Simulation First Unit 20112012

8/3/2019 Simulation First Unit 20112012

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VELAGAPUDI RAMAKRISHNA

SIDDHARTHA ENGINEERING COLLEGEDEPARTMENT OF INFORMATION TECHNOLOGYAccredited by NBA Approved by AICTE - Autonomous

4-May-12

Simulation and modeling

Unit I


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B L N Phaneendra kumar

DEPARTMENT OF Information TechnologyVR SIDDHARTHA ENGINEERING COLLEGE 2

Introduction to System

A Systemis defined to be a set of elements which interact or interrelated insome fashion Elements having no relationship with the set of elements that have been

chosen as system can not affect the system hence irrelevant A System may consist of sub systems or may be a part of a larger

system

Example: Factory system This system consists of two major components- fabrication department

and assembly department.

Elements that often make up the system are called Entities

Entities that comprise a system need not be tangible e.g, a queuingsystem is made up of customers, queue and servers Customers and servers are physical entities but queue itself is a

concept


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More components of a system

An Attributeis a property of a system

An Activityrepresents a time period of specified length

Stateof system is defined to be that collection of variablesnecessary to describe the system at any time , relative to the

objective of the study In the study of a bank possible state variables are number of

busy tellers, number of customers waiting in the queue or beingserved, arrival and service times of the next customer

An Eventis defined as an instantaneous occurrence that may

change the state of the system


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More terms of a system

Endogenous used to describe the activities and eventsoccurring within a system

Exogenous is used to describe activities and events inthe environment that affect the system

In the bank arrival of a customer is exogenous event andcompletion of service of a customer is endogenous event


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Examples: Traffic System

Entities Cars

Attributes (property of an entity) speed, distance

Activities (time period of specified length) driving

Events arrival, departure

State variables Number of busy tellers, number of customerswaiting


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Examples: Banking System

Entities Customers

Attributes (property of an entity) Checking account balance, makingdeposits, getting a draft made

Activities (time period of specified length) Time taken to make a

deposit, time taken to get a draft made Events arrival, departure

State variables Number of busy tellers, number of customerswaiting


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Examples: Rail System

Entities Commuters

Attributes (property of an entity) Origination ,Destination

Activities (time period of specified length) Traveling

Events arrival at station, arrival at destination

State variables Number of commuters waiting at eachstation, number of commuters traveling


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Examples: Production System

Entities Machines

Attributes (property of an entity) Speed , Capacity,Breakdown rate

Activities (time period of specified length) Welding,Cutting, Stamping

Events breakdown

State variables Status of machines busy, idle or

down


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Entities Messages

Attributes (property of an entity) Length , Destination

Activities (time period of specified length) Transmitting

Events arrival at destination State variables Number of messages waiting to be

transmitted

Examples: Communications System


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Examples: Inventory System

Entities Warehouse

Attributes (property of an entity) Capacity

Activities (time period of specified length) Issue,

Receipt Events Demand

State variables Level of inventory, Backloggeddemands


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Introduction to model

A model is a system that is used as a surrogate for another system

Reason for using a model

Helps in understanding the behaviour of a real system before itis built

Cost of building and experimenting with a model is less Models can be used to mitigate risk pilots can be taught how to

cope with wind sheer while landing

Models have the capability of scale time or space in favourablemanner wind sheer can be produced on demand


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Types of Models

Broadly there are two types

Physical

(Scale models, prototype plants,)

Mathematical

(Analytical queuing models, linear programs,simulation)


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Building a simulation gas station

Assume single pump served by a single service man arrival of cars as well their service times are random.

At first identify the: states: number of cars waiting for service and number of cars

served at any moment events: arrival of cars, start of service, end of service entities: these are the cars queue: the queue of cars in front of the pump, waiting for service random realizations: inter-arrival times, service times

distributions: we shall assume exponential distributions for boththe inter-arrival time and service time.


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Ten Types of Models

Iconic - physical models that are images of the real world;dimensions are usually scaled up or down; for example, models ofcars might be constructed and tested in a wind tunnel

Analog - model that substitutes one set of properties for another;may be iconic or mathematical; electric resistance often used as an

analog of the friction of a fluid flowing in a pipe; this approach is notas widely used as at one time digital computers have allowed thedevelopment of other modeling techniques that have replacedanalog models


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Ten Types of Models

Stochastic - probabilistic model that uses randomness to accountfor immeasurable factors (e.g., weather)

Deterministic - model that does not use randomness but usesexplicit expressions for relationships that may or may not involvetime rates of change

Discrete - model where state variables change in steps as opposedto continuously with time (e.g., number of cattle in a barn); may bedeterministic or stochastic


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Ten Types of Models

Continuous - model whose state variables change continuouslywith time (e.g., biomass in a field); usually sets of differentialequations used; initial conditions required (can be difficult to obtainfor some systems!)

Combined - model where some state variables changecontinuously and others change in steps at event times; forexample, a field of hay might be modeled using a combinedapproach with the biomass modeled continuously during growth andthen as a discrete event when harvested


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Ten Types of Models

Mathematical - abstract model usually written inequation form

Object-oriented - use objects that are abstractions ofreal world objects and develop relationships and actions

between objects; comes from field of artificial intelligence Heuristic - heuristics (rules) are used to model the

system; comes from field of artificial intelligence.


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B L N Phaneendra kumarDEPARTMENT OF Information TechnologyVR SIDDHARTHA ENGINEERING COLLEGE 18

Types of Simulation Models

System model

deterministic stochastic

static dynamic static dynamic

continuous discrete continuous discrete

Monte Carlosimulation

Discrete-eventsimulation

Continuoussimulation

Discrete-eventsimulation

Continuoussimulation


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Stochastic vs. Deterministic

Stochastic simulation: a simulation that contains random(probabilistic) elements, e.g.,

Examples Inter-arrival time or service time of customers at a restaurant or

store

Amount of time required to service a customer Output is a random quantity (multiple runs required to analyze

output)

Deterministic simulation: a simulation containing no randomelements

Examples Simulation of a digital circuit Simulation of a chemical reaction based on differential equations

Output is deterministic for a given set of inputs


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Static vs. Dynamic Models

Static modelsModel where time is not a significant variable

Examples Determine the probability of a winning solitaire hand

Static + stochastic = Monte Carlo simulation Statistical sampling to develop approximate solutions to

numerical problems

Dynamic modelsModel focusing on the evolution of the system under

investigation over time


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Continuous vs. Discrete

Discrete

State of the system is viewed as changing at discrete points intime: arrival of a customer in a queuing system

An event is associated with each state transition Events contain time stamp

Continuous

State of the system is viewed as changing continuously acrosstime: rise if water level in a dam

System typically described by a set of differential equations

Few systems in practice are wholly discrete or continuous


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B L N Phaneendra kumarDEPARTMENT OF Information TechnologyVR SIDDHARTHA ENGINEERING COLLEGE

Continuous / Discrete Systems

Continuous State and Discrete State Models

Example: Time spent by students in a weekly class vs.Number of jobs in Q.

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Combined Systems

Communication channel

Modeled as discrete if characteristics of movement ofeach message is important

Modeled as continuous if flow of messages as aggregate

over the channel is important


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Simulation

Simulation is defined as the process of creating a modelof anexisting or proposed systemin order to identify and understandthose factors which control the system and/or to predict the futurebehavior of the system.

Almost any system which can be quantitatively described usingequations and/or rules can be simulated.

Simulation is used to predict the future behavior of a system, anddetermine what we can do to influence that future behavior.

Simulation is a powerful and important tool because it provides a

way in which alternative designs, plans and/or policies can beevaluated without having to experiment on a real system, which maybe prohibitively costly, time-consuming, or simply impractical to do.

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When Simulation is the Appropriate Tool

Simulation enables the study of, and experimentation with, the internalinteractions of a complex system, or of a subsystem within a complexsystem.

Informational, organizational, and environmental changes can besimulated, and the effect of these alterations on the models behaviorcan be observed.

The knowledge gained in designing a simulation model may be of greatvalue toward suggesting improvement in the system under investigation. By changing simulation inputs and observing the resulting outputs,

valuable insight may be obtained into which variables are mostimportant and how variables interact.

Simulation can be used to experiment with new designs or policies prior

to implementation, so as to prepare for what may happen. Simulation can be used to verify analytic solutions. By simulating different capabilities for a machine, requirements can be

determined.

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When Simulation is not Appropriate

When the problem can be solved using common sense.

When the problem can be solved analytically.

When it is easier to perform direct experiments.

When the simulation costs exceed the savings.

When the resources or time are not available. When system behavior is too complex or cant be defined.

When there isnt the ability to verify and validate the model

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Advantages

the basic concept of simulation is easy to comprehend

easy to justify to management or customers than someof the analytical models

be more credible because its behavior has been

compared to that of the real system

requires fewer simplifying assumptions and hencecaptures more of the true characteristics of the systemunder study

can test new designs, layout, etc. without committingresources to their implementation

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Advantages contd..

can be used to explore new staffing policies, operatingprocedure, decision rules, organizational structures,information flows, etc. without disrupting the ongoingoperations

allows us to identify bottlenecks in information, materialand product flows and test options for increasing the flowrates

allows us to test hypothesis about how or why certain

phenomena occur in the system

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Advantages contd..

allows us to control time. Thus we can operate thesystem for several months or years of experience in amatter of seconds allowing us to quickly look at long timehorizons or we can slow down phenomena for study

allows us to gain insights into how a modeled systemactually works and understanding of which variables areimportant to performance

great strength is its ability to let us experiment with new

and unfamiliar situations and to answer what ifquestions

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Disadvantages

Model building requires special training. It is an art that is learnedover time and through experience. Furthermore, if two models areconstructed by two competent individuals, they may havesimilarities, but it is highly unlikely that they will be the same.

Simulation results may be difficult to interpret. Since mostsimulation outputs are essentially random variables (they are usually

based on random inputs), it may be hard to determine whether anobservation is a result of system interrelationships or randomness.

Simulation modeling and analysis can be time consuming andexpensive. Skimping on resources for modeling and analysis mayresult in a simulation model or analysis that is not sufficient for thetask.

Simulation is used in some cases when an analytical solution ispossible. This might be particularly true in the simulation of somewaiting lines where closed-form queuing models are available.

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Manufacturing Applications

Analysis of electronics assembly operations Design and evaluation of a selective assembly station for high-precision scroll

compressor shells Comparison of dispatching rules for semiconductor manufacturing using large-

facility models Evaluation of cluster tool throughput for thin-film head production

Determining optimal lot size for a semiconductor back-end factory Optimization of cycle time and utilization in semiconductor test manufacturing Analysis of storage and retrieval strategies in a warehouse Investigation of dynamics in a service-oriented supply chain Model for an Army chemical munitions disposal facility

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Applications

Construction Engineering Construction of a dam embankment Trenchless renewal of underground urban infrastructures Activity scheduling in a dynamic, multiproject setting Investigation of the structural steel erection process Special-purpose template for utility tunnel constructionMilitary Application Modeling leadership effects and recruit type in an Army recruiting station Design and test of an intelligent controller for autonomous underwater

vehicles Modeling military requirements for nonwarfighting operations Multitrajectory performance for varying scenario sizes Using adaptive agent in U.S Air Force pilot retention

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Logistics, Transportation, andDistribution Applications

Evaluating the potential benefits of a rail-traffic planning algorithm Evaluating strategies to improve railroad performance Parametric modeling in rail-capacity planning Analysis of passenger flows in an airport terminal Proactive flight-schedule evaluation

Logistics issues in autonomous food production systems forextended-duration space exploration

Sizing industrial rail-car fleets Product distribution in the newspaper industry Design of a toll plaza Choosing between rental-car locations Quick-response replenishment

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Applications contd..

Business Process Simulation

Impact of connection bank redesign on airport gate assignment

Product development program planning

Reconciliation of business and systems modeling

Personnel forecasting and strategic workforce planning

Human Systems

Modeling human performance in complex systems

Studying the human element in air traffic control

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Simulation vs. Analytical Methods

Comparison of specific aspects

Macro vs. micro

Uniformity vs. randomness

Effects of interactions

Single answer vs. range of outcomes

Numerical vs. animation

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1. Macro vs. Micro

Analytical methods ignore the differences betweenindividuals, and rely on the analysis of averagebehaviour.

Simulation models, on the other hand, use thedistribution of population behaviour, and can accountaccurately for peaking of demand during short timeintervals.

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B L N Phaneendra kumarDEPARTMENT OF Information Technology

VR SIDDHARTHA ENGINEERING COLLEGE

2. Uniformity vs. Randomness

Analytical models assume that processes are distributeduniformly and behave homogeneously over a period oftime.

Simulation models recognize and account for therandomness of processes.

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3. Effects of Interactions

Analytical methods are limited to evaluating the outcomeof a stand-alone process and cannot recognize theinteraction effects that parallel processes may have onthat process.

Simulation methods are able to explicitly model suchinteraction effects, allowing the analyst to measure theimpact of process interactions.

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4. Single Answer vs. Range ofOutcomes

The solution of analytical models yields one answer tothe question of interest.

Simulation models, in contrast, generate a variety ofstatistics that can be used to evaluate a systems

performance.

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5. Numerical vs. Animation

Analytical solutions give only numerical results, whichare simple, but less persuasive.

Simulation models, however, may provide computeranimation in addition to numerical results. This picture

of the result can be very persuasive in conveying theresult of analysis.

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VR SIDDHARTHA ENGINEERING COLLEGE 41

Steps in Simulation Study

Problem Formulation

Setting objectives & Plan

Data Collection

Model Conceptualization

Verify model

Validate model

Fundamentallyan iterative

processModel Translation

Experimental DesignOver to next

slide


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VR SIDDHARTHA ENGINEERING COLLEGE42

Steps in Simulation Study

Production run & Analysis

More runs?

Documentation & Reporting

Implementation

From previous slide


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Steps insimulation


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VR SIDDHARTHA ENGINEERING COLLEGE8001: Simulation and Modeling(2011-12) 44


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Problem Formulation

Initial step

Identify controllable and uncontrollable inputs

Identify constraints on the decision variables

Define measure of system performance and an objective function

Develop a preliminary model structure to interrelate the inputs andthe measure of performance

May be the problem needs reformulation as the study progresses


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Setting Objectives & Plan

What do you (or the customer) hope to accomplish with the model May be an end in itself

Predict the weather Train personnel to develop certain skills (e.g., driving)

More often a means to an end

Optimize a manufacturing process or develop the most costeffective means to reduce traffic congestion in some part of a city

Often requires developing a business case to justify the cost Improved efficiency will save the company $$$

Example: electronics

Even so, may be hard to justify in lean times

Goals may not be known when you start the project! One often learns things along the way


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Develop Conceptual Model

An abstract (i.e., not directly executable) representation of the system

What should be included in model? What can be left out?

What abstractions should be used

Level of detail

Often a variation on standard abstractions

Example: transportation Fluid flow?

Queuing network?

Cellular automation?

What metrics will be produced by the model?

Appropriate choice depends on the purpose of the model


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Data Collection

Regardless of the method used to collect the data, thedecision of how much to collect is a trade-off betweencost and accuracy

Constant inter play between construction of the model

and the collection of needed input Changes with the degree of complexity of the model

Data should be collected for the validation as well


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Model translation

Model requires great deal of information andcomputation

Needs to be translated into computer recognizableformat using either special purpose or general purpose

languages

Focus of this course will be using Excel for modelbuilding

Arena characteristics will be introduced


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Verification & Validation

Verification focuses on the internal consistency of amodel

Validation is concerned with the correspondencebetween the model and the reality

Validation is applied to those processes which seek todetermine whether or not a simulation is correct withrespect to the "real" system

Validation is concerned with the question "Are webuilding the right system?


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Verification & Validation

Verification seeks to answer the question "Are webuilding the system right?"

Verification checks that the implementation of thesimulation model (program) corresponds to the model

Validation checks that the model corresponds to reality Calibration checks that the data generated by the

simulation matches real (observed) data.


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Experimental Design

Alternatives to be simulated must be determinedGood experimental design Randomization

Replication

Local control For each system decisions needed Length of the initialization period

Length of the simulation run

Number of replication


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8001: Simulation and Modeling(2010-11) 53

Production runs and analysis

To measure performance of the simulation system sodesigned

Also to determine if more runs needed till results areconsistent


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Documentation & Reporting

Two types

Program

Needed if it is to be used again

May need to be applied for different system by different

people For modification

Progress

Provides important written history of simulation project

Should be frequent as the project progresses


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Implementation

Success depends how well previous steps were followed


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OTHER TYPES OF SIMULATION

Continuous simulation Typically, solve sets of differential equations numerically over

time

May involve stochastic elements

Some specialized software available; some discrete-eventsimulation software will do continuous simulation as well

Combined discrete-continuous simulation

Continuous variables described by differential equations

Discrete events can occur that affect the continuously-changingvariables

Some discrete-event simulation software will do combineddiscrete-continuous simulation as well


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A Monte Carlo method is a technique that involves using randomnumbers and probability to solve problems. The term Monte CarloMethod was coined by S. Ulam and Nicholas Metropolis in referenceto games of chance, a popular attraction in Monte Carlo, Monaco.

Monte Carlo simulation is a method for iterativelyevaluating adeterministic model using sets of random numbers as inputs. Thismethod is often used when the model is complex, nonlinear, orinvolves more than just a couple uncertain parameters.

A Monte Carlo method can be loosely described as a statisticalmethod used in simulation of data.

It is a simulation that makes use of internally generated (pseudo)random numbers

Example: CPU time on some of the fastest computers in the world isspent performing Monte Carlo simulations.

Monte Carlo Simulation


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The Monte Carlo method is just one of many methods foranalyzing uncertainty propagation, where the goal is todetermine how random variation, lack of knowledge,or erroraffects the sensitivity, performance,

or reliabilityof the system that is being modeled.

Monte Carlo simulation is categorized as a samplingmethod because the inputs are randomly generated

from probability distributionsto simulate the process ofsampling from an actual population.

Monte Carlo Simulation contd..


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Other Types of Simulation(contd.)

Monte Carlo simulationWide variety of mathematical problems

Example: Evaluate a difficult integral Let X~ U(a, b), and let Y= (ba) g(X)

Then


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The data generated from thesimulation can be representedas probability distributions (or

histograms) or convertedto error bars, reliabilitypredictions, tolerance zones,and confidence intervals.

Monte carlo Simulation contd..


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The Monte Carlo method provides approximate solutionsto a variety of mathematical problems by performingstatistical sampling experiments on a computer.

The method applies to problems with no probabilistic

content as well as to those with inherent probabilisticstructure.


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Steps in Monte Carlo Simulation

Step 1:Create a parametric model, y = f(x1, x2, ..., xq).

Step 2:Generate a set of random inputs, xi1, xi2, ..., xiq.

Step 3:Evaluate the model and store the results as yi.

Step 4:Repeat steps 2 and 3 for i= 1 to n.

Step 5:Analyze the results using histograms, summarystatistics, confidence intervals, etc.


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Monte Carlo Example:

Estimating p

Monte Carlo Simulation contd


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If you are a very poor dart player, it is easy to

imagine throwing darts randomly at the above figure,

and it should be apparent that of the total number of

darts that hit within the square, the number of darts

that hit the shaded part (circle quadrant) isproportional to the

area of that part. In other words,


Monte carlo Simulation contd


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Monte carlo Simulation contd..

Needle Experiment


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Buffon's original form was to drop a needle of length L at

random on grid of parallel lines of spacing D.

For L less than or equal D we obtain

P (needle intersects the grid) = 2 L / PI D.

If we drop the needle N times and count R intersections we obtain

P = R / N,

PI = 2 L N / R D.

Needle Experiment

Needle Experiment


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Needle Experiment

Needle Experiment


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Pi= 2 * L * N / R * D

Take L=1

D = 1Then Pi= 2 * N / R

Where

R is intersections(Hits) and

N is no of times needle

dropped

Needle Experiment

Needle Experiment


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Pi= 2 * L * N / R * D

Take L=1

D = 1

Then Pi= 2 * N / R

Where


N is no of times needle dropped

Needle Experiment

Needle Experiment


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Pi= 2 * L * N / R * D

Take L=1

D = 1

Then Pi= 2 * N / RWhere


N is no of times needledropped

Needle Experiment

Needle Experiment


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Pi= 2 * L * N / R * D

Take L=1

D = 1Then Pi= 2 * N / R

Where


N is no of times needle dropped

Needle Experiment

Documents

Simulation First Unit 20112012