Network flow optimization and distributed control algorithms

This thesis concerns the problem of designing distributed algorithms for achieving efficient and fair bandwidth allocations in a resource constrained network. This problem is fundamental to the design of transmission protocols for communication networks, since the fluid models of popular protocols such as TCP and Proportional Fair Controller can be viewed as distributed algorithms which solve the network flow optimization problems corresponding to some fairness criteria…

Contents

1 Introduction
1.1 Thesis Outline
2 Flow Control Models: From Packet Models to Fluid Models
2.1 Fluid Models by Direct Di®erentiation
2.1.1 Flow Controlled by TCP/Reno
2.1.2 Flow Controlled by Proportional Fairness Controller
2.2 Fluid Model by Many-Flows Asymptotics
2.2.1 Flow Controlled by TCP/Reno
2.2.2 Flow Controlled by Proportional Fairness Controller
2.3 Network of Congestion Controlled Flows and Flow Optimization
3 Stability Results for Networks with Time Varying Delays – Classical Source/Link Controllers
3.1 Introduction
3.2 Network Model
3.3 Literature Review
3.4 Stability Results
3.4.1 Primal Control Law
3.4.2 Dual Control Law
3.4.3 Primal/Dual Control Law
3.5 Implementation Issues
3.6 Discussion and Conclusion
4 Design of Scalable and Distributed Control Laws
4.1 Introduction
4.2 Problem Formulation
4.3 General Properties of Controllers
4.4 Design of Scalable Controller
4.4.1 The Case of Single User/Link Network
4.4.2 The Case of General Network
4.5 Conclusions
5 Design of Scalable Control Laws for Combined Routing and Flow Control – The Case of Multiple Path Routing
5.1 Introduction
5.2 Network Model
5.3 Literature Overview
5.4 Main Result
5.5 Conclusion
6 Combined Routing and Flow Control – The Case of Single Path Routing
6.1 Introduction
6.2 Price of Anarchy – A Case Study
6.3 Nash Equilibrium and Optimality – Asymptotic Results
6.4 Discussion
A Lyapunov-Krasovskii Functional for Delay-Independent Rate Controlled Net-work
B Proof of Lemma 4.4
Bibliography

Author: Chen, Huigang

Source: University of Maryland

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