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

PreliminariesHow 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.

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

Simulation

Where does simulation exist?

ArmyNavyAir ForceWackadoosRockysDisney QuestAt home!

Example

Nuclear Power Plant Simulation

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.

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

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.