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Simulation
| Credits |
6 credit points |
| Instructors |
Ridder, A.A.N. (Vrije Universiteit), Heidergott, B.F. (Vrije Universiteit) |
| E-mail |
aridder@feweb.vu.nl, bheidergott@feweb.vu.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 (5 weeks) simulation modeling and programming, model validation and verification, random number generators, generating random variates, statistical analysis; Part B (3 weeks) variance reduction techniques, Markov Chain Monte Carlo simulation; Part C (4 weeks) simulation optimisation.
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.
Part B reviews two special topics that attract huge attention in the scientific simulation literature.
We will discuss importance sampling techniques to estimate efficiently very small probabilities (E-6 or less) in stochastic systems, e.g., loss probabilities in queueing models, or the system unavailability in reliability models. And we will explain the Gibbs Sampler, a technique that is nowadays a standard tool in scientific computing and Bayesian statistics.
Part C concerns optimization, where one deals with methods to optimize parameters within simulation programs, e.g., service rates in queueing models. State-of-art approaches to combining simulation and stochastic optimization will be discussed. In particular, perturbation analysis, the score function method and weak differentiation will be addressed. All of these methods have in common that they combine Monte Carlo simulation and clever mathematical algorithms based on sample-path analysis. Specifically, we will discuss on-line optimization, an approach where a system can be optimized based on single realization. |
| Organization |
Classes start September 18, 2006 and end December 4, 2006. |
| Examination |
- Weekly simulation modeling and programming exercises.
- Simulation project.
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| Literature |
- Part A: Chapters 5, 7, 8, and 9 in A. Law & W. Kelton, Simulation Modeling and Analysis, McGraw-Hill, 3-rd ed. 2000.
- Part B: Chapters 8 and 10 in S.M. Ross, Simulation, Academic Press, 3-rd ed. 2002.
- Part C: Handouts.
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| Prerequisites |
- Basic stochastic modeling and simulation (e.g., chapters 8-11 in S.M. Ross, Introduction to probability models, Academic Press, 6-th ed. 1997, or 7-th ed. 2000).
- Programming skills (e.g. in C/C++/Java/Matlab).
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