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  Performance Evaluation of Networks

About the course

This course will expose the students to the basic concepts and tools used in probabilistic modeling, performance evaluation, optimization and control of large-scale computer networks and distributed systems. The course will cover the theory of Markov chains (discrete time, continuous time, irreducible, absorbing, birth and death processes), the theory of queues (classical M/M/1, M/M/1/K, M/M/c, M/M/c/c, M/G/1) and product-form network of queues (Jackson networks, Kelly networks). Numerous applications will be studied throughout the class, such as the modeling of IEEE 802.11 and the modeling of Web servers.


About the teacher

Sara Alouf
Inria - Project-team NEO
2004 Route des Lucioles
Sophia Antipolis, France

Office: L115
Email: Sara (dot) Alouf (at) inria (dot) fr
Website, ResearchGate, Google Scholar

Schedule

24 September 2019 Lecture 1: Introduction and Discrete-Time Markov Chains
Related exercises: 2015-2016, 2016-2017, 2017-2018
1 October 2019 Lecture 2: Continuous-Time Markov Chains
Teacher: Giovanni Neglia
Related exercises: 2015-2016, 2016-2017, 2017-2018
8 October 2019 Lecture 3: Absorbing Markov Chains
Related exercises: 2015-2016, 2016-2017, 2017-2018
15 October 2019 Lecture 4: Basic Queues and the Little Formula
Related exercises: 2015-2016, 2016-2017, 2017-2018
22 October 2019 Mid-term evaluation (to confirm)
Lecture 5: The General Service Time Queue
Related exercises: 2015-2016, 2016-2017, 2017-2018
29 October 2019 Lecture 6: Queueing Networks
Related exercises: 2015-2016, 2016-2017, 2017-2018
5 November 2019 Final exam

Exercises

In previous years, six homeworks were given one for each lecture. Students are encouraged to do the exercises on a regular basis.
Academic year 2015-2016 homework 1, homework 2, homework 3, homework 4, homework 5, homework 6
Academic year 2016-2017 homework 1, homework 2, homework 3, homework 4, homework 5, homework 6
Academic year 2017-2018 homework 1, homework 2, homework 3, homework 4, homework 5, homework 6

References

  • D. P. Bertsekas and R. G. Gallager, Data Networks, (2nd edition) Prentice Hall, 1992.
  • E. Gelenbe and I. Mitrani, Analysis and Synthesis of Computer Systems, Academic Press (London and New York), 1980.
  • M. Harchol-Balter, Performance Modeling and Design of Computer Systems, Cambridge University Press, 2013.
  • F. P. Kelly, Reversibility and Stochastic Networks, Wiley, Chichester, 1979.
  • L. Kleinrock, Queueing Theory, Vol. 1, J. Wiley $\&$ Sons, New York, 1975.
  • M. F. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, John Hopkins University Press, 1981.