Ebook: The Mathematics of Internet Congestion Control

Congestion control algorithms were implemented for the Internet nearly two decades ago, but mathematical models of congestion control in such a large-scale 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 stochastic 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 the routers of the network;

* A discussion of simple stochastic models for random phenomena on the Internet, such as very short flows and arrivals and departures 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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Congestion control algorithms were implemented for the Internet nearly two decades ago, but mathematical models of congestion control in such a large-scale 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 stochastic 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 the routers of the network;

* A discussion of simple stochastic models for random phenomena on the Internet, such as very short flows and arrivals and departures 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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Congestion control algorithms were implemented for the Internet nearly two decades ago, but mathematical models of congestion control in such a large-scale 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 stochastic 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 the routers of the network;

* A discussion of simple stochastic models for random phenomena on the Internet, such as very short flows and arrivals and departures 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.

Content:
Front Matter....Pages i-xi
Introduction....Pages 1-5
Resource Allocation....Pages 7-21
Congestion Control: A decentralized solution to the resource allocation problem....Pages 23-47
Relationship to Current Internet Protocols....Pages 49-66
Linear Analysis with Delay: The single link case....Pages 67-81
Linear Analysis with Delay: The network case....Pages 83-108
Global Stability for a Single Link and a Single Flow....Pages 109-115
Stochastic Models and their Deterministic Limits....Pages 117-134
Connection-level Models....Pages 135-140
Real-time Sources and Distributed Admission Control....Pages 141-154
Conclusions....Pages 155-156
Back Matter....Pages 157-164

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Congestion control algorithms were implemented for the Internet nearly two decades ago, but mathematical models of congestion control in such a large-scale 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 stochastic 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 the routers of the network;

* A discussion of simple stochastic models for random phenomena on the Internet, such as very short flows and arrivals and departures 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.

Content:
Front Matter....Pages i-xi
Introduction....Pages 1-5
Resource Allocation....Pages 7-21
Congestion Control: A decentralized solution to the resource allocation problem....Pages 23-47
Relationship to Current Internet Protocols....Pages 49-66
Linear Analysis with Delay: The single link case....Pages 67-81
Linear Analysis with Delay: The network case....Pages 83-108
Global Stability for a Single Link and a Single Flow....Pages 109-115
Stochastic Models and their Deterministic Limits....Pages 117-134
Connection-level Models....Pages 135-140
Real-time Sources and Distributed Admission Control....Pages 141-154
Conclusions....Pages 155-156
Back Matter....Pages 157-164
....