3054 EBII (Tel: 513-7406)

Email: dyeun@eos.ncsu.edu

An introduction to the theory of network design and optimization with applications to communication networks. This course will cover various analytic tools driven by networking applications including TCP congestion control, active queue management, network stability, cross-layer optimization in wireless networks, and network topology. In particular, students will learn basic tools in convex optimization, duality theorem, distributed algorithms for convex optimization, stability theory for congestion control, router buffer design, as well as some introduction to random graph and the power-law topology of the current Internet.

With the increasing complexity in the design of wired/wireless networks over multiple layers (cross-layers), the convex optimization and stability theory has been an indispensable tool for network design and analysis. This course will be methodological, application-driven, and principal approaches for network design and optimization in various setting will be given. The students will first lean basic theory of convex optimization and its dual solution and how this set of tools can be applied to a number of problems in various network settings that include TCP congestion control, cross-layer design in wireless networks, etc. Students will also learn how to design network components such that the network is stable and the connection between optimization approach and the system stability, as well as other various issues including router buffer sizing in high-speed networks. This course will also provide a brief introduction to a theory of random graph and other recent approach to generate power-law graphs, with applications to the current Internet topology. Throughput the course, proofs and intuitive remarks will be given to each topic as much as possible. In each topic, an effort will be made to cover background materials whenever necessary. A list of related papers and materials in recent networking literature will also be provided. This course will help students engage in advanced research topics and apply concepts and analytic tools covered in the course to their current research topics in wired/wireless networks.

1.
S. Boyd and L. Vandenberghe, **Convex Optimization**, Cambridge
University Press 2004. (Available online at
http://www.stanford.edu/~boyd/cvxbook/)

2.
R. Srikant, **The Mathematics of Internet Congestion Control**,
Birkhauser, 2004

3.
Romualdo Pastor-Satorras
and Alessandro Vespignani, **Evolution and Structure
of the Internet: A Statistical Physics Approach**, Cambridge University
Press, 2004

4. S. N. Dorogovtsev, J. F. F. Mendes, **Evolution of
Networks: From Biological Nets to the Internet and WWW, **Oxford University
Press, 2003

__Note__:
The books above are not required to buy, but are highly recommended. They will
be placed on-reserve in the library. Only parts of them will be used in the
class.

**References (Tutorial &
Survey papers, not exhaustive)**

1. Tutorials on "Rate adaptation, Congestion Control, and Fairness", by Jean-Yves Le Boudec

2. R. Srikant, "Models and Methods for Analyzing Internet Congestion Control Algorithms." In Advances in Communication Control Networks in the series "Lecture Notes in Control and Information Sciences (LCNCIS)," C.T. Abdallah, J. Chiasson and S. Tarbouriech (eds.), Springer-Verlag, 2004.

3. M. Chiang, S. H. Low, R. A. Calderbank, and J. C. Doyle, "Layering as Optimization Decomposition," Proceedings of IEEE, December 2006.

4. Leonidas Georgiadis, Michael Neely, and Leandros Tassiulas, "Resource Allocation and Cross Layer Control in Wireless Networks", Foundations and Trends in Networking, Apr. 2006

5.
Xiaojun Lin, Ness B. Shroff and R. Srikant, "A
Tutorial on Cross-Layer Optimization in Wireless Networks," to appear in *
IEEE Journal on Selected Areas in Communications, special issue on "Non-Linear
Optimization of Communication Systems," *2006

6. M. E. J. Newman, "The Structure and Function of Complex Networks", SIAM Review, vol. 45, Issue 2, pages 167-256, 2003

Introduction

Convex Optimization

o Convex set, convex functions

o Properties of convex functions and various inequalities

o Convex optimization problem in communications network

o Constrained optimization, Lagrange duality and applications

Optimization Approach to Internet

o Rate-control vs. Fairness

o TCP/AQM as a distributed solution to utility maximization problem

o Cross-layer design of the network: (joint-optimization and its distributed solution)

Network Stability and Design

o Lyapunov stability & Linear stability of a system

o Stability of the network and congestion control

o Variations of TCP algorithms: how things work

o Designing Routers and AQM (Active Queue Management)

o Issues on sizing router buffers

Network Topology

o How does the Internet look like?

o Introduction to random graph

o Simple models for generating internet-like power-law graph. Simple analysis for its characteristics

o Discussion on the impact of power-law topology on routing, Internet robustness, fragility, etc.

__
Note__*:
This is
a bit aggressive and extensive schedule. If this turns out to be too much, it
will be appropriately adjusted during the semester.

Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with Disability Services for Students at 1900 Student Health Center, Campus Box 7509, 515-7653. http://www.ncsu.edu/provost/offices/affirm_action/dss/ For more information on NC State's policy on working with students with disabilities, please see http://www.ncsu.edu/provost/hat/current/appendix/appen_k.html

All the provisions of the code of academic integrity apply to this course. In addition, it is my understanding and expectation that your signature on any test or assignment means that you neither gave nor received unauthorized aid.