The Resource Analytical methods for network congestion control, Steven H. Low, (electronic book)
Analytical methods for network congestion control, Steven H. Low, (electronic book)
Resource Information
The item Analytical methods for network congestion control, Steven H. Low, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Analytical methods for network congestion control, Steven H. Low, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 The congestion control mechanism has been responsible for maintaining stability as the Internet scaled up by many orders of magnitude in size, speed, traffic volume, coverage, and complexity over the last three decades. In this book, we develop a coherent theory of congestion control from the ground up to help understand and design these algorithms. We model network traffic as fluids that flow from sources to destinations and model congestion control algorithms as feedback dynamical systems. We show that the model is well defined. We characterize its equilibrium points and prove their stability. We will use several real protocols for illustration but the emphasis will be on various mathematical techniques for algorithm analysis. Specifically we are interested in four questions: 1. How are congestion control algorithms modelled? 2. Are the models well defined? 3. How are the equilibrium points of a congestion control model characterized? 4. How are the stability of these equilibrium points analyzed? For each topic, we first present analytical tools, from convex optimization, to control and dynamical systems, Lyapunov and Nyquist stability theorems, and to projection and contraction theorems. We then apply these basic tools to congestion control algorithms and rigorously prove their equilibrium and stability properties. A notable feature of this book is the careful treatment of projected dynamics that introduces discontinuity in our differential equations. Even though our development is carried out in the context of congestion control, the set of system theoretic tools employed and the process of understanding a physical system, building mathematical models, and analyzing these models for insights have a much wider applicability than to congestion control
 Language
 eng
 Extent
 1 PDF (xx, 193 pages)
 Contents

 1. Congestion control models  1.1 Network model  1.2 Classical TCP/AQM protocols  1.2.1 Windowbased congestion control  1.2.2 TCP algorithms  1.2.3 AQM algorithms  1.3 Models of classical algorithms  1.3.1 Reno/RED  1.3.2 Vegas/DropTail  1.3.3 FAST/DropTail  1.4 A general setup  1.4.1 The basic models  1.4.2 Limitations and extensions  1.5 Solution of the basic models  1.5.1 Existence and uniqueness theorems  1.5.2 Application to TCP/AQM models  1.5.3 Appendix: proof of lemma 1.3  1.5.4 Appendix: proof of theorem 1.10  1.6 Bibliographical notes  1.7 Problems 
 2. Equilibrium structure  2.1 Convex optimization  2.1.1 Convex program  2.1.2 KKT theorem and duality  2.2 Network utility maximization  2.2.1 Example: Reno/RED  2.2.2 Examples: Vegas/DropTail; FAST/DropTail  2.2.3 Equilibrium of dual algorithms  2.2.4 Equilibrium of primaldual algorithms  2.3 Implications of network utility maximization  2.3.1 TCP/AQM protocols  2.3.2 Utility function, throughput, and fairness  2.4 Appendix: existence of utility functions  2.5 Bibliographical notes  2.6 Problems 
 3. Global stability: Lyapunov method  3.1 Lyapunov stability theorems  3.2 Stability of dual algorithms  3.3 Stability of primaldual algorithms  3.4 Appendix: proof of lemma 3.10  3.5 Bibliographical notes  3.6 Problems 
 4. Global stability: passivity method  4.1 Passive systems  4.2 Feedback systems  4.3 Stability of primal algorithms  4.4 Stability of primaldual algorithms  4.5 Bibliographical notes 
 5. Global stability: gradient projection method  5.1 Convergence theorems  5.2 Stability of dual algorithms  5.3 Appendix: proof of lemma 5.2  5.4 Appendix: proof of lemma 5.4  5.5 Bibliographical notes 
 6. Local stability with delay  6.1 Linear model with feedback delay  6.2 Nyquist stability theory  6.2.1 LTI systems, transfer functions, and realizations  6.2.2 Stability of LTI systems  6.2.3 Feedback systems and loop functions  6.2.4 Stability of closedloop systems  6.2.5 Generalized Nyquist stability criterion  6.2.6 Unity feedback systems  6.3 Stability of primal algorithms  6.4 Stability of dual algorithms  6.5 Appendix: proof of theorem 6.14  6.6 Bibliographical notes  6.7 Problems 
 Bibliography  Author's biography
 Isbn
 9781627055994
 Label
 Analytical methods for network congestion control
 Title
 Analytical methods for network congestion control
 Statement of responsibility
 Steven H. Low
 Language
 eng
 Summary
 The congestion control mechanism has been responsible for maintaining stability as the Internet scaled up by many orders of magnitude in size, speed, traffic volume, coverage, and complexity over the last three decades. In this book, we develop a coherent theory of congestion control from the ground up to help understand and design these algorithms. We model network traffic as fluids that flow from sources to destinations and model congestion control algorithms as feedback dynamical systems. We show that the model is well defined. We characterize its equilibrium points and prove their stability. We will use several real protocols for illustration but the emphasis will be on various mathematical techniques for algorithm analysis. Specifically we are interested in four questions: 1. How are congestion control algorithms modelled? 2. Are the models well defined? 3. How are the equilibrium points of a congestion control model characterized? 4. How are the stability of these equilibrium points analyzed? For each topic, we first present analytical tools, from convex optimization, to control and dynamical systems, Lyapunov and Nyquist stability theorems, and to projection and contraction theorems. We then apply these basic tools to congestion control algorithms and rigorously prove their equilibrium and stability properties. A notable feature of this book is the careful treatment of projected dynamics that introduces discontinuity in our differential equations. Even though our development is carried out in the context of congestion control, the set of system theoretic tools employed and the process of understanding a physical system, building mathematical models, and analyzing these models for insights have a much wider applicability than to congestion control
 Cataloging source
 CaBNVSL
 http://library.link/vocab/creatorName
 Low, Steven H.
 Dewey number
 004.24
 Illustrations
 illustrations
 Index
 no index present
 LC call number
 TK5105.5485
 LC item number
 .L682 2017
 Literary form
 non fiction
 Nature of contents

 dictionaries
 abstracts summaries
 bibliography
 Series statement
 Synthesis lectures on communication networks,
 Series volume
 18
 http://library.link/vocab/subjectName

 Computer networks
 Internet
 Target audience

 adult
 specialized
 Label
 Analytical methods for network congestion control, Steven H. Low, (electronic book)
 Bibliography note
 Includes bibliographical references (pages 187191)
 Carrier category
 online resource
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type MARC source
 rdacontent
 Contents

 1. Congestion control models  1.1 Network model  1.2 Classical TCP/AQM protocols  1.2.1 Windowbased congestion control  1.2.2 TCP algorithms  1.2.3 AQM algorithms  1.3 Models of classical algorithms  1.3.1 Reno/RED  1.3.2 Vegas/DropTail  1.3.3 FAST/DropTail  1.4 A general setup  1.4.1 The basic models  1.4.2 Limitations and extensions  1.5 Solution of the basic models  1.5.1 Existence and uniqueness theorems  1.5.2 Application to TCP/AQM models  1.5.3 Appendix: proof of lemma 1.3  1.5.4 Appendix: proof of theorem 1.10  1.6 Bibliographical notes  1.7 Problems 
 2. Equilibrium structure  2.1 Convex optimization  2.1.1 Convex program  2.1.2 KKT theorem and duality  2.2 Network utility maximization  2.2.1 Example: Reno/RED  2.2.2 Examples: Vegas/DropTail; FAST/DropTail  2.2.3 Equilibrium of dual algorithms  2.2.4 Equilibrium of primaldual algorithms  2.3 Implications of network utility maximization  2.3.1 TCP/AQM protocols  2.3.2 Utility function, throughput, and fairness  2.4 Appendix: existence of utility functions  2.5 Bibliographical notes  2.6 Problems 
 3. Global stability: Lyapunov method  3.1 Lyapunov stability theorems  3.2 Stability of dual algorithms  3.3 Stability of primaldual algorithms  3.4 Appendix: proof of lemma 3.10  3.5 Bibliographical notes  3.6 Problems 
 4. Global stability: passivity method  4.1 Passive systems  4.2 Feedback systems  4.3 Stability of primal algorithms  4.4 Stability of primaldual algorithms  4.5 Bibliographical notes 
 5. Global stability: gradient projection method  5.1 Convergence theorems  5.2 Stability of dual algorithms  5.3 Appendix: proof of lemma 5.2  5.4 Appendix: proof of lemma 5.4  5.5 Bibliographical notes 
 6. Local stability with delay  6.1 Linear model with feedback delay  6.2 Nyquist stability theory  6.2.1 LTI systems, transfer functions, and realizations  6.2.2 Stability of LTI systems  6.2.3 Feedback systems and loop functions  6.2.4 Stability of closedloop systems  6.2.5 Generalized Nyquist stability criterion  6.2.6 Unity feedback systems  6.3 Stability of primal algorithms  6.4 Stability of dual algorithms  6.5 Appendix: proof of theorem 6.14  6.6 Bibliographical notes  6.7 Problems 
 Bibliography  Author's biography
 Control code
 201705CNT018
 Dimensions
 unknown
 Extent
 1 PDF (xx, 193 pages)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9781627055994
 Media category
 electronic
 Media MARC source
 isbdmedia
 Other control number
 10.2200/S00778ED1V01Y201705CNT018
 Other physical details
 illustrations.
 Reformatting quality
 access
 Specific material designation
 remote
 System details
 System requirements: Adobe Acrobat Reader
 Label
 Analytical methods for network congestion control, Steven H. Low, (electronic book)
 Bibliography note
 Includes bibliographical references (pages 187191)
 Carrier category
 online resource
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type MARC source
 rdacontent
 Contents

 1. Congestion control models  1.1 Network model  1.2 Classical TCP/AQM protocols  1.2.1 Windowbased congestion control  1.2.2 TCP algorithms  1.2.3 AQM algorithms  1.3 Models of classical algorithms  1.3.1 Reno/RED  1.3.2 Vegas/DropTail  1.3.3 FAST/DropTail  1.4 A general setup  1.4.1 The basic models  1.4.2 Limitations and extensions  1.5 Solution of the basic models  1.5.1 Existence and uniqueness theorems  1.5.2 Application to TCP/AQM models  1.5.3 Appendix: proof of lemma 1.3  1.5.4 Appendix: proof of theorem 1.10  1.6 Bibliographical notes  1.7 Problems 
 2. Equilibrium structure  2.1 Convex optimization  2.1.1 Convex program  2.1.2 KKT theorem and duality  2.2 Network utility maximization  2.2.1 Example: Reno/RED  2.2.2 Examples: Vegas/DropTail; FAST/DropTail  2.2.3 Equilibrium of dual algorithms  2.2.4 Equilibrium of primaldual algorithms  2.3 Implications of network utility maximization  2.3.1 TCP/AQM protocols  2.3.2 Utility function, throughput, and fairness  2.4 Appendix: existence of utility functions  2.5 Bibliographical notes  2.6 Problems 
 3. Global stability: Lyapunov method  3.1 Lyapunov stability theorems  3.2 Stability of dual algorithms  3.3 Stability of primaldual algorithms  3.4 Appendix: proof of lemma 3.10  3.5 Bibliographical notes  3.6 Problems 
 4. Global stability: passivity method  4.1 Passive systems  4.2 Feedback systems  4.3 Stability of primal algorithms  4.4 Stability of primaldual algorithms  4.5 Bibliographical notes 
 5. Global stability: gradient projection method  5.1 Convergence theorems  5.2 Stability of dual algorithms  5.3 Appendix: proof of lemma 5.2  5.4 Appendix: proof of lemma 5.4  5.5 Bibliographical notes 
 6. Local stability with delay  6.1 Linear model with feedback delay  6.2 Nyquist stability theory  6.2.1 LTI systems, transfer functions, and realizations  6.2.2 Stability of LTI systems  6.2.3 Feedback systems and loop functions  6.2.4 Stability of closedloop systems  6.2.5 Generalized Nyquist stability criterion  6.2.6 Unity feedback systems  6.3 Stability of primal algorithms  6.4 Stability of dual algorithms  6.5 Appendix: proof of theorem 6.14  6.6 Bibliographical notes  6.7 Problems 
 Bibliography  Author's biography
 Control code
 201705CNT018
 Dimensions
 unknown
 Extent
 1 PDF (xx, 193 pages)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9781627055994
 Media category
 electronic
 Media MARC source
 isbdmedia
 Other control number
 10.2200/S00778ED1V01Y201705CNT018
 Other physical details
 illustrations.
 Reformatting quality
 access
 Specific material designation
 remote
 System details
 System requirements: Adobe Acrobat Reader
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