The mathematics of internet congestion control
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| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2012
|
| Ausgabe: | [softcover repr. of the original 1. ed. 2004] |
| Schriftenreihe: | Systems and control : foundations and applications
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
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| 100 | 1 | |a Srikant, Rayadurgam |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The mathematics of internet congestion control |c R. Srikant |
| 250 | |a [softcover repr. of the original 1. ed. 2004] | ||
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2012 | |
| 300 | |a XI, 164 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Systems and control : foundations and applications | |
| 650 | 4 | |a Internet - Modèles mathématiques | |
| 650 | 4 | |a Télécommunications - Trafic - Gestion - Mathématiques | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Internet |x Mathematical models | |
| 650 | 4 | |a Telecommunication |x Traffic |x Management |x Mathematics | |
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Datensatz im Suchindex
| _version_ | 1819583151200010240 |
|---|---|
| adam_text | Contents
Preface
....................■.....■.............................
vii
1
Introciuction
...........................,..,.,..,....,...,.. 1
2
Resource Allocation
.......................................
У
2.1
Resource allocation as an optimization
problem
........,.,,,
ľ>
2.2
A general class of utility functions
......................... 1.3
2.3
Appendix: Convex optimization
........................... Vi
3
Congestion Control: A decentralized solution
.............. 23
3.1
Primal algorithm
........................................ 23
3.2
Dual algorithm
.......................................... 27
3.3
Exact penalty functions
.................................. 29
3.4
Primal-dual approach
.................................... 32
3.5
Other variations in the primal approach
.................... 33
3.5.1
Exponentially averaged rate feedback
................ 33
3.5.2
One-bit marking in the primal method
............... 34
3.6
REM: A
one-bit marking scheme
.......................... 35
3.7
Miiltipath routing
....................................... 36
3.8
Multirate multicast congestion control
..................... 3?
3.9
A pricing interpretation of proportional
fairaosfä
.......,,.,., 43
3.10
Appendix: Lyapunov stability
.,...,,.....,,...,.,,..,.,... 46
4
Relationship ¡;o Current
Xi iterïioi;
PvoitnioL·
................ 49
4.1
Window flow control
..................................... 49
4.2
Jacobson s adaptive window flow control algorithm
,,.,,,.,,. bü
4.2.1
TCP and resource allocation
........................ 69
4.3
TCP« Vegas
...........,............................ . . . ,
в і
4.4
Random Early Detection (RED)
........................... 63
4.5
Explicit Congestion Notification (EON)
.................... 65
4.6
High-throughput TCP
...................................
6b
χ
Contents
5 Linear
Analysis with Delay: The single link case
........., . 67
5.1
Single TCP-Reno source with droptail
..................... 67
5.2
Multiple TCP sources with identical RTTs
.................. 69
5.3
TCP-Reno and RED
..................................... 72
5.4
Proportionally-fair controller
.............................. 75
5.5
High-throughput TCP
................................... 76
5.6
Dual algorithm
.......................................... 77
5.7
Primal-dual algorithm
.................................... 79
5.8
Appendix: The Nyquist criterion
.......................... 80
6
Linear Analysis with Delay: The network case
............. 83
6.1
Primal controllers
....................................... 83
6.1.1
Proportionally-fair controller
........................ 83
6.1.2
High-throughput TCP with rate-based feedback
....... 87
6.1.3
Exponentially smoothed rate feedback
............... 90
6.1.4
High-throughput TCP with probabilistic marking
..... 92
6.1.5
A general nonlinear increase/decrease algorithm
....... 94
6.1.6
High-throughput TCP and AVQ
.................... 96
6.2
Dual algorithm
..........................................101
6.2.1
Fair dual algorithm
................................103
6.3
Primal-dual algorithm
....................................104
6.4
Appendix:
Multivariable
Nyquist criterion
..................108
7
Global Stability for a Single Link and a Single Flow
.......109
7.1
Proportionally-fair controller over a single link
..............109
8
Stochastic Models and their Deterministic Limits
..........117
8.1
Deterministic limit for proportionally-fair controllers
.........118
8.2
Individual source dynamics
...............................125
8.3
Price feedback
..........................................128
8.4
Queue-length-based marking
..............................129
8.5
TCP-type congestion controllers
...........................131
8.6
Appendix; The weak law of large numbers
..................133
9
Connection-level Models
...................................135
9.1
Stability of weighted proportionally-fair controllers
.......... 135
9.2
Priority resource allocation
............................... (.39
10
Real-time Sources and Distributed Admission Control
.....141
10.1
Resource sharing between elastic and inelastic users
.........
10.2
Probing and distributed admission control
..................144
10.3
A simple model for qucueing at the Link buffer
..............146
10.4
Appendix: Diffusion approximation
........................148
10.4.1
Brownian motion through a queue
...................149
10.4.2
A lower bound for limt^oo P(q(t)
>
x)
...............151
Contents xi
10 4.3 Computing
the steady-state density using PDE s
......152
1
1
Conclusions
................................................155
References
.....................................................
157
Index
..........................................................
163
Congestion
control algorithms were implemented for the Internet
nearly two decades ago, but mathematical models of congestion
control in such a large-scale network are relatively new. This text
presents models for the development of new protocols that can
help make Internet data transfers virtually loss- and delay-free.
Introduced are tools from optimization, control theory, and stochas¬
tic processes integral to the study of congestion control algorithms.
Features and topics include:
•
A presentation of Kelly s convex program formulation of resource
allocation on the Internet
•
A solution to the resource allocation problem, which can be
implemented in a decentralized manner, both in the form of
congestion control algorithms by end users and as congestion
indication mechanisms by routers of networks
•
A discussion of simple stochastic models for random phenomena
on the Internet, such as very short flows and arrivals and depar¬
tures of file transfer requests
Intended for graduate students and researchers in systems theory
and computer science, the text assumes basic knowledge of first-
year, graduate-level control theory, optimization, and stochastic
processes, but the key prerequisites are summarized in an appendix
for quick reference. The work s wide range of applications to the
study of both new and existing protocols and control algorithms
make the book of interest to researchers and students concerned
with many aspects of large-scale information flow on the Internet.
|
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| discipline | Informatik Mathematik |
| edition | [softcover repr. of the original 1. ed. 2004] |
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| id | DE-604.BV042327044 |
| illustrated | Illustrated |
| indexdate | 2024-12-24T04:20:11Z |
| institution | BVB |
| isbn | 9781461264989 |
| language | English |
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| physical | XI, 164 S. Ill. |
| publishDate | 2012 |
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| publisher | Birkhäuser |
| record_format | marc |
| series2 | Systems and control : foundations and applications |
| spellingShingle | Srikant, Rayadurgam The mathematics of internet congestion control Internet - Modèles mathématiques Télécommunications - Trafic - Gestion - Mathématiques Mathematik Mathematisches Modell Internet Mathematical models Telecommunication Traffic Management Mathematics Mathematisches Modell (DE-588)4114528-8 gnd Internet (DE-588)4308416-3 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4308416-3 |
| title | The mathematics of internet congestion control |
| title_auth | The mathematics of internet congestion control |
| title_exact_search | The mathematics of internet congestion control |
| title_full | The mathematics of internet congestion control R. Srikant |
| title_fullStr | The mathematics of internet congestion control R. Srikant |
| title_full_unstemmed | The mathematics of internet congestion control R. Srikant |
| title_short | The mathematics of internet congestion control |
| title_sort | the mathematics of internet congestion control |
| topic | Internet - Modèles mathématiques Télécommunications - Trafic - Gestion - Mathématiques Mathematik Mathematisches Modell Internet Mathematical models Telecommunication Traffic Management Mathematics Mathematisches Modell (DE-588)4114528-8 gnd Internet (DE-588)4308416-3 gnd |
| topic_facet | Internet - Modèles mathématiques Télécommunications - Trafic - Gestion - Mathématiques Mathematik Mathematisches Modell Internet Mathematical models Telecommunication Traffic Management Mathematics Internet |
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