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8/10/2019 DISCSIM Reviewer

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DISCSIM REVIEWERCHAPTER 1: Discrete Event Simulation

-Tool for understanding system behavior

Simulation-

1)

Imitation of a real-world system over time.

2)

Generation of an artificial history.

3)

Numerical method of solving.

What does it do for us?

1)

Allows us to draw inferences concerning theoperating characteristics of the real system.

2)

Shows the behavior of a system as it evolves

through time.

When can we use Simulation?

1)

When no analytical solution is possible.

2)

When system involves too many random

factors.

3)

When experimentation is needed.

4)

When performing validation or testing of a

solution.

Advantages1)

Changes can be explored without disrupting the

system.

2)

No investment for acquisition

3)

Time compressed or expanded.

4)

Obtained insights on variables and their

interaction on the performance of the system.

5)

Bottleneck analysis can be performed.

Disadvantages of Simulation

1)

Model building requires special training.

2)

Simulation results may be difficult to interpret.

3)

Modeling and analysis can be time consuming

and expensive.

4)

Tendency to be used instead of an analytical

solution.

Applications of Simulation

1)

Manufacturing Systems

2)

Public Systems

3)

Transportation Systems

4)

Construction Systems

5)

Restaurant and Entertainment System

6)

Business Process Reengineering

7)

Food Processing8)

Computer Performance Systems

Components of a System

1.

Entity - object of interest in the system

2.

Attribute - property of an entity

3.

Activity - time period of specified length

4.

State - collection of variables that describes a

system

5.

Event - occurrence that changes the state of a

system. (exogenous or endogenous)

Discrete vs Continuous Systems

1)

Discrete System -state variables change only at

a discrete set of time points

2)

Continuous System -state variables change

continuously over time.

How do you represent a system?

1.

Model -a representation of a system for thepurpose of studying it

2.

components that are relevant

3.

Sufficiently detailed to permit valid conclusions

4.

Classes of Simulation Models

5.

Static or dynamic

6.

Deterministic or stochastic

7.

Discrete or continuous

Discrete-Event System Simulation

1.

Analyzed by numerical methods rather than

analytical methods.

2.

Steps

3.

Problem Formulation

4.

Objective Setting

5.

Model Conceptualization and Data Collection

6.

Model Translation

7.

Verification and Validation

8.

Experimental design, Model runs, and Analysis

9.

Documentation, reporting, and Implementation

CHAPTER 2: Manual Simulation

-Simulation without the aid of a computer

Steps in Manual Simulation

1.

Determine characteristics of each of the input

to the simulation. They are normally expressed

in the form of a distribution.

2.

Construct a simulation table.

3.

For each repetition, generate a value for each o

the inputs and evaluate the responses.

A Simple Queueing System

1.

Components are Calling Population, Waiting

Line, and a Server.

2.

Generate flowcharts for Departure and Arrival

Events.

3.

Generate table for Queue and Server status

when entity enters and leaves the system.

How do we simulate?

Maintain:

1)

Event List-contains the times at which different

types of event occur for each entity in the

system.


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2) Simulation Clock.-Inject randomness by using

random numbers to represent uncertainty of

events.

CHAPTER 3: General Principles of Discrete Event

Simulation

Terminologies

1)

System

2)

Model3)

System State

4)

Entity

5)

Attributes

6)

List

7)

Event

8)

Event Notice

9)

Event List

10)

Activity

11)

Delay

12)

Clock

What is Discrete Event Simulation?

DES is used for systems where the state of a system

changes in discrete points in time.

A system can change in only countable number of

points in time.

Makes use of a Time-Advance Algorithm.

Time-Advance Algorithm (Event Scheduling)

This method requires an event list.

The Simulation Clock Time willprogress only up to the

time when the event is expected to occur.

Time-Advance Algorithm (Event Scheduling)

World Views

It is the orientation or perspective that the modeler will

adapt when modeling.

1)

Event Scheduling- analyst concentrates on

events and their effect on system state.

2)

Process-Interaction

The analyst thinks in terms of the processes.

The process is the life cycle of the entity inside the

system.

The life cycle consist of various events and activities.

These processes will force the entity to interact (such as

queue and wait)

A process is a time-sequence list of events, activities,

and delays that define the cycle of one entity as it

moves through the system.

3) Activity Scanning

Can lead to slow run times due to repeated

scanning of the activity list and check whetheran activity can begin.

CHAPTER 4: Modeling Variability

Random numbers

main ingredient for simulation model

Sequence of numbers that appear in random

order.

Follow the properties of uniformity and

independence.

represented as real numbers from 0 to 1 and

are converted to random integers

Generating Random Numbers

RAND function in Excel

Pseudo Random Numbers are created to represent

random numbers

Linear Congruential Method

A pseudo random number generator

Where:

Xi= stream of pseudo random numbers integers from

the interval (0, m-1)

a = multiplier constant

c = additive constant

m = modulus or remainder of m

Using Random Numbers to generate events

Example: Service Frequency Data

If RN = 47, then Service Time = 3 minutes

Random Variates- randomly sampled information

which will be used as inputs to the simulation model.

Random numbers are together with empirical orstatistical distributions to generate random variates.

Conceptual Modeling

Most critical part of the simulation modeling

process.

Model design can impact the following:

1)

Data requirements

2)

Speed and ease of model development

3)

Validity of the model

4)

Speed of experimentation


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5)

Level of confidence on the simulation results

It expects the modeler to have a thorough

understanding of the operations of the system

being modeled.

Often the least understood and removed from

the modeling process

It is considered as an art due to the lack of

defined methods and procedures

What is conceptual modeling? A non-software specific description of the

simulation model that is to be developed

(Robinson, 2004)

It describes the input, output, content,

assumptions, and simplifications of the model in

relation to the system problem and objectives

Elements

Problem and Objectivespurpose of the model and the

simulation project

Inputselements that can be altered to create animprovement (experimental factors)

Outputsresults of the simulation model

Contentcomponents in the model and their

interactions

Assumptionsuncertainties or beliefs about the real

world being modeled

Simplificationsways of reducing the complexity of the

model

Representing the Conceptual Model

System Component ListDescription of the

components in the model

Ex. Supermarket Payment System

Entities = CustomerInter-arrival time

Attribute = Paying customers

Activity = Coding of purchased items, payment, and

packing

Process Flow Diagramprocess map of the flow of the

entities across processes

Logic Flow Diagramprocess map involving logical

decisions across the process flow.

Framework for Conceptual Modeling

Methods of Model Simplification

Model simplificationWay of handling the complexity

of the model.

Done by: Removing of components and

interconnections that have little effect on model

accuracy

Representing more simply the components and

interconnections while maintaining a satisfactory level

of model accuracy

Simplification Approaches

Aggregation of components

Black box modeling

Grouping of entities

Excluding component details

Replacing components with random variables

Excluding infrequent events

Reducing set rules

Splitting models

Guidelines for simplification

Use judgment whether simplification will have a

significant effect on model accuracy. Get agreement

with client. Aim is faster development time

Do a comparison between with and without

simplification and compare performance. Bettercertainty on the simplification, but longer development

time.

Simplification should not compromise transparency and

result to a loss of confidence by the client or decision

maker

Data Collection

Uses of Data in the simulation modeling process:

Preliminary or contextual data

Qualitative information leading to understanding of the

problem and its situation

Model realization data

Quantitative data for developing and running the mode

Model validation data

Quantitative and qualitative data of the real world

system for comparison to the output of the simulation

model

Types of Data

Data that is readily available

Layout, throughput, staffing levels, schedules, servicetimes

Data that is NOT available but collectible

Arrival patterns, machine failure rates, repair times,

nature of decision making

Data that is NOT available and NOT collectible

Rare failure times, availability of personnel for data

collection, machine failures, lost transactions

Dealing with Unobtainable Data


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Data may estimate from other sources. Use surrogate

data from similar systems. Example: predetermined

time and motion information, standard times, etc

Consider data as an experimental factor. Example: if

machine failure is not available, what should the

acceptable machine failure to achieve desired

throughput?

Other Data Issues

Data Accuracyhistorical data is not necessarily a good

indicator of future patterns. Example: historical

breakdown patterns and arrival patterns may not occur

in the future

Data Formatcontextual meaning of the data should

be explicit. Example: time between failures (TBF)

Data Representing Unpredictable Variability (Random)

TracesStream of data based actual sequence of

events of the real world system

Empirical DistributionsSummarize Trace dataconverted into a frequency distribution

Statistical Distributionsknown probability density

functions

Bootstrappingre-sampling from a small data set

Verification and Validation

Verificationprocess of ensuring that the conceptual

model has been successfully transformed into a

computer model

Validationprocess of ensuring that the model is

sufficiently accurate to represent the real world system

being modeled.

CHAPTER 7:RANDOM NUMBER GENERATION

Properties of Random Numbers

Uniformity

Independence

Characteristics

Continuous uniform distribution between 0 to

1.

If the interval (0,1) is divided into n classes, n/n.The probability of observing a particular value is

independent of previous numbers.

Psuedo-Random Numbers:

A sequence of numbers between 0 to 1 which

simulates the ideal properties of uniform

distribution and independence as closely as

possible.

Possible errors of Psuedo-Random Numbers

Generated numbers may not be uniformly

distributed

Numbers may be discrete valued instead of

continuous

Mean and variance may be too high or too low

Cyclic variations may occur such as

autocorrelation, successive numbers, groupings

of numbers

Characteristics of Routines (Generators):

Fast

Portable

Long cycle

Replicable

Imitate randomness

Techniques for Generating Psuedo-Random Numbers

o

Mid square method

o

Mid product method

o

Linear Congruential method

o

Combined Congruential methodoLinear Congruential method

oproposed by Lehmer (1951)

oproduces a sequence of integers between

0 to m-1

o if c = 0, multiplicative Congruential

method

o if c is not equal 0, mixed Congruential

method

Where X0= seed

Xi= random integer

C = incrementA = constant multiplier

M = modulus

Ri = random numbers = Xi/ m

Combined Congruential method

combination of two or more multiplicative

congruential generators

Hypothesis Tests for Random Numbers

Hypothesis when testing for uniformity:

Hypothesis when testing for independence:

Test for Random Numbers:

a.

Frequency test

i.

Kolmogorov-Smirnov test

ii.

Chi-square test

b.

Runs test

Ho R U

H R U

i

i

: [ , ]

: [ , ]

0 1

0 11

H R independently

H R independently

o i

i i

:

:


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i.

Runs up

ii.

Runs down

iii.

Runs above the mean

iv.

Runs below the mean

c.

Autocorrelation test

d.

Gap test

e.

Poker test

f.

Other Tests

i.

Goods Serial Test [1953, 1967]ii.

Median-Spectrum Test [Cox and

Lewis, 1966, Durbin, 1967]

iii.

A Variance Heterogeneity Test

[Cox and Lewis, 1966]

CHAPTER 9: RANDOM VARIATE GENERATION

Random Variate- A value being sampled from a proven

distribution of an input variable.

Ex. inter-arrival time and service time.

RV generatorstechniques used to generate

random variates.Techniques in Generating Random Variates

1)

Inverse Transform Technique

This technique is used to sample from

distributions such as exponential, weibull,

triangular, and empirical distributions. Most

straightforward, but not always the most

efficient.

Steps in an Inverse Transform Technique

1.

Compute the cdf of the desired random variable

x.

2.

Set F(X)=R on the range of X.

3.

Solve the equation F(X)=R for X in terms of R.

X=f-1(r).

4.

Generate uniform random numbers and

compute the desired random variates by Xi= f-

1(Ri).

Derivation of RV generator for an exponential

distribution

Ex. Given exponential distribution,

Thus, the Random Variate Generator is

2)

Uniform Distribution

Thus, the RVG is

3)

Triangular Distribution

Thus, the RVG is (if a=0, b=1, and c=2)

4)

Direct Transformation for the Normal

Distribution Normal distribution

Using 2 normal random variables, plotted as a

point and represented in a polar coordinates as

)2sin())(2(

)2cos())(2(

2/1

2

2/1

1

ii

ii

RRLnZ

RRLnZ

and

ii ZX

5)

Convolution Method

The probability distribution of a sum of two or

more independent random variables is called a

convolution of the distributions of the original

variables.

The convolution method refers to adding

together two or more random variables to

f x e x

otherwise

x

( ) ,

,

10

0

1

x R

or

x R

i i

i i

ln( )

ln( )

1

f x b aa x b

otherwise( )

,

,

1

0

x a b a Ri i ( )

f x

x a x b

c x b x c

otherwise

( )

,

,

,

0

x

R R

R R

2 0 1

2

2 2 1 1

21

,

( ) ,

x-dtexft

x2

2

2

1)(


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obtain a new random variable with the desired

distribution. This technique is useful for Erlang

and binomial variates.

For Erlang distribution:

Acceptance and Rejection Technique

The efficiency of the technique depends on

being able to minimize the number of

rejections.

Example of Acceptance Rejection Technique

Generate uniformly distributed random variates

[1/4,1]:

STEP 1: generate RN

STEP 2: if RN > or = , accept, let X=RN. If RN < , reject

and return to 1.

STEP 3:if another uniform random Variate on [1/4,1] is

needed, go to step 1.

Analysis of Simulation Data

Data Collection

Identification of Distribution of Data Parameter Estimation

Goodness of fit Test

CHAPTER 9: Input Modeling

4 Steps to Input Modeling

1.

Collect data from real system

Substantial time and resources

When data is unavailable (due to time

limit or no existing process):

Use expert opinion

Make educated guess based

from knowledge of the process

2.

Identify probability distribution to represent

input process

Develop frequency distribution or

histogram

Choose a family of distributions

3.

Choose the parameters of the distribution

family.

These parameters are estimated from the

data.4.

Evaluate the chosen distribution and its

parameters.

Goodness of fit test : chi-square or KS

test.

This is an iterative process of selecting

and rejecting the different distributions

until the desired is found.

If none is found, create an empirical

distribution.

Data Collection Problems

a.

Inter-arrival times are not homogenous

b.

Service times which are dependent on other

factors

c.

Service time termination

d.

Machine breakdowns

Data Problems with Simulation

a.

No Datab.

Old Data

c.

Missing Data

d.

Guesstimates

e.

Erroneous Data

f.

No resource

g.

Simplifying assumptions

h.

Using Averages

i.

Outliers

j.

Optimistic Data

k.

Politics

Consequence of Data Problems

a.

Bad data equals bad models

b.

The Best models fail under bad data

c.

Successful simulation is unlikely with bad

data

Guidelines in Data Collection

a.

Always question data

b.

Electronic data does mean good data.

c.

Know the source

d.

Allocate sufficient time to collect and

analyze data

Suggestions to facilitate data collection:

1.

Plan

Collect data while pre-observing

Create forms and be prepared to modify

them when needed

Video tape is possible and extract date

later

2.

Analyze.

Determine if data is adequate.

Do not collect superfluous data.

3.

Try to combine homogenous data.

Use two sample t-test.

4.

Be wary of data censoring.

5.

Look for relationships between variables using a

scatter plot.

6.

Be aware of autocorrelations within a sequence

of observations.


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CHAPTER 10: Validation and Verification

Adapted from Jerry Banks

Verification

Concerned with building the model right

Comparison of conceptual model and computer

representation

Is the model implemented correctly in the

computer?

Are the inputs and logical parametersrepresented properly?

Validation

Concerned with building the right model

Accurate representation of the real system

This is achieved through the calibration of the

model

Iterative process until accuracy is acceptable

Model Building, Verification, and ValidationCommon sense suggestions for verification

a.

Have someone check the computerized model

b.

Make a flow diagram (with logical actions for

each possible event)

c.

Examine model output for reasonableness

d.

Print the input parameters at the end of the

simulation

e.

Make the computerized representation as self

documenting as possible

f.

If animated, verify what is seen

g.

Use IRC or debuggers

h.

Use graphical interface

Three Classes of Techniques for Verification

a.

Common sense techniques

b.

Thorough documentation

c.

Traces

Calibration and Validation

Validation is the overall process of comparing

the model and its behavior to the real system

and its behavior Calibration is the iterative process of comparing

the model to the real system and making

adjustments to the model, and so on.

Iterative Process of Calibration

3 Step Approach by Naylor and Finger (1967)

Build a model with high face validity

Validate model assumptions

Compare the model input-output

transformations to corresponding input-output

transformations of the real system

Possible validation techniques in order of

increasing cost-value ratio by Van Horn (1971)

a.

High face validity. Use previous

research/studies/observation/experience

b.

Conduct statistical test for data

homogeneity, randomness, and goodnessof fit test

c.

Conduct Turing test. Have a group of

experts compare model output versus

system output and detect the difference

d.

Compare model output to system output

using statistical tests

e.

After model development, collect new data

and apply previous 3 tests

f.

Build a new system or redesign the old one

based on simulation results and use this

data to validate the modelg.

Do little or no validation. Implement results

without validating

h.

CHAPTER 11: Output Analysis of a Single Model

Purpose

Analysis of data generated by a simulation.

To predict and compare performance of a

model

Simulation exhibits randomness, thus it is

necessary to estimate the: Performance measure of the model, .

And by the models precision of the point

estimator or std. Error (variance).

Types of simulation w/ respect to output analysis:

Terminating/transient simulation

Nonterminating/steady state simulation

Terminating/transient simulation

One that runs for some duration TE, where E is a

specified event (or set of events) which will stop

the simulation.

Such a model opens at time 0 under specified

conditions and closes at TE.

Nonterminating/Steady state simulation

Simulation whose objective is to study the long

run, or steady state, behavior of nonterminating

systems.

The system opens at time 0 under defined

initial conditions by the analyst, and runs for

some analyst-specified period of TE.

Measures of Performance and their estimation:


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Point estimation of the performance values

from the model.

Two types:

A. Within replication.

B. Among replication.

Interval estimation.

For Terminating Simulations:

Compute for confidence intervals with fixed

replications using same formulas except that n

= R.

Compute for confidence intervals with specified

precision using half length criterion.

For Steady State Simulations:

Choose the run length with the following

considerations:

A.) Bias in the point estimator due to

artificial or arbitrary initial condition.

B.) Bias can be severe if run length is too

short, but decreases as run length is increased.C.) Precision of the estimator is measured

based on an estimate of point-estimator

variability.

D.) Budget constraints on computer

resources.

Initialization Bias can be minimized by:

Intelligent initialization - initialized based on

expected long run state

A.) Use existing data of a system as basis

(if system exists)

B.) Use results from a simplified model (if

system does not exists)

Deletion - reduce impact of initial conditions by

dividing a run into two phases. Let the first

phase be from t = 0 to t = to, followed the 2nd

phase which is from toto TE., Thus the

simulation will stop at time t = to+ TE.

Deletion can be done is the following ways:

Ensemble averages. Plotting the mean and

confidence limits. The intervals can used tojudge whether or not the plot is precise enough

to judge that bias has diminished. Preferred

method.

Using Cumulative averages. Useful in situations

where single replication is only possible.

Computing for the sample size in steady state

simulation:

1. Solve for R, based on initial sample of Ro.

2. Compute for R/Ro.

3. Apply it to first phase, (R/Ro)( to), and (R/Ro)(

to+TE), for the second phase.

CHAPTER 12: Comparison and Evaluation of

Alternative Designs

2 Statistical techniques used in comparing Systems:

Independent Samplingthe systems are

responding in negative correlation between

each other. This has been observed in some

inventory problems.

Correlated Sampling or Common Random

Numbersresponds in the same direction for

each input of random variates (monotonic). This

is common for certain simple queuing

problems.

Comparing 2 Systems:

It is necessary to make use of confidence

intervals when comparing two systems.

The confidence interval should be thedifference between two systems.

Three possible scenarios when computing for the

confidence interval of the differences (90%, 95%, or

99%):

When using independent sampling:

Independent sampling with equal variances

Independent sampling with unequal variances

When using correlated sampling:

Dedicate a random number stream for a specific

purpose. Use as many as needed.

Use attributes of an entity to consistently apply

same service times, order quantity, etc. (which

are dependent on the entity)

Use a specific stream for activities with cycles.

Examples are changes in shifts.

Synchronize if possible. Otherwise, use

independent random numbers

Comparison of Several Designs

Possible Goals of an Analyst:

Estimate each performance measure Compare each performance measure to a

present system (control)

All possible comparison

Selection of the best

Using Bonferroni Approach for Comparison:

When making statements about several

alternatives, an analyst would like to be


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confident that all statements are true

simultaneously.

This method can be used in three ways:

Individual C.I.s of a single system with multiple

performance measures. The alpha is simply the

product of all alphas used in the comparison.

They are assumed to be independent.

Comparison to a present system. Construct a 1-

alpha confidence interval for each comparison.

All possible comparison. Use the equation

above. This assumes that correlated sampling

was used.

Selecting the Best

Determining the best of the alternatives

Determining how much the best is relative to

the rest of the alternatives

NOTE: It might be possible that selecting the

second best is more practical, less costly, more

feasible, but still very insignificantly close tobeing the best.

Understanding the Effect of the Design

Alternatives:

Use the power of design of experiments

Some of the tools under DOE are:

Factorial Designs(useful for understanding the

effects of the alternatives)

Screening, these are fractional factorial and

Placket Burman (useful for trimming down the

unimportant alternatives)

Response Surface, these are Central Composite

and Box Benhken (useful for identifying the

optimal setup in an alternative)

Metamodeling

Constructing a relationship between the

performance measure, Y, and the design

variables, X.

Some common relationships are: Simple Linear

Regression, Nonlinear relationships, MultipleLinear Regression.

To verify whether these relationships are

reliable for predicting the effect on the

performance measure, it is necessary to test the

significance of the regressions (ANOVA is used).

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