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Simulation

Simulation. The Monte Carlo Method. Preliminaries. Element An item having characteristics or attributes that have logical or numerical values. System A set of related elements that may interact Two types: Internal External. Preliminaries. How do we study Systems? Models

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Simulation

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  1. Simulation The Monte Carlo Method

  2. Preliminaries • Element • An item having characteristics or attributes that have logical or numerical values. • System • A set of related elements that may interact • Two types: • Internal • External

  3. Preliminaries • How do we study Systems? • Models • A model is an abstraction of a real system that can be used for prediction and control. • The purpose of a model is to enable one to determine how one or more changes in variables effect the system.

  4. Simulation • What is simulation? • A numerical technique for studying models of systems, typically on a digital computer. • What types of models can we simulate? • Abstract models • Physical models • Ex: Theme Park line – Abstract Solar System - Physical

  5. Simulation • Where does simulation exist? Army Navy Air Force Wackadoos Rockys Disney Quest At home!

  6. Example Nuclear Power Plant Simulation

  7. Monte Carlo Method • What is it? • A stochastic technique – uses random numbers and statistical techniques • Method of using independent random variables (pseudo random numbers) to study the outcomes of a system. • Where did it originate? • Term “Monte Carlo” was introduced by von Neumann and Ulam during World War II as a code word for the secret work at Los Alamos. • The method was named after a city in the Monoco principality, because a roulette, a simple random number generator.

  8. Monte Carlo Method • How does it work? • With respects to problem solving • Lets attempt to calculate PI by a “hit and miss” integration. • Can it be used to solve other problems? • Buffon’s Needle Problem: • Simply stated: Given a needle and two lines, determine the probability of the needle crossing one of the lines on the page. • Monty Halls 3-Door Problem

  9. Monte Carlo Method • Can it be used to solve other problems? • Traveling Salesman problem • Numerical Integration - Estimating the value of a definite integral or sum • Knapsack Problem – Estimating the most valuable subset of items that will fit into a knapsack.

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