| Course label : | Markov chains and waiting lines |
|---|---|
| Teaching departement : | MIN / Applied Mathematics and General Computing |
| Teaching manager : | Mister AUGUSTIN MOUZE / Mister PIERRE-ANTOINE THOUVENIN |
| Education language : | |
| Potential ects : | 0 |
| Results grid : | |
| Code and label (hp) : | SMD_SDI_CMF - Chaînes de Markov fil attente |
Education team
Teachers : Mister AUGUSTIN MOUZE / Mister PIERRE-ANTOINE THOUVENIN / Mister OLIVIER GOUBET
External contributors (business, research, secondary education): various temporary teachers
Summary
The lecture introduces the most important notions associated to discrete-time Markov chains (transition matrix, recurrent and transient states, invariant measure, convergence in large times), and then presents a few applications: queuing theory (with generalization in continuous time), Metropolis-Hastings algorithm and Simulated Annealing algorithm. 1. Markov Chains in discrete time 2. Poisson Processes and Queues 3. Monte Carlo Methods (Metropolis-Hastings algorithm), simulated annealing
Educational goals
- Be able to analyze a discrete-time Markov chains, its characteristics and its large time behavior. Simulate Markov chains in Python. - Compute the invariant measure associated to a queue process, and analyze its behavior - Implement Metropolis-Hastings algorithm and Simulated Annealing algorithm
Sustainable development goals
Knowledge control procedures
Continuous Assessment
Comments: 1 homework, 2 graded lab reports, final exam, each assessed by a grade on 20 points
Weights of the activities in the final grade: (exam * 7 + DM + TP1 + TP2)/10
Grading scale: (min) 0 – 20 (max) - Passing grade = 10/20
Online resources
Pedagogy
Lectures (7x2h), tutorial sessions (5x2h, including 2x2h practical sessions) Language of instruction: French.
Sequencing / learning methods
| Number of hours - Lectures : | 14 |
|---|---|
| Number of hours - Tutorial : | 10 |
| Number of hours - Practical work : | 0 |
| Number of hours - Seminar : | 0 |
| Number of hours - Half-group seminar : | 0 |
| Number of student hours in TEA (Autonomous learning) : | 0 |
| Number of student hours in TNE (Non-supervised activities) : | 0 |
| Number of hours in CB (Fixed exams) : | 0 |
| Number of student hours in PER (Personal work) : | 0 |
| Number of hours - Projects : | 0 |
Prerequisites
Notions in probability and Python programming.