 66
5.5 Proofs of convergence properties of left AIMD products.... 67
5.6 Proofs of convergence properties of right AIMD products... 69
5.7 Further reading........................................... 72
II STOCHASTIC LINEAR AIMD 73
6 HD AIMD AND ERGODICITY 75
6.1 A preamble on general versions of AIMD.................... 75
6.2 The limit distribution.................................... 79
6.3 Invariant distribution.................................... 83
6.4 The ergodic property and Breiman’s condition............. 85
6.5 Further reading........................................... 87
7 AIMD WITH STATE-DEPENDENT TRANSITION PROBABILITIES 89
7.1 The state-dependent AIMD model............................ 89
7.2 A contractive property of AIMD matrix sets................ 91
7.3 An attractive invariant distribution...................... 92
7.4 The ergodic property.................................... 94
7.5 Implications of ergodicity for asymptotic behavior........ 94
7.6 Further reading........................................... 99
8 A MARKOV CHAIN MODEL FOR CAPACITY EVENTS 101
8.1 The Markov chain AIMD model ............................. 101
8.2 The limit distribution................................. 104
8.3 Invariant distribution................................... 110
8.4 The ergodic property..................................... 110
8.5 The first moment of the invariant distribution .......... Ill
8.6 Further reading ......................................... 114
9 MATHEMATICAL BACKGROUND FOR PART II 115
9.1 Markov chains on finite state spaces..................... 115
9.2 Markov chains on topological spaces ..................... 117
9.3 Proof of Theorem 7.4: Outline of main ideas .......... 127
9.4 Proof of Theorem 7.4: Further details................... 132
9.5 Further reading.......................................... 140
III NONLINEAR AIMD 141
10 A PRIMER ON NONLINEAR AIMD 143
11 SYNCHRONIZED HOMOGENEOUS NONLINEAR AIMD 147
11.1 Introduction............................................. 147
11.2 A general nonlinear increase-decrease algorithm.......... 148
11.3 Assumptions ............................................ 151
Contents
vii
11.4 Convergence ........................................... 152
11.5 AINLD.................................................. 155
11.6 Characterization of equilibria......... ................ 163
11.7 Uniqueness of equilibrium ............................ 163
11.8 Development of main result............................. 164
11.9 Generalized algorithm................................ 168
11.10 Example ............................................. 171
11.11 Further reading..................................... 174
12 NONSYNCHRONIZED NONHOMOGENEOUS NAIMD 175
12.1 Introduction....................................... 175
12.2 AINLD.............................................. 176
12.3 Deterministic AINLD................................. 178
12.4 Stochastic AINLD . ................................... . 182
12.5 Further reading................................. 187
13 NONSYNCF1RONIZED ALGORITHMS WITH STOCHASTIC STATE»
DEPENDENT GROWTH RATES 189
13.1 Introduction.......................................... 189
13.2 Nonsynchronized AINLD with stochastic growth rates .... 190
13.3 Convergence and ergodicity............................. . 194
13.4 Further reading (and an open question)............... 194
IV APPLICATIONS OF AIMD ALGORITHMS 195
14 THREE SAMPLE APPLICATIONS OF AIMD 197
14.1 Application 1. Congestion control in the Internet...... 197
14.2 Application 2. Charging electric vehicles.............. 199
14.3 Application 3. Virtual power plants.................... 200
14.4 Conclusions............................................ 201
15 ANOTHER APPLICATION: NETWORK UTILITY OPTIMIZATION 203
15.1 Introduction........................................... 203
15.2 Problem description.................................. 203
15.3 Convergence analysis................................... 207
15.4 Example.......................................... 213
15.5 Further reading........................................ 214
16 MATHEMATICAL BACKGROUND FOR PART IV 215
16.1 Convexity........................................... 215
16.2 Optimization and the KKT conditions................... 217
223
Bibliography
Index
233
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| id | DE-604.BV043376757 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:24:17Z |
| institution | BVB |
| isbn | 9781611974218 |
| language | English |
| lccn | 015038343 |
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| physical | XIV, 235 Seiten Diagramme |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Society for Industrial and Applied Mathematics |
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| series | Advances in design and control |
| series2 | Advances in design and control |
| spelling | AIMD dynamics and distributed resource allocation M. Corless, Purdue University, West Lafayette, Indiana, C. King, Northeastern University, Boston, Massachusetts, R. Shorten, University College Dublin, Dublin, Ireland, F. Wirth, University of Passau, Passau, Germany Philadelphia Society for Industrial and Applied Mathematics [2016] XIV, 235 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Advances in design and control 29 Mathematik Mathematisches Modell Queuing theory Mathematics Stochastic systems Mathematical models AIMD algorithms Ressourcenallokation (DE-588)4129283-2 gnd rswk-swf Überlastkontrolle (DE-588)4521193-0 gnd rswk-swf Überlastkontrolle (DE-588)4521193-0 s Ressourcenallokation (DE-588)4129283-2 s DE-604 Corless, Martin J. Sonstige (DE-588)173616674 oth King, C. Sonstige oth Shorten, R. Sonstige oth Wirth, Fabian Sonstige (DE-588)1051221269 oth Advances in design and control 29 (DE-604)BV021715022 29 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028795554&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | AIMD dynamics and distributed resource allocation Advances in design and control Mathematik Mathematisches Modell Queuing theory Mathematics Stochastic systems Mathematical models AIMD algorithms Ressourcenallokation (DE-588)4129283-2 gnd Überlastkontrolle (DE-588)4521193-0 gnd |
| subject_GND | (DE-588)4129283-2 (DE-588)4521193-0 |
| title | AIMD dynamics and distributed resource allocation |
| title_auth | AIMD dynamics and distributed resource allocation |
| title_exact_search | AIMD dynamics and distributed resource allocation |
| title_full | AIMD dynamics and distributed resource allocation M. Corless, Purdue University, West Lafayette, Indiana, C. King, Northeastern University, Boston, Massachusetts, R. Shorten, University College Dublin, Dublin, Ireland, F. Wirth, University of Passau, Passau, Germany |
| title_fullStr | AIMD dynamics and distributed resource allocation M. Corless, Purdue University, West Lafayette, Indiana, C. King, Northeastern University, Boston, Massachusetts, R. Shorten, University College Dublin, Dublin, Ireland, F. Wirth, University of Passau, Passau, Germany |
| title_full_unstemmed | AIMD dynamics and distributed resource allocation M. Corless, Purdue University, West Lafayette, Indiana, C. King, Northeastern University, Boston, Massachusetts, R. Shorten, University College Dublin, Dublin, Ireland, F. Wirth, University of Passau, Passau, Germany |
| title_short | AIMD dynamics and distributed resource allocation |
| title_sort | aimd dynamics and distributed resource allocation |
| topic | Mathematik Mathematisches Modell Queuing theory Mathematics Stochastic systems Mathematical models AIMD algorithms Ressourcenallokation (DE-588)4129283-2 gnd Überlastkontrolle (DE-588)4521193-0 gnd |
| topic_facet | Mathematik Mathematisches Modell Queuing theory Mathematics Stochastic systems Mathematical models AIMD algorithms Ressourcenallokation Überlastkontrolle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028795554&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021715022 |
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