6.976 Quantitative Foundations of Engineering Systems

Spring 2006

Devavrat Shah and Sanjoy Mitter, Instructors

Monday and Wednesday, 1-2:30 pm

CLASS WILL BE HELD IN 66-154

Recitation, Friday 3:30-5pm (NOTE CHANGE IN TIME)

Scribe Schedule/Info FINAL EXAM Course Notes Problem Sets Handouts

COURSE DESCRIPTION:

This interdisciplinary course aims to teach quantitative principles of design and analysis of large complex engineering systems at the beginning graduate level. The course will teach principles of modeling, systems design, control and performance analysis using ideas from control, optimization, algorithms and stochastic processes. The course will be more conceptual and less technical (mathematical). That is, use of mathematics (sometimes sophisticated) will be taught but the detailed proofs will usually be omitted. The concepts will be supported and explained with examples drawn from the Internet. This course will provide the necessary background for advanced courses on foundations of engineering systems.

READING MATERIAL:

(a) Notes on optimization by P.P. Varaiya.
(b) Convex optimization by Stephen Boyd, Lieven Vandenberghe (available online from S. Boyd's home-page).
(c) Introduction to probability by Dimitri P. Bertsekas, John N. Tsitsiklis.
(d) The mathematics of Internet congestion control by R. Srikant.
(e) Calculus by Tom Apostle.

COURSE ADMINISTRATION:

Office Hours

Prof. S.K. Mitter (mitter@mit.edu) -- by appointment -- call 2-2666 and speak with Rachel
Prof. D. Shah (devavrat@mit.edu) -- Monday 2:30-3:30pm in 32-D670
TA: M. Agarwal (magar@mit.edu)

Course Admin.: Rachel Cohen (rcohen@mit.edu)

ADDITIONAL COURSE INFORMATION: (in pdf)

Course Objective

Teach quantitative principles of system design
Specifically, we will focus on

modeling

architecture design & control

performance analysis

Course will emphasize concepts

use of mathematics, but details will be omitted

Throughout the course, concepts taught will be supported via examples drawn from Internet.

This course will be followed up by an advance course on Principles of system design.

Overview

Course will concentrate on three essential principles of system design

Modeling

faithful mathematical description of a system behavior
allows one to employ mathematical tools for design & performance analysis

Architecture, Design & Control
- governed by desired system utility
- methods of design and control lead to good architecture
Performance Analysis
- quantifies the utility of system

-->> Learn above in the context of Internet.

Topics

I. Architecture

Design philosophy
Interplay: Theory & architecture
Internet architecture

II. Internet: Routing

Modeling, algorithms & analysis
Broad implications

III. Internet: Congestion control

Modeling, algorithms & analysis
Broad implications

IV. Internet: Web-server scheduling

Modeling, algorithms & analysis
Broad implications

V. Internet: Security

Issues and solutions (?)
Broad implications

VI. Miscellaneous

Simulation methods, etc