EE650: Advanced Topics in Computer Networks - Useful mathematical tools for analyzing wired and wireless networks
Over the last 10 years the Internet has grown from a small scale research network to an immense world wide infrastructure. Analyzing the performance of such a large scale system is a challenging task that requires either extensive/costly experiments, or carefully chosen mathematical tools. At the same time, it has become apparent that wireless networks are going to play an increasingly important role in the world of communications. It is envisioned that in the near future the global network will consist of an Internet-like core and a number of wireless edge-networks like sensor, mobile ad-hoc, delay tolerant, and mesh networks. The goal of this course is to expose graduate students to the mathematical tools that have been successfully used in the last 5-10 years to model and analyze wired networks like the Internet and wireless networks like sensor and ad-hoc ones.
The course will briefly revise basic probability and queueing principles through some examples. It will then present some or all of the following (time permitting) : (i) the use of Lyapunov functions in proving various stability and throughput results for network switches, (ii) some combinatorics used to analyze scheduling mechanisms in switches, (iii) fluid models used in modelling long-lived TCP flows, (iv) random walks on graphs and other random processes used to model mobility in wireless networks and, (v) probabilistic and combinatorial techniques used to analyze contention and routing performance in wireless networks, (vi) basic information theory concepts used to study the capacity of ad-hoc networks, (vi) basic elements of game theory used to devise network pricing schemes, and (vii) the notions of heavy-tailed distributions, self-similarity, and long range dependence that play an important role in the analysis of web and network traces.
For each topic, we will first introduce the corresponding research problem/area (e.g. switching), then we will present the corresponding mathematical tools/analysis (e.g. Lyapunov functions), and finally we will go through recent publications (from networking venues, e.g. IEEE INFOCOM, ACM SIGCOMM, ACM SIGMETRICS, IEEE/ACM Transactions in Networking, ACM MOBIHOC, IEEE SECON, ACM MOBICOM) that have successfully applied these tools/analysis.
related to lectures
Office hours: TTh 10:00am-11:00am
Class web site
EE465: Probabilistic Methods in Computer Systems Modelling
Probabilistic tools are among the most useful for modelling real systems
and doing performance analysis. This course is designed to provide students
with the ability to understand and conduct computer systems modelling and
performance analysis. To establish the necessary background, the course starts
with an introduction to basic probability tools and concepts. It then builds
up to more advance topics that are particularly useful in modelling, such
as Markov models, single queues, and networks of queues. Further, the course
will cover basic methods for conducting simulations. Several case studies
will be analyzed throughout the course, including some topics related to
Lecture: non-DEN TuTh 11:00am-12:20pm, DEN TuTh 12:30pm-1:50pm
Office hours: TuTh 10:00am-11:00am
Class Syllabus (from Fall 2008)
Class web site