Stochastic modelling

linma2470  2019-2020  Louvain-la-Neuve

Stochastic modelling
Note from June 29, 2020
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
5 credits
30.0 h + 22.5 h
Chevalier Philippe; Jungers Raphaël (compensates Chevalier Philippe);
A probability course and a background in mathematical modelling
Main themes
Introduction to stochastic models in operations research. Study of renewal processes, Markov chains, Markov Processes, Markov Decision Processes. Applications to inventory models, queuing models, branching processes, random walks, etc.
  • Poisson processes and their properties
  • Markov chains with a finite number of states
  • Renewal processes and stopping rules
  • Markov chains with an infinite number of states
  • The notion of reveribility
  • Markov processes
  • Birth and death processes
  • Queueing theory and networks of queues
  • Fluid models for queues
  • Various applications, such as inventory management, replacement, reliability and job shop modeling.
Teaching methods
The course consists in weekly lectures and 11 exercice sessions. One of the courses will be devoted to the student presentations of their simulation projects and another session will host a practioner to present a real world application of the course contents.
Evaluation methods
Students will be evaluated through a written exam based on the objectives of the course. The exam consists in exercices applying the concepts viewed in the course. Many examples of questions of previous exams are solved during the exercice sessions.

The students will have to build a simulation model in order to analyse and understand the behavior of a congested stochastic system. This assignment is done in groups. This assignement cannot be done again for the session in September.
Lecture recommandée : livre "Stochastic Processes: Theory for applications" de R. Gallagher, 2013, disponible en ligne :
Faculty or entity

Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Master [120] in Data Science Engineering

Master [120] in Mathematics

Master [120] in Computer Science and Engineering

Master [120] in Mathematical Engineering

Master [120] in Computer Science

Master [120] in Data Science: Information Technology