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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
Schedule
This year, the course is scheduled on Tuesdays mornings from 9:30 am until 12:45 am with a 15 minutes break.
| 4 January 2022 |
Lecture 1: Introduction and Discrete-Time Markov Chains
Related exercises:
2015-2016,
2016-2017,
2017-2018 |
| 11 January 2022 |
Return homework 1
Lecture 2: Continuous-Time Markov Chains
Related exercises:
2015-2016,
2016-2017,
2017-2018 |
| 18 January 2022 |
Return homework 2
Lecture 3: Absorbing Markov Chains
Related exercises:
2015-2016,
2016-2017,
2017-2018 |
| 25 January 2022 |
Return homework 3
Lecture 4: Basic Queues and Little Formula
Related exercises:
2015-2016,
2016-2017,
2017-2018 |
| 1 February 2022 |
Return homework 4
Lecture 5: The General Service Time Queue
Related exercises:
2015-2016,
2016-2017,
2017-2018 |
| 8 February 2022 |
Return homework 5
Lecture 6: Queueing Networks
Related exercises:
2015-2016,
2016-2017,
2017-2018 |
| 15 February 2022 |
Return homework 6
Lecture 7: Use case studies |
| 22 February 2022 |
Written 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
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| Academic year 2016-2017 |
homework 1,
homework 2,
homework 3,
homework 4,
homework 5,
homework 6
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| Academic year 2017-2018 |
homework 1,
homework 2,
homework 3,
homework 4,
homework 5,
homework 6
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References
- D. P. Bertsekas and R. G. Gallager, Data Networks, (2nd edition) Prentice Hall, 1992.
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E. Gelenbe and I. Mitrani, Analysis and Synthesis of Computer Systems, Academic Press (London and New York), 1980.
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M. Harchol-Balter, Performance Modeling and Design of Computer Systems, Cambridge University Press, 2013.
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F. P. Kelly, Reversibility and Stochastic Networks, Wiley, Chichester, 1979.
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L. Kleinrock, Queueing Theory, Vol. 1, J. Wiley $\&$ Sons, New York, 1975.
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M. F. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, John Hopkins University Press, 1981.
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