Simulation The Monte Carlo Method Preliminaries Element n

Preliminaries Element n An item having characteristics or attributes that have logical or numerical

Preliminaries How do we study Systems? Models n n A model is an abstraction

Simulation What is simulation? n A numerical technique for studying models of systems, typically

Simulation Where does simulation exist? • Army • Navy • Air Force • Wackadoos

Monte Carlo Method What is it? n n A stochastic technique – uses random

Monte Carlo Method How does it work? n n With respects to problem solving

Monte Carlo Method Can it be used to solve other problems? n n n

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Simulation The Monte Carlo Method

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

Preliminaries How do we study Systems? Models n n 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.

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

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

Example Nuclear Power Plant Simulation

Monte Carlo Method What is it? n n 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? n n 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.

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

Monte Carlo Method Can it be used to solve other problems? n n n 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.