Stochastic modelling

Teacher(s)

Chevalier Philippe; Jungers Raphaël (compensates Chevalier Philippe);

Language

English

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.

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.

Bibliography

Lecture recommandée : livre "Stochastic Processes: Theory for applications" de R. Gallagher, 2013, disponible en ligne : http://www.rle.mit.edu/rgallager/notes.htm

Faculty or entity

MAP