
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 largescale 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 productform 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
12 January 2021 
Lecture 1: Introduction and DiscreteTime Markov Chains
Related exercises:
20152016,
20162017,
20172018 
19 January 2021 
Return homework 1
Lecture 2: ContinuousTime Markov Chains
Related exercises:
20152016,
20162017,
20172018 
26 January 2021 
Return homework 2
Lecture 3: Absorbing Markov Chains
Related exercises:
20152016,
20162017,
20172018 
2 February 2021 
Return homework 3
Lecture 4: Basic Queues and Little Formula
Related exercises:
20152016,
20162017,
20172018 
9 February 2021 
Return homework 4
Lecture 5: The General Service Time Queue
Related exercises:
20152016,
20162017,
20172018 
16 February 2021 
Return homework 5
Lecture 6: Queueing Networks
Related exercises:
20152016,
20162017,
20172018 
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 20152016 
homework 1,
homework 2,
homework 3,
homework 4,
homework 5,
homework 6

Academic year 20162017 
homework 1,
homework 2,
homework 3,
homework 4,
homework 5,
homework 6

Academic year 20172018 
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. HarcholBalter, 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, MatrixGeometric Solutions in Stochastic Models: An Algorithmic Approach, John Hopkins University Press, 1981.
