Stochastic modelling

Teacher(s)

Chevalier Philippe; Madani Mehdi (compensates Chevalier Philippe);

Language

English
> French-friendly

Prerequisites

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.

Content

• 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.
• Markov decision processes and Reinforcement learning

Teaching methods

The course consists in weekly lectures and 11 exercice sessions. Part of the lectures will be presented by student groups.

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 make a class presentation of some theory chapter or an application of the theory. This presentation is done in groups and counts for 25% of the grade. This presentation cannot be done again for the session in September.

Bibliography

Lecture recommandée :
 "Stochastic Processes: Theory for applications" de R. Gallagher, 2013, disponible en ligne : http://www.rle.mit.edu/rgallager/notes.htm
"Reinforcement Learning: An Introduction" de R. Sutton et A. Barto, disponible en ligne : http://incompleteideas.net/book/RLbook2020.pdf 

Faculty or entity

> MAP