Simulation

Credits	6 credit points
Instructors	Tijms, H.C. (Vrije Universiteit), Blanc, H. (Universiteit van Tilburg)
E-mail	tijms@feweb.vu.nl, j.p.c.blanc@uvt.nl
Aim	The course gives a comprehensive treatment of the basic aspects of discrete event simulations in stochastic operations research models such as queueing, manufacturing, reliability, and it presents new developments of advanced simulation techniques.
Description	The topics covered include: Part A (8 weeks): Simulation modeling and programming, model validation and verification, random number generators, generating random variates, statistical analysis, variance reduction techniques, and experimental design. Part B (4 weeks) : Markov Chain Monte Carlo simulation, Metropolis-Hastings algorithm, Gibbs sampler, simulated anneaking. Part A treats the basic stochastic simulation techniques after which the student should be able to develop his/her own simulation study of a stochastic OR system. Also the student is taught to become aware not only of the success stories of simulations but also of their fallacies. In the topic of variance reduction techniques, the main focus will be on applying importance sampling to finite queueing models in order to estimate very small loss probabilities. Part B reviews special topics. We discuss simulation from the multivariatedensities including the special case of the multivariate normal distribution. Much attention will be paid to the Metropolis-Hastings algorithm which is a generalized acceptance-rejection method for generating from a multivariate density that is given up to a multiplicative constant. This widely used algorithm is based on the concept of reversible Markov chains and has applications in Bayesian statistics amongst others The Gibbs sampler being a special case of the Metroplis-Hastings algorithm will also be discussed. Also, attention will be given to the simulation approach simulated annealing for finding the optimum of a function on a large discrete set. This approach is alo based on the concept of reversible Markov chains.
Examination	- Homework problems and programming exercises. - Simulation projects.
Literature	The topics covered include: Part A (8 weeks): Simulation modeling and programming, model validation and verification, random number generators, generating random variates, statistical analysis, variance reduction techniques, and experimental design. Part B (4 weeks) : Markov Chain Monte Carlo simulation, Metropolis-Hastings algorithm, Gibbs sampler, simulated anneaking. Part A treats the basic stochastic simulation techniques after which the student should be able to develop his/her own simulation study of a stochastic OR system. Also the student is taught to become aware not only of the success stories of simulations but also of their fallacies. In the topic of variance reduction techniques, the main focus will be on applying importance sampling to finite queueing models in order to estimate very small loss probabilities. Part B reviews special topics. We discuss simulation from the multivariatedensities including the special case of the multivariate normal distribution. Much attention will be paid to the Metropolis-Hastings algorithm which is a generalized acceptance-rejection method for generating from a multivariate density that is given up to a multiplicative constant. This widely used algorithm is based on the concept of reversible Markov chains and has applications in Bayesian statistics amongst others The Gibbs sampler being a special case of the Metroplis-Hastings algorithm will also be discussed. Also, attention will be given to the simulation approach simulated annealing for finding the optimum of a function on a large discrete set. This approach is alo based on the concept of reversible Markov chains.
Prerequisites	- Basic stochastic modeling and simulation (at the level of the course Introduction to Stochastic Processes). - The student should have experience with programming in Matlab or C++.

Last changed: 08-09-2010 09:56