Simulation

Code:

M268

Acronym:

M268

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2014/2015 - 1S

Active?	Yes
Web Page:	https://moodle.up.pt/course/view.php?id=2300
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:AST	2	Plano de Estudos a partir de 2008	3	-	7,5	-
L:B	1	Plano de estudos a partir de 2008	3	-	7,5	-
L:F	1	Plano de estudos a partir de 2008	3	-	7,5	-
L:G	0	P.E - estudantes com 1ª matricula anterior a 09/10	3	-	7,5	-
		P.E - estudantes com 1ª matricula em 09/10	3	-	7,5	-
L:M	25	Plano de estudos a partir de 2009	3	-	7,5	-
L:Q	0	Plano de estudos Oficial	3	-	7,5	-

Teaching language

Portuguese

Objectives

Knowledge of basic statistical simulation. Strong computational component, aiming a practical multidisciplinary application in the multiple interactions with Probability, Statistics and Operations Research.

Learning outcomes and competences

 

The student must be able to:

 

- Understand when suitable to apply simulation techniques.

 

- Understand the importance of using good uniform random number generators and know efficient statistical distributions generators.

 

- Apply Monte Carlo methods. Perform output statistical analysis and apply variance reduction techniques.

 

- Develop statistical simulation projects. Illustrate, with real or simulated data, the studied themes and critically apply the adequate tools in problems and case studies.

 

 -Analyze/implement simple stochastic simulation situations or with practical real life application, as  Poisson  and birth-death processes, including performance evaluation measures in queuing systems.

 

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Calculus ; Probability and Statistics

Program

 

I. Simulation and Monte Carlo method

Statistical aspects of simulation. Simulation of data (discrete and continuous distributions): general methods, transformations and mixtures; critical use of available current generators. Monte Carlo integration and estimation of expected values. Statistical analysis of simulated data and resampling methods. Variance reduction techniques.

 

II. Introduction to stochastic processes simulation and queuing systems analysis

Poisson processes, random walk and renewal processes.

Birth-death processes and queueing systems: modeling/simulation and performance analysis.

 

Mandatory literature

Ross Sheldon M.; Simulation. ISBN: 0-12-598063-9
Law Averill M.; Simulation modeling and analysis. ISBN: 0-07-116537-1

Complementary Bibliography

Morgan Byron J. T.; Elements of simulation. ISBN: 0-412-24590-6 (Morgan B.J.T., Elements of Simulation, Chapman and Hall, 1984.)
Hillier Frederick S.; Introduction to operations research. ISBN: 007-123828-X
Ross Sheldon M.; Introduction to probability models. ISBN: 978-0-12-375686-2

Teaching methods and learning activities

Lectures T where the topics are presented and illustrated. Lectures TP for Problems / Projects with strong laboratorial computation component (Matlab, R).

Software

Matlab
R Project
Pythonxy-Simpy

keywords

Physical sciences > Mathematics > Applied mathematics > Operations research
Physical sciences > Mathematics > Statistics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	60,00
Participação presencial	0,00
Prova oral	20,00
Trabalho escrito	20,00
Total:	100,00

Eligibility for exams

Computational work / project  presented according to the due schedule (P>=40%).

Calculation formula of final grade

Computational work/project (P), evaluated orally (presentation and discussion) and by a written report, presented according the schedule, and final exam (E). Minimum mark in each component E and P (40%). Final classification (E*12+P*8)/20.

 

Examinations or Special Assignments

n.a.

Special assessment (TE, DA, ...)

n.a.

Classification improvement

Component E

Observations

Exams evaluation panel in 2013/14: Ana Paula Rocha, Margarida Brito