This course will expose the students to a variety of modern mathematical tools entering the modeling, performance evaluation, optimization and control of large-scale computer networks and distributed systems. These tools include the theory of Markov chains (including absorbing Markov chains), basic elements of queueing theory, game theory, stochastic geometry, mean-field approximations, network calculus, dynamic programming and extreme value theory. Numerous applications will be studied throughout the class, including the modeling of TCP and of Web servers, service differentiation, sized-based scheduling, mobility models, file sharing systems (e.g. BitTorrent), distributed storage systems, routing in mobile ad hoc networks.
- Prof. P. Nain (Maestro, INRIA)
- Prof. G. Neglia (Maestro, INRIA)
New resources (2011)
First part, Markov Chains
- Lectures: here
- Performance Analysis of Communication Networks: slides and paper (2010)
- PageRank analysis: here (2010)
- Proof that sojourn times are exponentially distributed in a C-MC here (2010)
Second part, Game Theory
- Lectures: all lectures, part 1, part 2, part 3, part 4, part 5
- Problems: list of problems no. 1 and homework no. 1, solution for homework no.1, exercises (2010)
- Bibliography: Philip D. Straffin. Game Theory and Strategy. Mathematical Association of America Textbooks. Part I, Two-persons Zero-Sum Games: chapters 1, 2, 3, 7, 9, 10. Part II, Two-persons Non-Zero-Sum Games: chapters 11, 12, 14, 15. Part III, N-Person Games: chapters 19, 21, 23, 25, 26.
Old Exams Info (2010)
- Mid-term exam. All documents/Books/etc authorized. No electronic equipment.
- Final exam. You can use any reference material (books, slides, lecture notes), also from your laptop, but its wireless communication interfaces (WiFi, Bluetooth, etc.) have to be disabled.
- Exam example: second exam, February 2010