© Copyright 2015 Dr. Jeffrey Strickland Discrete Event Simulation with ExtendSim Chapter 1 Introduction to Modeling and Simulation

© Copyright 2015 Dr. Jeffrey Strickland

Discrete Event Simulation with ExtendSimChapter 1

Introduction to Modeling and Simulation

NASA Ares I

NASA planned to use Ares I to launch Orion, the spacecraft intended for NASA human spaceflight missions after the Space Shuttle was retired in 2011.

However, the Constellation program, including Ares I was canceled in October 2010 by the passage of the 2010 NASA authorization bill.

Dr. Strickland and a team of engineers design the Reliability and Launch Availability of the Ares I using ExtendSim.

© Copyright 2015 Dr. Jeffrey Strickland8/12/2015 Chapter 1 -2


Why simulation is important

Simulation involves designing a model of a system and carrying out experiments on it as it progresses through time.

Models enable you to see how a real-world activity will perform under different conditions and test various hypotheses at a fraction of the cost of performing the actual activity.

One of the principal benefits of a model is that you can begin with a simple approximation of a process and gradually refine the model as your understanding of the process improves.

This “stepwise refinement” enables you to achieve good approximations of very complex problems surprisingly quickly. As you add refinements, the model more closely imitates the real-life process1

1 ExtendSim user’s guide

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8/12/2015 © Copyright 2015 Dr. Jeffrey Strickland Lesson 1 -4

What is a Model?

A physical, mathematical, or otherwise logical representation of a system, entity, phenomenon, or process

An abstraction of a real world problem, based on simplifying assumption.

Since a modeling is a representation, abstraction, or approximation of the “system” being modeled, we must understand that it is not an “exact” representation, i.e., we can’t model every aspect of the system.

Example: Weather Model

Many degrees of freedom (DOF) with a vast array of environmental factors

Simplify model with only a few of the most important factors (other non-representative factors represent the error in the model)

Example: Marketing Model

People have a propensity to buy due to demographics, online activity, visual stimulation, emotions, etc.

Model model based on demographics and online activity


Model Definitions & Contrasts

Physical model

Mock-up model

Scale model

Iconic model

Fashion model

Symbolic Model

Narrative model

Graphical model

Tabular model

Software model

Mathematical model

x f (x) f ' (x)0 0 01 1 22 4 43 9 64 16 8

Specifications:• 30 GB HD• 1 GB RAM• CD RW/DVD


Contrasting Model Examples

Deterministic (Static) modelsStochastic (Dynamic) models

Descriptive modelsPredictive models

Discrete modelsContinuous models


A Sampling of Model Examples


A Sampling of ExamplesAccounts Receivable at Spring Mills

0

400

800

1200

1600

2000

2400

0.0 7.5 15.0 22.5 30.0 37.5 45.0

Days

Am

ou

nt

Correlation = 0.489

Scatterplot of Amount versus Days for All Customers: Data Model


A Sampling of ExamplesCompetitive Bidding by SciTools Incorporated

FALSE 0

0 0

Bid?

12200

30.0% 0.3

20000 15000

TRUE Any competing bid?

0 12200

80.0% 0.56

20000 15000

70.0% Win bid?

0 11000

20.0% 0.14

0 -5000

TRUE How much to bid

-5000 12200

30.0% 0

25000 20000

FALSE Any competing bid?

0 9500

40.0% 0

25000 20000

70.0% Win bid?

0 5000

60.0% 0

0 -5000

30.0% 0

30000 25000

FALSE Any competing bid?

0 6100

10.0% 0

30000 25000

70.0% Win bid?

0 -2000

90.0% 0

0 -5000

SciTools Bidding

No

Yes

$115K

$120K

$125K

No

Yes

Yes

No

No

Yes

Yes

No

No

Yes

Yes

No

Decision Tree Model


A Sampling of Examples

Analysis of Auditing Example: Parameter Model (Confidence Interval for a Mean)

Auditing example for an exact Confidence Interval Width

Confidence Level 95%sample mean 1500

sample standard deviation 390sample size 45

z value 1.9600

upper confidence limit 1613.95lower confidence limit 1386.05

width of CI 227.9000

upper confidence limit 1575.00lower confidence limit 1425.00Goal Seek for CI width 150.00

sample size needed 103.8757


A Sampling of ExamplesExplaining Overhead Costs at Bendrix

Data for new employees: Regression Model

Training Weeks (X)

# of completed Projects

(Y)1.2 1010.8 921.0 1101.3 1200.7 900.8 821.0 930.6 750.9 911.1 105


A Sampling of ExamplesQuarterly Sales at Intel

Time series plot of Sales

Exponential trend line

y = 292.46e0.0664x

R2 = 0.9848

0

2000

4000

6000

8000

Quarter

Sale

s

Time Series Plot of Quarterly Sales at Intel: Forecasting Model


A Sampling of ExamplesBasic Combat Attrition Model

aydt

dx

bxdt

dy

0 510 15 20 25 30 35 40 45 50

55

60

X(t)Y(t)

0

5

10

15

20

25

30

Fo

rce

Str

eng

th

Time

Square Law Time Solutions

X(t)

Y(t)

0 510 15 20 25 30 35 40 45 50

55

60

X(t)Y(t)

0

10

20

30

40

50

60

Fo

rce

Str

eng

th

Time

Square Law Time Solutions

X(t)

Y(t)

Y(0) ↑ 60

b ↑ 0.16

X(0) = Y(0) = 30

a = b = 0.14


A Sampling of ExamplesTracking Market Shares of Two Dominant Companies in the Iced Tea Market

Iced tea market share simulation

Input section

Current market shares of dominant companies Sweetness 0.49 IceT 0.49

Current data on small companiesNumber 3Combined market share 0.02

Probability any small company will exit industry in any year0.5

Mean number of new entries in any year (Poisson distributed)1

Percentage of market share of each exiter that goes to Sweetness - the rest go to IceT (triangularly distributed)

Minimum Most likelyMaximum0.4 0.5 0.6

Percentage of companies' market shares lost to each other and to small companiesMinimum Most likelyMaximum

Sweetness to IceT 0.01 0.05 0.1 to each small company 0.005 0.01 0.03IceT to Sweetness 0.01 0.05 0.1 to each small company 0.005 0.01 0.03Small companies to Sweetness 0.05 0.1 0.15 to IceT 0.05 0.1 0.15

Input for Iced Tea Example: Monte Carlo Simulation Model


A Sampling of ExamplesDiscrete Event Simulation of a Transportation System


What is Simulation?

A simulation is the execution of a model over time ot other parameter.

Simulation involves designing a model of a system and carrying out experiments on it.

The purpose of these "what if” experiments is to determine how the real system performs and to predict the effect of changes to the system as time progresses.

For example, you use simulation to answer questions like:

Will this change to our process result in higher yields or quality?

How many people are required to maintain service at a specified level, for example, in a processing station?

Can we design this weapon system with fewer components and still maintain measures of performance, such as availability or lethality?

Does this force structure meet the capability requirement specified by the commander?

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Formal Definitions of Simulation

A formal definition of simulation is given by the Department of Defense Directive:

Definition 1: A method for implementing a model over time. Also, a technique for testing, analysis, or training in which real-world systems are used, or where real-world and conceptual systems are reproduced by a model.

Another definition is given by Winston & Albright, in Practical Management Science, 2001:

Definition 2: A simulation model is a computer model that imitates a real-life situation

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Different Kinds of Simulation

Monte Carlo SimulationEstimate stochastic, static model quantities that are difficult to compute by exact computations. A scheme employing random numbers which is used for solving certain stochastic problems where the passage of time plays no substantive role.

1

Dynamic SimulationDynamic system simulations observe the behavior of the system models over time. The time advance mechanism used here include continuous, discrete time, and discrete event.

2

Differential Equation System Specification (DESS)2a

Discrete Time System Specification (DTSS)2b

Discrete Event System Specification (DEVS)2b

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Discrete-Event Simulation

Estimate stochastic, dynamic, and discrete model outputs. A scheme for modeling a system as it evolves over time by a representation in which state variables change instantaneously at separate points in time.In simple terms, DES describes how a system with discrete flow units or jobs evolves over time.Technically, this means that a computer tracks how and when state variables, such as queue lengths and resource availability, change over time.State variables change as the result of an event (or discrete event) occurring in the system.A characteristic is that discrete-event models focus only on the time instances when these discrete events occur.This feature allows for significant time compression because it allows the model to skip through all time segments between events when the state of the system remains unchanged.

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Bank Model

Hierarchical modeling

Statistics collection

Buttons

Notebooks

Ghost Connectors

Multiple random inputs

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Circuit Card Assembly

Multiple queuesMultiple servicesParallel servises

Serial servicesConveyer beltsBatching

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Transportation

Labor pools

Task completion delays

Transferring goods

Transporting goods8/12/2015 Chapter 1 -22


Languages for Simulation

1950’s began seeking languages specifically designed for simulation problemsGeneral Simulation Program (GSP) 1960

The First Simulation-specific Programming LanguageBy K.D. Tocher and D.G. Owen, General ElectricProceedings of the Second International Conference on Operations Research

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Evolved Definition of Simulation Language

Six key characteristics:

Generate Random Numbers

Transformation for Statistical Distributions

List Processing

Statistical Analysis

Report Generation

Timing Execution

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Typical Simulation Program

Finished?

Start

Stop

0. Invoke Initialization1. Invoke Timing2. Invoke Event Handler

Main

0. Update state variables1. Increment counters2. Generate future events

Event Routines

1. Compute interest data2. Write reports

Reports

1. Select next event2. Advance sim clock

Timing

1. Statistical distributions2. Mathematical operations

Mathematics

1. Set clock2. Set state variables3. Load event list

Initialization

NO

YESLegend

Programmer’sresponsibility

Language’sResponsibility

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Activity

Scan

GSP

SIMPAC

CSL

ESP

ECSL

OPS-1,2

OPS-3

OPS-4

1960

1965

1970

1980

1990

GPSS V6000

ProcessInteraction

GPSS

GPSS II

GPSS III

GPSS/360

GPSS IV

GPSS/H

GPSS 85GPSS PC

GPSS PL/I

SIMULA I

SIMULA 67

NGPSS

CONSUM

EventInteraction

GASP

GASP II

GERTS

GASP IV

GASP PL/I

SLAM

SIMAN SLAM II

GEMS

SPS-1

SIMSCRIPT

QUICKSCRIPT

SIMSCRIPT II

SIMSCRIPT II+

SIMSCRIPT II.5

SIMFACTORY II.5

MOSIM

NETWORK II.5

COMNET II

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Sim Language Comparisons

GPSS/H

SIMULATEGENERATE RVEXPO(1,1.0)QUEUE SERVERSEIZE SERVER

LVEQ DEPART SERVERQTEST L N$LVEQ, 1000, STOPADVANCE RVEXPO(2,0.5)

STOP RELEASE SERVERTERMINATE 1START 1000END

SLAM II

GEN, 1,,,,,,72;LIM,1,1,100;NETWORK;

RESOURCE/SERVER(1),1CREATE,EXPON(1.0,1),1,1;AWAIT(1),SERVER;COLCT,INT(1),DELAY IN QUEUE,,2;

ACTIVITY,EXPON(0.5,2),,DONE;ACTIVITY,,,CNTTR;

DONE FREE,SERVERTERM;

CNTR TERM,1000;END;

;INIT;FIN;

SIMAN

BEGIN

CREATE,,EX(1,1):EX(1,1);MARK(1);QUEUE, 1;SEIZE :SERVER;TALLY :1, INT(1);COUNT :1,1;DELAY :EX(2,2);RELEASE :SERVER;DISPOSE;

END;

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Visual Interactive Simulation (1)

Arena (SIMAN)SimProcess (SimScript II.5)

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Visual Interactive Simulation (2)

ExtendOPNET

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Alan Pritsker’s Seven Principles

1. Conceptualizing a model requires system knowledge, engineering judgment, and model-building tools.

2. The secret to being a good modeler is the ability to remodel3. The modeling process is evolutionary because the act of modeling reveals important

information piecemeal.4. The problem or problem statement is the primary controlling element in model-base problem

solving.5. In modeling combined systems, the continuous aspects of the problem should be considered

first. The discrete aspects of the problem should then be developed.6. A model should be evaluated according to its usefulness. From an absolute perspective, a

model is neither good or bad, nor is it neutral.7. The purpose of simulation modeling is knowledge and understanding, not models.

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“All models are wrong; but some are useful.”

George E.P. Box

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References

Banks, J., Carson, J.S. II, Nelson, B., & Nicol, D.M. (2001). Discrete-Event System Simulation. Prentice Hall.Cloud, D.J. & Rainey, L.B. (Eds.). (1998). Applied Modeling and Simulation: An integrated Approach to Development and Operation. McGraw-Hill.Law, A.M. & Kelton, D.W. (1998). Simulation Modeling & Analysis, 2nd Ed., 234-266. McGraw-Hill.Schriber, T.J. & Brunner, D.T. (1998). How discrete-event simulation software works. In Handbook of Simulation, 765-811. Wiley. Chapter 24. Zeigler, B.P, Praehofer, H., & Kim, T.G. (2000). Theory of Modeling and Simulation, 2nd Ed., 75-96. Academic Press.

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© Copyright 2015 Dr. Jeffrey Strickland Discrete Event Simulation with ExtendSim Chapter 1 Introduction to Modeling and Simulation