Simulation Lectures Final Copy

7/28/2019 Simulation Lectures Final Copy

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COM 321: SIMULATION AND

MODELING

BY: TAREMWA DAN

[email protected]
mailto:[email protected]:[email protected]


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CHAPTER ONE

INTRODUCTION TO SIMULATION

AND MODELING


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In this chapter you will learn:

Definitions and explain systems and

experiments

Definitions of model and simulation

Application of modeling and simulation

Advantages and disadvantages

Need for simulation and modeling Types of modeling and simulation paradigms


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Systems and Experiments

Definition:

A system is any set of interrelated components

acting together to achieve a common

objective.


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inputs

The inputsof a system are variables of

the environment that influence the

behavior of the system. These inputs mayor may not be controllable by us.


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outputs

The outputsof a system are variables that are

determined by the system and may influence

the surrounding environment. In many

systems the same variables act as both inputs

and outputs.


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METHODS OF STUDYING VARIABLES

EXPERIMENTATION

STATISTICS

SIMULATION


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Definition: experiment

An experimentis the process of extracting

information from a system by exercising its

inputs.

PRACTICAL PROBLEMS ASSOCIATED WITH


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PERFORMING AN EXPERIMENT

The experiment might be too expensive:

investigating ship durability by building ships

and letting them collide is a very expensive

method of gaining information.

The system needed for the experiment might

not yet exist. This is typical of systems to be

designed or manufactured.


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PERFORMING AN EXPERIMENT

The experiment might be too dangerous:

training nuclear plant operators in handling

dangerous situations by letting the nuclear

reactor enter hazardous states is not

advisable.

The shortcomings of the experimental

method lead us over to the model concept


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The Model Concept

A modelof a system is anything an

"experiment" can be applied to in order to

answer questions about that system.

A computer model is a data-driven system

that uses an inbuilt set of rules to predict the

results of a process or to simulate how a given

set of conditions will change over time


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Mathematical model

Definition:

Mathematicalmodel a description of a system

where the relationships between variables of

the system are expressed in mathematical

form. Variables can be measurable quantities

such as size, length, weight, temperature,

unemployment level, information flow, bitrate, etc.


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Modeling

Definition:

Modeling is the process of obtaining a set of

equations (mathematical model) that

describes the behavior of the system. A model

describes the mathematical relationship

between inputs and outputs.


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Physicalmodel

Physicalmodelthis is a physical object that

mimics some properties of a real system, to

help us answer questions about that system.

For example, during design of artifacts such asbuildings, airplanes, etc.,


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simulation

A simulationis an experiment performed on a

model.

formal definition of simulation: ``the process of

designing a model of a real system and

conducting experiments with this model for the

purpose either of understanding the behavior of

the system of or evaluating various strategies(within the limits imposed by a criterion or a set

of criteria) for the operation of the system.''


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Simulation is the imitation of the operation of a

real world system over time.


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WHEN IS SIMULATION AN APPROPRIATE TOOL?

Study Complex Systems

Evaluate effect of variables

Experiment with different designs Test scientific models


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WHEN IS SIMULATION AN APPROPRIATE TOOL?

Prior to building a real-world system

Provide training environment

Validate design Create proof of concept


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When NOT to Use Simulation

System is too simple

System is too complex

System is not understood well enough Real-world experiments are easier

Cost/benefit ratio > 1

No experts available to build simulator Simulation has already been done


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Advantages of simulation

Test new hardware before buying it

Insight about system can be gained

Speed up design-build-test-redesigncycle

Can be used to verify models ortheories

Can be used AS COMMUNICATIONTOOL


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9

Advantages of Simulation -contd.

Building consensus.

Preparing for change.

Cost effective investment. Training aid capability.

Specification of requirements.


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Disadvantages of Simulation

Model building often difficult and not unique

Results may be hard to interpret

Model and simulator may be too expensive May lead to false conclusions

Results are as good as the model

Bugs in software are unavoidable Requires human experts


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10

Disadvantages of Simulation

Training required.

Interpretation of results required.

Time consuming/expensive. Inappropriately used.


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11

Application Areas

Manufacturing/ Materials Handling

Public and Health Systems

Military Natural Resource Management

Transportation

Computer Systems Performance Communications


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Applications of Simulations

Designing and analyzing manufacturing

systems

Evaluating H/W and S/W requirements for a

computer system

Evaluating a new military weapons system or

tactics

Determining ordering policies for an inventory

system


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Applications of Simulation

Designing communications systems andmessage protocols for them

Designing and operating transportation

facilities such as freeways, airports, subways,or ports

Evaluating designs for service organizations

such as hospitals, post offices, or fast-foodrestaurants

Analyzing financial or economic systems


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Applications of Simulation

COMPUTER SYSTEMS: hardware components, softwaresystems, networks, data base management, information

processing, etc..

MANUFACTURING: material handling systems, assembly

lines, automated production facilities, inventory control

systems, plant layout, etc..

BUSINESS: stock and commodity analysis, pricing policies,

marketing strategies, cash flow analysis, forecasting, etc..

GOVERNMENT: military weapons and their use, military

tactics, population forecasting, land use, health care

delivery, fire protection, criminal justice, traffic control, etc..


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CHAPTER TWO

DEVELOPING SIMULATIONMODELS


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MODEL DEVELOPMENT PROCESS

The different phases of model development

The products at each phase of the model

development


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12

Steps in Simulation Modeling

Problem Formulation

Goal Setting

Model Conceptualization Data Collection

Model Translation

Verification and Validation

Experimental Design


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13

Steps in Simulation -contd.

Production Runs and Analysis

Documentation/Reporting

Implementation


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Simulation Procedure

Step 1: Define objective, scope, requirements

Step 2: Collect and analyze system data

Step 3: Build model

Step 4: Validate Model

Step 5: Conduct experiments

Step 6: Present resultsNote: Iterations required among steps


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Simulation Project Steps

a.- Problem Definition

b.- Statement of Objectives

c.- Model Formulation and Planning

d.- Model Development and Data Collectione.- Verification

f.- Validation

g.-Experimentation

h.- Analysis of Resultsi.- Reporting and Implementation

A Seven Step Approach for Conducting a


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A Seven-Step Approach for Conducting aSuccessful Simulation Study

In Figure 1 we present a seven-step

approach for conducting a successful

simulation study. Having a definitiveapproach for conducting a simulation

study is critical to the studys success in

general and to developing a valid model

in particular.


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Step 1. Formulate the Problem

Problem of interest is stated by the decision-

maker

A kickoff meeting(s) for the simulation project

is (are) conducted, with the project manager,

the simulation analysts, and subject-matter

experts (SMEs) in attendance.


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The overall objectives of the study

The specific questions to be answered by the

study (without such specificity it is impossible

to determine the appropriate level of model

detail)

The performance measures that will be used

to evaluate the efficacy of different system

configurations


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The scope of the model

The system configurations to be modeled

The time frame for the study and the required

resources

Step 2 Collect Information/Data


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Step 2. Collect Information/Data

Collect information on the system layout and

operating procedures.

Collect data to specify model parameters and

probability distributions (e.g., for the time to

failure and the time to repair of a machine).


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Construct a Conceptual Model

Develop Causal loop diagrams which studies

the relationship between variables

Document the model assumptions,

algorithms, and data summaries in a written

conceptual model.


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Step 3. Is the Conceptual Model Valid?

Perform a structured walk-through of the

conceptual model before an audience that

includes the project manager, analysts, and

SMEs. This is called conceptual-modelvalidation.


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Is the Conceptual Model Valid?

If errors or omissions are discovered in the

conceptual model, which is almost always the

case, then the conceptual model must be

updated before proceeding to programming inStep 4.


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Step 4. Program the Model

Program the conceptual model in

either a commercial simulation-

software product or in a general-purpose programming language

(e.g., C or C++).

Verify (debug) the computer

program.


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Step 5. Is the Programmed Model Valid?

If there is an existing system, then

compare model performance

measures with the comparableperformance measures collected

from the actual system (see Step 2).

This is called results validation.


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What isface validity?

Regardless of whether there is an existing

system, the simulation analysts and SMEs

should review the simulation results for

reasonableness. If the results are

consistent with how they perceive the

system should operate, then the

simulation model is said to haveface

validity.


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What is Sensitivity analysis?

Sensitivity analyses should be

performed on the programmed

model to see which model factorshave the greatest effect on the

performance measures and, thus,

have to be modeled carefully.


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Step 6. Design, Make, and Analyze

Simulation Experiments

For each system configuration of

interest, decide on tactical issues

such as run length, warm up period,and the number of independent

model replications.

Analyze the results and decide if

additional experiments are required.

S 7 D d P h


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Step 7. Document and Present the

Simulation Results

The documentation for the model (and

the associated simulation study) should

include the conceptual model (critical forfuture reuse of the model), a detailed

description of the computer program,

and the results of the current study.

S 7 D d P h


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Step 7. Document and Present the

Simulation Results

The final presentation for the

simulation study should includeanimations and a discussion of the

model building/validation process to

promote model credibility.


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CHAPTER THREE

SYSTEM DYNAMICS


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More Goals of this course.

To learn how transfer CLDs to Stock & FlowDiagrams, SFDs

To learn how to implement SFDs in VENSIM

To learn how to parameterize a VENSIMmodel

To learn how to validate a VENSIM model

To learn how to conduct what-ifexperiments

To do sensitivity studies


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Definitions and Terms

ST--Systems Thinking

SD--Systems Dynamics

CLD--Causal Loop Diagram

BOT--Behavior Over Time Chart SFD--Stock & Flow Diagram

Also called Forrester Schematic, or simply FlowDiagram

quantity--any variable, parameter, constant, oroutput

edge--a causal link between quantities


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What is SYSTEM DYNAMICS?

Definition:

System dynamics is an approach to

understanding the behavior of complex

systems over time. It deals with internal

feedback loops and time delays that affect the

behavior of the entire system.


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System Dynamics Software

STELLA and I think High Performance Systems, Inc.

best fit for K-12 education

Vensim Ventana Systems, Inc. Free from downloading off their web site:

www.vensim.com

Robust--including parametric data fitting and optimization

best fit for higher education

PowerSim What Arthur Andersen is using


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What is system dynamics?

A way to characterize systems as stocks and flows

between stocks

Stocks are variables that accumulate the affects of

other variables Rates are variables the control the flows of material

into and out of stocks

Auxiliaries are variables the modify information as it

is passed from stocks to rates


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A Simple Methodology

Collect info on the problem

List variables on post-it notes

Describe causality using a CLD

Translate CLD into SFD

Enter into VENSIM

Perform sensitivity and validation studies

Perform policy and WHAT IF experiments Write recommendations


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Causal Modeling

A way to characterize the physics of the

system

Lacking: a Newton to describe the causality in

these socioeconomic systems


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Key Benefits of the ST/SD

A deeper level of learning Far better than a mere verbal description

A clear structural representation of the

problem or process A way to extract the behavioral implications

from the structure and data

A hands on tool on which to conduct WHATIF


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WHY A SYSTEMS PERSPECTIVE?

Problems facing us are more complexdue to increase

in

information flow

interdependencies

rate of change

Facilitates leadership by leveraged action

integrating competing priorities

acknowledging and handling unintendedconsequences


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The significant problems we face today

cannot be solved at the same level of thinkingat which they were created.

- Albert Einstein


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Examining how

WE CREATE OUR OWN PROBLEMS

Seeing the

BIG PICTURE

Recognizing thatSTRUCTURE INFLUENCES PERFORMANCE

WHAT IS SYSTEMS THINKING?


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Causal Loop Diagrams - a useful way to represent

dynamic interrelationships

Provide a visual representation with which to

communicate that understanding

Make explicit one's understanding of a system

structure - Capture the mental model

SYSTEMS THINKING TOOLS

Causal Loop Diagrams [CLDs]


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Causal Loop Diagrams [CLD s]


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Definition

Causal Loop Diagrams (CLDs) are structural

pictures used to convey understanding about

the interactions, or influences, within a

structure. A CLD is used to explicitly show the nature of

the influence relations between the elements

of a structure.

MAIN CONVENTIONS FOR


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MAIN CONVENTIONS FOR

REPRESENTING CLDS

There are two main conventions

for representing CLDs, one using"+" and "-" and another using "S"and "O" as indicators on the

influence from one element toanother.


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Meaning of +

A --> B with a "+" on the arrow

indicates that "A" adds to "B". If "A"

increases it adds even more to "B". If"A" decreases is adds less readily to

"B" though it still adds.


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Meaning of -

A --> B with a "-" on the arrow indicates that

"A" subtracts from "B". If "A" decreases is

subtracts even more readily to "B". If "A"

increases is still subtracts from "B" though notas readily.

Influence Structures


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Influence Structures

If I have two things, thing 1 and thing 2, there are onlytwo ways thing 1 can influence thing 2.

As indicated in Fig 1, thing 1 can add to thing 2, as

indicated by a "+" sign, thus increasing thing 2.
http://www.systemdynamics.org/wiki/index.php/File:Stint01.gi


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examples


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Example

Costs Profits

--

Costs Losses

+


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EXAMPLE: POPULATION

Consider a simple population with infinite resources--food, water, air, etc. Given, mortality information interms of birth and death rates, what is thispopulation likely to grow to by a certain time?

Over a period of 200 years, the population isimpacted by both births and deaths. These are, inturn functions of birth rate norm and death ratenorm as well as population.

A population of 1.6 billion with a birth rate norm of.04 and a death rate norm of .028


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We Listed the Quantities

Population

Births

Deaths

Birth rate norm

Death rate norm


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CLD

Births

population

Deaths

Birth rate normal

Death rate normal

R

B

+

+

+

+

+

--


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Using VENSIM TO CONSTRUCT CLDs

Use the variable auxiliary/constant tool to establish

the quantities and their locations

Use the arrow tool to establish the links between

the quantities Use the Comment tool to mark the polarities of

the causal edges (links, arrows)

Use the Comment tool to mark the loops as

reinforcing or balancing


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Experiments with growth models

Models with only one rate and one state

Average lifetime death rates

Models in which the exiting rate is not a

function of its adjacent state


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Example:

Build a model of work flow from work undone towork completed.

This flow is controlled by a work rate.

Assume there are 1000 days of undone work

Assume the work rate is 20 completed days a month

Assume the units on time are months

Assume no work is completed initially.


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Causation vs. Correlation

Ice Cream Sales Murder rate

Ice Cream Sales 0 Murder rate 0

Average

Temperature

f


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Inadequate cause: Confusion

Market Share Unit Costs

--

Market Share Unit Costs

Production

Volume

Cumulative Production

Experience+ +

-

l d f


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Validation of CLDs

Clarity Quantity existence

Connection edge existence

Cause sufficiency Additional cause possibility

Cause/effect reversal

Predicted effect existence

Tautology


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CLD Examples

Salary VS Performance

Salary Performance

Performance Salary

Salary Performance

Tired VS Sleep Tired sleep

Sleep tired

Tired Sleep

Augmenting CLD 1


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Augmenting CLD 1

(Labeling Link Polarity)

Signing: Add a + or a sign at each arrowhead to

convey more information

A + is used if the cause increase, the effect increases

and if the cause decrease, the effect decreases A - is used if the cause increases, the effect

decreases and if the cause decreases, the effect

increases

Si i A


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Signing Arcs

Salary Performance

+

+

+

-

Tired Sleep

Reinforcing Loop


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Reinforcing Loop

Definition 1: A reinforcing loop is one in whichthe interactions are such that each action adds to

the other. Any situation where action produces a

result which promotes more of the same action,it is representative of a reinforcing loop.

An increase in quantity 1 produces an increase in

quantity 2

A decrease in quantity 1 produces a decrease in

quantity 2

EXAMPLE


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EXAMPLE

EXAMPLE


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EXAMPLE

Fig 1 indicates what happens in a typical

savings account. The principal in the

savings account interacts with the

interest rate and adds to the interest.

Note that interest rate is considered to

be a constant in this example. Interest

then adds to the principal.

Balancing Loop


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g p

Definition 1:

A balancing loop is one in which

action attempts to bring two thingsto agreement. Any situation where

one attempts to solve a problem or

achieve a goal or objective isrepresentative of a balancing loop.

EXAMPLE


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EXAMPLE

EXPLANATION


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EXPLANATION

Fig 2 provides the basic form of the balancingloop. The desired state interacts with the

current state to produce a gap. The gap adds

to the action and the action adds to thecurrent state. The current state then subtracts

from the gap.

Si f l


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Signs of loops

reinforcing loops have an even number ofnegative links (zero also is even, see example

above)

Balancing loops have an uneven number ofnegative links.

Si f l
http://en.wikipedia.org/wiki/Reinforcing_loophttp://en.wikipedia.org/w/index.php?title=Balancing_loop&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Balancing_loop&action=edit&redlink=1http://en.wikipedia.org/wiki/Reinforcing_loop


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Sign of loops

B l i LOOP


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Balancing LOOP

Note: A Negative sign on an information link

can be seen by saying either of:

An increase in quantity 1 produces a decrease

in quantity 2

Population model


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Population model

Augmenting CLD 2


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g g

(Determining Loop Polarity)

Positive feedback loops Have an even number of signs

Some quantity increase, a snowball effect takes over and thatquantity continues to increase

The snowball effect can also work in reverse

Generate behaviors of growth, amplify, deviation, and reinforce

Notation: place symbol in the center of the loop

Negative feedback loops Have an odd number of signs

Tend to produce stable, balance, equilibrium and goal-seekingbehavior over time

Notation: place symbol in the center of the loop

+

-

CLD i h P i i F db k L


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CLD with Positive Feedback Loop

Salary Performance, Performance Salary

Salary Performance

The better I perform

The more salary I get



+

+

+



CLD i h N i F db k L


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CLD with Negative Feedback Loop

Tired Sleep

The more tired I amThe more I sleep

The more I sleep The less tired I am

The less tired I am

The less I sleep

The less I sleep The more tired I am

+

-

-

Tired Sleep, Sleep Tired

Loop Dominance


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Loop Dominance

There are systems which have more than one feedbackloop within them

A particular loop in a system of more than one loop is most

responsible for the overall behavior of that system

The dominating loop might shift over time

When a feedback loop is within another, one loop must

dominate

Stable conditions will exist when negative loops dominate

positive loops

CLD with Combined Feedback Loops


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p

(Population Growth)

Birth rate Polulation Death rate-+

+ +

+ -

CLD with Nested Feedback Loops


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(Self-Regulating Biosphere)

Sunshine

EvaporationA mount of

water on earth

RainClouds

Earths

temperature-

+

-

+

+

+

+ +

+

+

+-

-

Evaporation clouds rain amount of water evaporation

E It


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Exogenous Items

Items that affect other items in the system but are not

themselves affected by anything in the system

Arrows are drawn from these items but there are no

arrows drawn to these items

Sunlight reaching

each plant Density of plants

Sunlight +

+

-

-

Reinforcing Loop: Structure


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Reinforcing Loop: Structure

Growth rate

Population

Sales

Satisfied

Custome

ositive word of

mouth

Reinforcing Loop: Behavior


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Reinforcing Loop: Behavior

Population

20 B

10 B

00 20 40 60 80 100 120 140 160 180 200

Time (Year)

Population : pop1

Population : Current

Balancing Loop: Structure


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Balancing Loop: Structure

Desired

Inventory

Actual

inventory

Inventory

gapOrder rate

OB

Balancing Loop: Behavior


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Balancing Loop: Behavior

Inventory

1,000

500

0

0 10 20 30 40 50 60 70 80 90 100

Time (Month)

Inventory : inv1

Importance of Causal Loop Diagrams


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(CLDs).

Causal Loop diagrams are used to documentrelevant factors and the causal relationships

between them.

CLDs consist of factors and links connectingthe factors. Any link has annotations about its

polarity and delay.

Used as a communication tool


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CHAPTER FOUR

STOCK AND FLOW DIAGRAMS

SYSTEMS DYNAMICS


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Definition: System dynamics is an approachto understanding the behavior of complex

systems over time. It deals with internal

feedback loops and time delays that affect thebehavior of the entire system.

DYNAMIC MODEL BUILDING BLOCKS


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STOCKS

FLOWS

CONNECTORS CONVERTORS

stock


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stock

In STELLA terminology, a stock is a noun andrepresents something that accumulates.

Some examples of stocks are population,

radioactivity, enzyme concentration, self-esteem, and money.

Principle of Accumulation


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Principle of Accumulation

In system dynamics modeling, dynamicbehavior is thought to arise due to the

Principle of Accumulation. According to the

principle of accumulation, dynamic behaviorarises when something flows through the pipe

and faucet assembly and collects or

accumulates in the stock.

flow


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flow

While a stock is a noun in the language of

STELLA, a flow is a verb. A flow is an activity

that changes the magnitude of a stock. Someexamples of such activities are births in a

population, decay of radioactivity, formation

of an enzyme, improvement of self-esteem,and growth of money.

Figure 2: Example stock and flow


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Figure 2: Example stock and flow

structure with an inflow and outflow

Total Population Derived From Other


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Quantities

Children

Births Coming to Age

Total Population

Adult population

Dearths

Identifying Stocks and Flows


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Stocks usually represent nouns Flows usually represent verbs.

Stocks do not disappear if time is

(hypothetically) stopped (i.e., if a snapshotwere taken of the system);

Flows do disappear if time is (hypothetically)stopped.

Stocks send out signals (information about thestate of the system) to the rest of the system.



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Converter :

converts, stores equation or constant,

does not accumulateConnector: transmits inputs and

information

Characteristics of stock


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Characteristics of stock

Have memory,

Change the time shape of flows,Decouple flows,

Create delays.

HAVE MEMORY,


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If the inflow to the stock is shut-off, thenumber of entities in the stock will not

decrease, but rather stay at the level it is

at when the inflow stops. An outflow inexcess of the inflow is required to

decrease the number of entities in the

stock.

CHANGE THE TIME SHAPE OF FLOWS


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CHANGE THE TIME SHAPE OF FLOWS

A second important characteristic ofstocks is that they (i.e., the accumulation

process) usually change the time shape

of flows. This can be seen by simulatingthe simple stock-flow structure shown in

Figure 1, with different time shapes for

the flow.

PRESENTS THE TIME SHAPE OF THE STOCK


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WHEN THE FLOW IS AT A CONSTANT LEVEL

OF 5 UNITS/TIME

STOCKS DECOUPLE FLOWS
http://www.systemdynamics.org/DL-In


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A third important characteristic of stocksis that they "decouple" or

interrupt/change flows. A stock thus

makes it possible for an inflow to bedifferent from an outflow and hence for

disequilibrium behavior to occur.

Population model


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10/10/2012 120

Population model

Taremwa and Lydon

Examples where flows are decoupled

b t k


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by stocks

CREATES DELAYS


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CREATES DELAYS

Systems often respond sluggishly

From the example below, once the trees are planted, the

harvest rate can be 0 until the trees grow enough to

harvest

# of growing trees Harvest rate

Planting rate+

+

-

-

delay

Some rules for translating CLDs into

SFDs


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SFDs

There are two types of causal links in causalmodels (but we dont distinguish betweenthem)

Information

Flow

1. Information proceeds from stocks andparameters/inputs toward rates where it isused to control flows

2. Flow edges proceed from rates to states(stocks) in the causal diagram always

Figure : casual loop diagram of the

k t d l


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pocket money model

Stock and flow diagrams


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g

Stock and Flow Notation--Quantities


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STOCK

RATE

Auxiliary

Stock

Rate

i1

i2

i3

Auxiliary

o1

o2

o3

Stock and Flow Notation--Quantities


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Input/Parameter/Lookup

Have no edges directed toward them

Output

Have no edges directed away from them

i1

i2

i3

o

o2

o3

Inputs and Outputs


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p p

Inputs

Parameters

Lookups

Outputs

Input/Parameter/Lookup

a

b

c

Stock and Flow Notation--edges


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g

Information

Flow

a b

x


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e


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System Dynamics

Modeling with

STELLA software

Learning objective


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After this class the students should be able to: Understand basic concepts of system dynamics,

Stock Variable;

Flow Variable;

Information Flow;

Material Flow; and Time Delay;

Understand how these basics elements interact withpolicies and decisions to determine the behavior ofdynamic systems.

Time Management


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The expected time to deliver this module is 50

minutes. 20 minutes are reserved for teampractices and exercises and 30 minutes for

lecture.

System Dynamics


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Methodology to study systems behavior

It is used to show how the interaction between structures of the

systems and their policies determine the system behavior

Approach developed to study system behaviors taking into

account complex structures of feedbacks and time delays

Warm-up


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Each team is invited to describe through any kind of diagram the

process to fill a cup of water.

Imagine this as an exercise of operation management

(5 minutes)

Feedback Loop


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Feedback refers to the situation of X affecting Y and Y inturn affecting X perhaps through a chain of causes and

effects.

Z

XY

Time Delay


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\Its the time between the action and the result(consequence) of this action.

Y

X

Time Delay

Causal Diagram


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DesiredWater

Level

Perceived

Gap

Faucet

Position

Water

Flow

Current

Water

Level

Population Dynamic


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feedbacks and time delays

Births Population Deaths

++

+ -

Basic Elements


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This methodology use five basics elements:

Stock Variable;

Flow Variable;

Information Flow;

Material Flow; and Time Delay

Object Oriented Language


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Activity

Material Flow

Information Flow

Stock

Converter

A Model


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Control

Material Flawto Stock

Add Newinformation

Sendinformation

from the Stock

Control

Material Flawfrom Stock

Stock

Exploring a simple example


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To explore modeling with STELLA, we will developinteractively with you, a basic model of the dynamics of a

fish population.

Assume you are the owner of a pond thatis stocked with

200 fish that all reproduce at a fixed rate of 5% per year. For simplicity, assume also that none of the fish die. How

many fish will youown after 20 years?

Stock - Fish Inventory


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We begin with the first tool, a stock (rectangle). Inour example model, the stock will represent the

number of fish in our pond.

This stock is known as a reservoir. In our model, thisstock represents the number of fish we have in this

time are in our the pond

Figure 1

Click here to

open the stella

software

What control the number of fish


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As we assumed that the fish in our pond never die,

we have one control variable: REPRODUCTION.

We use the flow tool (the right-pointing arrow, second from

the left) to represent the control variable, so named because it

controls the states (variables).

Figure 2

200 Fishes

Converter


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Next we need to know how the fish in our populationreproduce, that is, how to accurately estimate the numberof new fish per annum. Remember? We assumed our fishpopulation reproduce at 5% per year.

This can be represented as a transforming variable. Atransforming variable is expressed as a converter, the circlethat is second from the right in the STELLA toolbox.

Connector


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At the right of the STELLA, toolbox is the connector(informationarrow). We use the connector to pass on information about the

REPRODUCTION RATE to REPRODUCTION and another to pass on

information from FISH population to REPRODUCTION.

Figure 3

Our first model


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Once you draw the information arrow from the transformingvariable REPRODUCTION RATE to the control and from the stockFISH to the control, open the control (REPRODUCTION) andconverter (REPRODUCTION RATE) and type respectively 5/100and the equation: REPRODUCTION RATE* FISH

Figure 4

200

5/100

REPRODUCTION RATE*FISH

Run the model


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We get Figure 5. We see a graph of exponential growth of thefish population in your pond.

Figure 5

What-if?


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From now on, the professor can practice what-if with the teams

For example:

What would happen if we decided to extract fish at a constant rate of

3% per year, and the reproduction rate varied with the fish population as

it is seen in figure 6?

Figure 6

New model


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Results


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Figure 7

Reference


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The Fifth Discipline. Peter Senge, Currency Doubleday,1994, Chapter 5.

Modeling Dynamic Economic System. Ruth, M. & Hannon,B. Springer, 1997, Chapter 1


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MORE EXAMPLES

Increasing Crime


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Behaviour

System Structure

EventsDrugs are a big worry for me. Not leastbecause of the crimes that people commit

to fund their dependency. We want the

policy to bust these rings and destroy the

drugs. They say theyre doing it and they

keep showing us sacks of cocaine that they

seized but the crime problem seems to be

getting worse

Increasing Crime


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Behaviour

System Structure

EventsWhat are the main variables described in the statement?

What is the reference mode (behaviour) of this system?

Time

Increasing Crime


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Behaviour

System Structure

Events

What is the structure of this system?

What is the causal loop diagram whichexplains the observed behaviour?

Call for Police

Action

Drug Seizures

Supply

Price

Demand

Drug Related

Crime

Building construction


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Problem statement Fixed area of available land for construction

New buildings are constructed while old buildings are demolished

Primary state variable will be the total number of buildings over time

Causal Graph

Industrial

buildingsDemolitionConstruction

Fraction ofland occupied

Construction

fractionAverage

lifetimefor buildings

Average area

per building

Land available for

Industrial buildings

+

+

+

+

+

+ -

-

-

-

Simulation models


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Industrial

Buildings (B)

Construction (C) Demolition (D)

Construction

fraction

(CF)Fraction of

land occupied

(FLO)Land available for

industrial buildings (LA)

Average area per

building (AA)

Average lifetime for

buildings (AL)

Equations

dBl/dt = Cr Dr

Cr = f1(CF, Bl)

Dr = f2(AL,Bl)CF = f3(FLO)

FLO = f4(LA,AA,Bl)

Flow Graph


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SIMULATION MODEL VALIDATION

AND CREDIDILITY

SIMULATION MODEL VALIDATION


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Validation ensures that the model meets itsintended requirements in terms of the methods

employed and the results obtained

The ultimate goal of model validation is to make

the model useful in the sense that the model

addresses the right problem, provides accurate

information about the system being modeled and

to makes the model actually used.

Definition: Validation


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Validation is theprocess of determiningwhether a simulation model (as opposed

to the computer program) is an accurate

representation of the system,for theparticular objectives of the study.

Definition: Operational validation


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Operational validation is defined asdetermining that the models output

behavior has sufficient accuracy for the

models intended purpose over thedomain of the models intended

applicability

Definition: Data validity


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Data validityis defined as ensuring thatthe data necessary for model building,

model evaluation and conducting the

model experiments to solve the problemare adequate and correct.

Definition: Verification


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Verification is concerned withdetermining whether the conceptual

simulation model (model assumptions)

has been correctly translated into acomputer program, i.e., debugging the

simulation computer program.

Verification


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A simulation model and its results havecredibilityif the manager and other project

personnel accept them as "correct.

A credible model is not necessarily valid, and

vice versa.

The following things help establishcredibility for a model:


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The decision-makers understanding andagreement with the models assumptions

Demonstration that the model has been

validated and verified (i.e., that the modelcomputer program has been debugged)

The decision-makers ownership of and

involvement with the project Reputation of the model developers

Model validation process


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TECHNIQUES FOR INCREASING


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TECHNIQUES FOR INCREASING

MODEL VALIDITY ANDCREDIBILITY

Formulating the Problem Precisely


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It is critical to formulate the problem of

interest in a precise manner. This should

include an overall statement of the problem tobe solved, a list of the specific questions that

the model is to answer, and the performance

measures that will be used to evaluate the

efficacy of particular system configurations.

Interviewing Subject-Matter Experts


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There will never be a single person that knows

all of the information necessary to build a

simulation model. Thus, it will be necessaryfor the simulation analysts to talk to many

different SMEs to gain a complete

understanding of the system to be modeled.

Interacting with the Decision-Maker

on a Regular Basis


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One of the most important ideas for

developing a valid and credible model is

for the analyst to interact with thedecision-maker and other members of

the project team on a regular basis.

Collect high-quality information and

data on the system


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Conversation with subject matter experts in MS,machine operators, engineers, maintenancepersonnel, schedulers, managers, vendors,

Observation of the system

Data are not representative of what one reallywants to model

Data are not of the appropriate type or format

Data may contain measurement, recording, or rounding

errors Data may be biased because of self interest

Data may be inconsistent

Interact with the manager on a

regular basis


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There may not be a clear idea of theproblem to be solved at initiation of the

study.

The managers interest and involvement inthe study are maintained.

The managers knowledge of the system

contributes to the actual validity of themodel

This approach has the following keybenefits:


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Helps ensure that the correct problem is solved

The exact nature of the problem may not be initiallyknown.

The decision-maker may change his/her objectivesduring the course of the study.

The decision-makers interest and involvement in thestudy are maintained.

The model is more credible because the decision

maker understands and agrees with the modelsassumptions.

QUESTION


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A military analyst worked on a simulationproject for several months without interacting

with the general who requested it. At the final

Pentagon briefing for the study, the general

walked out after five minutes stating, Thats

not the problem Im interested in.

Using Quantitative Techniques to

Validate Components of the Model


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USING STATISTICAL RESULTS

If one has fit a theoretical probability

distribution (e.g., exponential or normal) to aset of observed data, then the adequacy of

the representation can be assessed by using

graphical plots and goodness-of-fit tests

Documenting the Conceptual Model


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Communication errors are a major reason whysimulation models very often contain invalidassumptions. Documenting all assumptions,

algorithms, and data summaries can lessenthis problem. This report is the majordocumentation for the model and should be

readable by analysts, SMEs, and decision-makers alike.

Performing Sensitivity Analyses to

Determine Important Model Factors


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An important technique for determiningwhich model factors have a significant

impact on the desired measures of

performance is sensitivity analysis. If aparticular factor appears to be

important, then it needs to be modeled

carefully.

MODEL VERIFICATION


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Step 1: Write and debug the computerprogram on modules or subprograms.

Step 2: More than one person review the

computer program (structured walkthroughof the program).

Step 3: Run the simulation under a variety of

settings of input parameters, and check tosee that the output is reasonable.

MODEL VERIFICATION


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Step 4: "trace", interactive debugger.

Step 5: The model should be run under

simplifying assumptions for which its true

characteristics are known or can easily becomputed.

Step 6: Observe an animation of the

simulation output.

MODEL VERIFICATION


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Step 7: Compute the sample mean andvariance for each simulation input probability

distribution, and compare them with the

desired mean and variance.

Step 8: Use a commercial simulation package

to reduce the amount of programming

required.

VALIDATION SCHEMES


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Structure-Verification Test: This test ismeant to answer the following question

Is the model structure not in

contradiction to the knowledge aboutthe structure of the real system, and

have the most relevant structures of the

real system been modeled?

Dimensional-Consistency Test:


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Do the dimensions of the variablesin every equation balance on each

side of the equation? This test

verifies whether all equations are

dimensionally constant.


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Boundary-Adequacy Test:


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This test verifies whether the modelstructure is appropriate for the model

purpose.Is the model aggregation

appropriate and includes all relevantstructure containing the variables and

feedback effects necessary to address

the problem and suit the purposes of thestudy?


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CHAPTER SIXBUILT IN FUNCTIONS

BUILT IN FUNCTIONS


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The software's test input Builtins enable youto conduct controlled experiments on your

model. Typically, a PULSE, RAMP or STEP is

appended to an inflow or outflow equation.

When the Built-in is activated (at the time you

specify) it will knock the system out of its

previous state. You can then observe how your

model responds to this idealized test.

PULSE FUNCTION


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PULSE([,,]) The PULSE function generates a pulse input of

a specified size (volume). In using the PULSE

function, you have the option of setting thetime at which the PULSE will first fire (first

pulse), as well as the interval between

subsequent PULSEs (interval).

PULSE FUNCTION


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Each time that it fires a pulse, the softwarepulses the specified volume over a period of

one time step (DT). Thus, the instantaneous

value taken on by the PULSE function is

volume/DT. Volume can be either variable or

constant. First pulse and interval should be

specified as constants.

EXAMPLE


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Draw the stock and flow pattern generated bythe following equations:

Flow = PULSE(20,10,10)

Flow = PULSE(10,15,10) Flow = PULSE(20,30,40)

REFER TO STELA HELP.

RAMP


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RAMP([,]) The RAMP function generates a linearly

increasing or decreasing input over time with aspecified slope (slope). Optionally, you may set

the time at which the ramp begins. Slope andtime can be either variable or constant.

As the simulation progresses, the RAMP willreturn a 0 before its time to begin has been

reached. If you do not set the RAMP's time, it willbegin at the outset of the simulation.

EXAMPLE


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Pamp_Input =RAMP(25,5)




STEP FUNCTION


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STEP(,) The STEP function generates a one-time step

change of specified height (height), which

occurs at a specified time (time). Height andtime can be either variable or constant.

Example:

Step_Input = 5 + STEP(5,10) generates thebehavior pattern.

EXAMPLE


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Step_Input = STEP(20, 20)

Step_Input = 10 + STEP(20, 20)

Step_Input = 20 + STEP(20, 20)

Step_Input = 5 + STEP(20, 10) + STEP(20, 20)

Step_Input = 10 + STEP(10, 20)+ STEP(25, 20)

Graphical Functions


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The Become Graph button at the lower left ofthe dialog enables you to define the converter

as a graphical function. Graphical functions

also may be defined from within a flow dialog.

Definition: graphical function


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A graphical function is a sketch of arelationship between some input (which itself

can be an algebraic relationship defined from

the Required Inputs list and/or Builtins list)

and an output.

Using graphical function


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Once the input has been defined in theequation box, a click on Become Graph leads

you to the graphical function define dialog.



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Set the min and max values for the X-axis.Type numbers within the two fields below thegraphical function grid. The number in the leftfield (the min value) must be less than the

number in the right field (the max value). Hitthe tab key to move from field to field. Theminimum and maximum values you choosefor the X-axis will be reflected in the non-

editable left column (input), to the right of theaxes.



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Set the min and max values for the Y-axis.Type numbers within the two fields to the left

of the graphical function grid. The number in

the bottom field (the min value) must be less

than the number in the top field (the max

value). Hit the tab key to move from field to

field.



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Set the number of data points. Type a numberinto the Data Points field, found below the

two columns of numbers. You must have at

least two data points in a graphical function.

You can have up to 1500 data points. When a

graphical function contains more than 13 data

points, the grid becomes scrollable. To view

the entire function, depress the alt key(Windows) or option key (Macintosh).



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Create a relationship. Click-and-hold thecursor within the grid. As you drag the cursor,

a curve will be drawn, following your mouse

movements. In addition, the Y-axis

coordinates of the curve will be displayed in

the right column (output) at the far right of

the dialog.

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