
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
24 September 2019 
Lecture 1: Introduction and DiscreteTime Markov Chains
Related exercises:
20152016,
20162017,
20172018 
1 October 2019 
Lecture 2: ContinuousTime Markov Chains
Teacher: Giovanni Neglia
Related exercises:
20152016,
20162017,
20172018 
8 October 2019 
Lecture 3: Absorbing Markov Chains
Related exercises:
20152016,
20162017,
20172018 
15 October 2019 
Lecture 4: Basic Queues and the Little Formula
Related exercises:
20152016,
20162017,
20172018 
22 October 2019 
Midterm evaluation (to confirm)
Lecture 5: The General Service Time Queue
Related exercises:
20152016,
20162017,
20172018 
29 October 2019 
Lecture 6: Queueing Networks
Related exercises:
20152016,
20162017,
20172018 
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 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.
