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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

12 January 2021 Lecture 1: Introduction and Discrete-Time Markov Chains
Related exercises: 2015-2016, 2016-2017, 2017-2018
19 January 2021 Return homework 1
Lecture 2: Continuous-Time Markov Chains
Related exercises: 2015-2016, 2016-2017, 2017-2018
26 January 2021 Return homework 2
Lecture 3: Absorbing Markov Chains
Related exercises: 2015-2016, 2016-2017, 2017-2018
2 February 2021 Return homework 3
Lecture 4: Basic Queues and Little Formula
Related exercises: 2015-2016, 2016-2017, 2017-2018
9 February 2021 Return homework 4
Lecture 5: The General Service Time Queue
Related exercises: 2015-2016, 2016-2017, 2017-2018
16 February 2021 Return homework 5
Lecture 6: Queueing Networks
Related exercises: 2015-2016, 2016-2017, 2017-2018
23 February 2021 Return homework 6
Lecture 7: Use case studies
2 March 2021 Return homework 7

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.