582363: Mathematical Modelling for Computer Networks  Part II
582363: Mathematical Modelling for Computer Networks  Part II
Autumn 2013 (29.10.2013 to 06.12.2013)
Contents:
General Info
 The course is a 2 credit advanced level module optional course.
Instructors: Laila Daniel and Krishnan Narayanan
Email: {ldaniel, narayana}@cs.helsinki.fi
Office hours: C 213, Thursday 12:00  13:00 or by appointment.
Class Timings and Location.
Lecture class: Tue 1416, B119
Exercise class: Fri 1214, B119
Course Description
As networking systems such as the Internet, wireless and mobile
networks are becoming increasingly versatile and complex, mathematical
methods for modelling, analysis and design of computer networks and
their protocols have become important.
The course focusses on two topics, Network coding and Large Deviation analysis, of active current interest in networking in which mathematical modelling and analysis plays a crucial role. Modelled along the lines of an earlier course, Mathematical Modelling of Computer Networks offered in Spring 2013, it develops the mathematical tools in conjunction with their applications in networking. However, the previous course (Mathematical Modelling of Computer Networks Part I) is not a prerequisite for taking this course. We focus on a couple of key results in each topic and build up the mathematical background to the extent needed to understand these results.
Course Audience
This course is an advancedlevel course and is offered in the stream
of Computer networks for students at the masters and research level in
Computer Science, Communications Engineering and Applied
Mathematics. This course can also be taken by anyone interested in the
mathematical principles/theory of computer networking.
Prerequisites
Data communications and (or) Computer networks, Algorithms, Discrete mathematics and probability.
Course Structure
The course has two modules.
Module 1: Network coding and TCP
Module 2: Large Deviations and Wireless Scheduling
Three lecture classes and three exercise classes are devoted to each module. Lecture notes will be provided for each of the modules adapted from the original papers/books that are given in the reference section of each module. The papers and books are labelled as Pxx  Paper xx, and Bxx  Book xx.
Module 1: Network Coding and TCP
Network coding, a nascent branch of networking, has made rapid
strides from theory to practice in the recent years. Among other applications of network coding, we discuss how TCP can be enhanced with Network
Coding (without any changes to the network routers) to improve its
performance in wireless networking.
References
P11. T. Ho, R. Koetter, M. Medard, M. Effros, J. Shi, and D. Karger. A Random Linear Network Coding Approach to Multicast. IEEE Transactions on Information Theory,
Volume 52 Issue 10, October 2006, Page 44134430
P12. J. K. Sundararajan, D. Shah, M. Medard, S. Jakubczak, M. Mitzenmacher and J. Barros. Network Coding Meets TCP: Theory and Implementation, Proceedings of the IEEE , vol.99, no.3, pp.490512, March 2011.
P13. C. Fragouli, J.Y. Le Boudec and J. Widmer. Network coding: an instant primer
P14. S. Katti, H. Rahul, W. Hu, D. Katabi, M. Medard, J. Crowcroft. XORs in the Air: Practical Wireless Network Coding. IEEE/ACM Transactions on Networking, Vol. 16, No. 3, June 2008. 497510
P15. R.W. Yeung, S.Y.R. Li, N. Cai, and. Z. Zhang. Network Coding Theory, Foundation and Trends.
P16. R. Bassoli, H. Marques, J. Rodriguez, K. W. Shum and R. Tafazolli. Network Coding Theory: A Survey. IEEE Communications Surveys & Tutorials, 2013.

Module 2: Large Deviations and Wireless Scheduling
 Large deviations, an active modern research topic in probability, has found many uses in networking such as assessing the qualitative behaviour of scaling effects and determining (and controlling) the asymptotic decay rates probabilities of overflow events in wireless networks to provide QoS guarantees for delay sensitive traffic. We present informally the basic concepts of this theory and show how this theory can be applied to get interesting results in wireless scheduling
References
P21. Ying , R. Srikant , A. Eryilmaz , G. E. Dullerud. A Large Deviations Analysis of Scheduling in Wireless Networks. IEEE Transactions on Information Theory, Vol. 52, no. 11 (2006): 50885098.
B21. L. Jiang and J. Walrand. Scheduling and Congestion Control for Wireless and Processing Networks. Morgan \& Claypool publishers, 2010
Useful Mathematical References
V. Shoup. A Computational Introduction to Number Theory and Algebra
Sage: Open Source Mathematics Software
R.A. Beezer. Sage for Linear Algebra. A Supplement to A First Course in Linear Algebra
S. Gao and D. Panario. Irreducibility test for polynomials over finite fields.
J.T. Lewis and R. Raymond. An elementary introduction to the Large Deviations Theory.

Passing the Course
Taking the course exam (25 points) at the end of the course and preparing a term paper (45 pages) on a suitably chosen topic and presenting it (25 points).
Active participation in the weekly exercises (max. 10 points).
A passing grade requires at least 30 points in total.
Course Slides
Introduction to the course
Network Coding
Lecture 1: Introduction to Network Coding
Lecture 2: Linear Network Coding and Multicast Capacity
Lecture 3: Network Coding and TCP
Wireless Scheduling
Lecture 1: Wireless Scheduling
Lecture 2: Maximum Weighted Matching scheduling algorithm
Lecture 3: Large Deviations and Wireless Scheduling
Exercises
Network Coding
Exercise 1
Exercise 2
Exercise 3
Wireless Scheduling
Exercise 4
Exercise 5
Announcements
 Course Results Announced
 Exercise 5 is online. The exercise class is in room A 217 from 14:00  16:00 on Friday 29th November 2013.
 Lecture slides for Nov 19th and 26th are online.
 Exercise 4 is online. The exercise class is in room A 217 from 14:00  16:00 on Friday 22nd November 2013.
 The course exam is on Thursday 12th of December at 16.00 in
auditorium B123.
 Exercise 3 is online.
 Lecture slides for Nov 5th and 12th are online.
 Exercise 2 is online.
 Exercise 1 is online.
 Lecture slides for 29th October is online.
 The first lecture class is on Tue., October. 29th, 2013.
 The first exercise class is on Fri., November. 1st, 2013.
 Welcome!