• course outline
• Lectures part 1
• Lectures part 2
• Lectures part 3 (access and admission control)
• Lectures part 4 (Effective bandwidths part 1), also check Frank Kelly's paper as well as this paper! Finally check the proposed project area part e) related to effective bandwidths.

• Background material:

You may find background material on probability and stochastic processes in Professor Gray's website at Stanford. The lecture slides can be also found here

New! You may wish to check Professor Ingemar Kaj's web site and in particular his Stochastic Simulation Using Matlab

• Homework Problems:
   

Homework #1 and its latex file in case you wish to compile it yourself. Also instructions on how to use the LAtex software are included in the homework.

Homework #2 and its latex file in case you wish to compile it yourself. Furthermore the homework can be extended into a course project as explained here.

• Proposed projects:

I would like to suggest the following projects for the course. Students who already have thought about a project please let me know by submitting half  a page with title and description. Students can form teams of up to two students per team.I am planning to propose a couple more areas. Keep checking. Also I am open to your proposals too!

a) Video traffic modelling:

The project will examine different methods for modelling a generating variable bit rate video. An excellent resource (which is readily accesible for the computers in campus but not  from your house!) is the following:

IEEE Journal on Selected areas in Communications, vol. 7, issue 5, June 1989

http://ieeexplore.ieee.org/xpl/tocresult.jsp?isYear=1989&isnumber=1402&Submit32=Go+To+Issuend

  A good place to start is the IEEE JSAC web page listed in  project a) above. Please also go to the library and find the following paper:

D. Anick, D. Mitra and M. Sondhi, "Stochastic Theory of Data-Handling Systems," The Bell System Technical Journal, Vol. 61, No. 8, pp. 1871-1894, Oct. 1982.

  The goal of this project is to present traffic modeliing techniques and investigate their queueing performance. Further material is provided here

c)  Reversible Markov Chains

 This is a  more mathematically oriented project. I can  loan you the book "reversibility and stochastic networks" by F. Kelly. Also material can be found in the book by Harrison and Patel as well as Robertazi. The goal is to provide insight on what is reversibility and how it can be used to solve problems using product form solutions. Some papers can be found here

 d)   Self-Similar Traffic modelling
.
           The goal of this project is to present the notion of Self-Similarity and Long range dependence in Internet traffic. You should explain why the POisson/Markovian assumptions
            fail for characterizing traffic in modern networks such as the Internet. Some papers can be found here. Also consult your notes from Ingemar Kaj.

  e) Effective Bandwidths and Stochastic Bounds in Queues
 

 The goal of this project is to understand the notion of effective bandwidth and explain how it can be used to provide bounds for tail distributions in queues. This is a more mathematical and  VERY interesting area. Some papers can be found here.