Ensimag Rubrique Formation 2022

Probability for computer science - 4MMPIEP6

  • Number of hours

    • Lectures 16.5
    • Projects -
    • Tutorials 16.5
    • Internship -
    • Laboratory works -
    • Written tests -


    ECTS 3.0


Random processes are basic tools for modeling communication networks and computer systems for their design. They allow on one hand to understand the phenomena of heavy/low traffic and on the other hand to develop management policies (protocols, allocation, optimization...)
The purpose of this course is to lead to:

  • Know how to model a computer system using Markov processes;
  • Be able to analyze the behavior of random processes using
    formal methods or simulations;
  • Be able to analyze the behavior of classic protocols of communication.




1. Modeling of computer systems and performance evaluation;
2. Basic tools in probability;
3. Fundamentals of Performance Evaluation;
4. Markov chains : automata and probabilities;
5. Poisson process : Quality of service, traffic models and loss analysis;
6. Reversibility, Markov algorithm : contention and network of queueing systems
7. Robustness of Markov models.


Applied Probability and Statistical Principles and Methods (1rst year Ensimag).


1st session : Written exam 2h

2nd session : Written exam 2h

  1. Lexique
    CC = contrôle continu # non rattrapable
    E1 = examen de session 1
    E2 = examen de session 2
  1. Notes transmises à la scolarité
    N1=(2 x E1+CC)/3 # note finale de session 1 si examen en présenciel
    N1=CC # si pas d'examen en présenciel
    N2=(2 x E2+CC)/3 # note finale après rattrapage


The course exists in the following branches:

see the course schedule for 2023-2024

Additional Information

Course ID : 4MMPIEP6
Course language(s): FR

The course is attached to the following structures:

You can find this course among all other courses.


O. François : Notes de Cours de Probabilités Ensimag 1ère année.
O. Gaudoin : Principe et Méthode Statistique Ensimag 2ème année.
S.M. Ross : Probability Models for Computer Science, Academic Press, 2001.

Cours de Gérard Hébuterne à l'INT
Le livre de Jean-Yves Le Boudec en évaluation de performances

Orienté évaluation de performances (pratique)

P.Brémaud Markov Chains, Gibbs Fields, Monte Carlo Simulation and Queues, Springer 1999.
J. Banks, J. S. Carson II, B. L. Nelson et D. M. Nicol, Discrete-Event System Simulation, Pearson 2010
R. Jain, The Art of Computer Systems Performance Analysis Techniques for Experimental Design, Measurement, Simulation, and Modeling, Wiley 1991