chapter 11 output analysis of a single model

8/10/2019 Chapter 11 Output Analysis of a Single Model

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Output Analysis of a SingleModel

Adapted from J. Banks


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PurposeAnalysis of data generated by a

simulation.

To predict and compare performance ofa model


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Simulation exhibits randomness, thus

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

And by the models precision of the pointestimator or std. Error (variance).


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Types of simulation w/ respect to

output analysis:

Terminating/transient

simulationNonterminating/steady state

simulation


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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 underspecified conditions andclosesat TE.


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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 underdefined initial conditions by the analyst,

and runs for some analyst-specifiedperiod of TE.


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Measures of Performance and

their estimation: Point estimation of the performance

values from the model.

Two types:

A. Within replication.

B. Among replication.

Interval estimation. ( ) ( )/ , / , t tf f2 2

( ) S

n

2

t

( )

S

Y

n

i

i

n2

2

1 1

( )

1

1n Yi

i

n


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For Terminating Simulations: Compute for confidence intervals with

fixed replications using same formulas

except that n = R.

Compute for confidence intervals withspecified precision using half length

criterion.

h lt S

R

R o. .

/ , 2 1 R t S Z S R o o

/ . /2 1

2

2

2


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For Steady State Simulations: Choose the run length with the following

considerations:

A.) Bias in the point estimator due to artificial orarbitrary initial condition.

B.) Bias can be severe if run length is too short, butdecreases as run length is increased.

C.) Precision of the estimator is measured based onan estimate of point-estimatorvariability.

D.) Budget constraints on computer resources.


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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 systemexists)

B.) Use results from a simplified model (if systemdoes not exists)

Deletion - reduce impact of initial

conditions by

dividing a run into two phases. Let the first phase befrom t = 0 to t = to, followed the 2nd phase which isfrom toto TE., Thus the simulation will stop at time t

= to+ TE.


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Deletion can be done is the

following ways: Ensemble averages. Plotting the mean

and confidence limits. The intervals can

used to judge whether or not the plot isprecise enough to judge that bias hasdiminished. Preferred method.

Using Cumulative averages. Useful insituations where single replication isonly possible.


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chapter 11 output analysis of a single model

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