Event description:

Optimization, Pricing and Control in Networks

In the last decade, a new theoretical foundation for quantitative network research has emerged. Its key ingredients are the following: economic models to formulate network resource allocation as a convex optimization problem; use of optimization methods to devise decentralized solutions to these problems, in terms of dynamic adaptation of the relevant variables; tools of control theory to understand the dynamic properties of these methods. The resulting body of theory has been highly successful in providing models for TCP congestion control, describing how local protocols should be designed to allow for interesting global properties to emerge. From here, recent research has advanced this methodology to other layers of the protocol stack. In this course we will provide an introduction to this interdisciplinary field of research.

Tentative outline:

Lecture 1: Convex optimization and tools from economic theory.Convex functions and sets, convex optimization problems. Duality. Elements of microconomic theory, examples from network resource allocation.
Lecture 2: Dynamics and control. Lyapunov stability of differential equations. Feedback control loops, tools for stability analysis, effect of feedback delay. Examples from congestion control.
Lecture 3: Congestion control. Formulation of the congestion control problem in terms of utility maximization. Primal, dual, and primal-dual algorithms and their stability. Application to modeling of current TCP.
Lecture 4: TCP stability and delay, introduction to scalable protocols. Application of control theory tools for TCP stability Implications on protocol design.
Lecture 5: Introduction to cross layer optimization. Examples of joint resource allocation in multiple layers of the protocol hierarchy.

Contact Seminar Instructor: paganini@ort.edu.uy

The seminar will be conducted in English