Analysis ofSimulation Results

Chapter 25

Overview

Analysis of Simulation Results Model Verification TechniquesModel Validation TechniquesTransient RemovalTerminating SimulationsStopping Criteria: Variance EstimationVariance Reduction

Model Verification vs. Validation

Model Verification Techniques

5

Would like model output to be close to that of real system Made assumptions about behavior of real systems 1st step, test if assumptions are reasonable

Validation, or representativeness of assumptions 2nd step, test whether model implements assumptions

Verification, or correctness Mutually exclusive.

Ex: what was your project 1?

Analysis of Simulation ResultsAlways assume that your assumption is invalid.

– Robert F. Tatman

Top Down Modular Design

Antibugging

Antibugging consists of including additional checks and outputs in the program that will point out the bugs, if any.

for example, the model counts the number of packets sent by a number of source nodes as well as the number received by the destination nodes. Say, total packets = packets sent + packets received If not, can halt or warn

Structured Walk-Through

Structured walk-through consists of explaining the code to another person or a group. The code developer explains what each line of code does

Deterministic Models

The key problem in debugging simulation models is the randomness of variables.

a deterministic program is easier to debug than a program with random variables

But by specifying constant (deterministic) distributions, the user can easily determine output variables and thus debug the modules

Run Simplified Cases

The model may be run with simple casesOf course, a model that works for simple cases

is not guaranteed to work for more complex cases. Therefore, the test cases should be as complex as can be easily analyzed without simulation

Only one packet Only one source Only one intermediate node

Trace

On-Line Graphic Displays

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Slight change in input should yield slight change in output, otherwise error and bug in the simulation

Continuity tests

Th

rput

(Debugged)

Th

rput

(Undebugged)

Degeneracy tests

• Try extreme configuration and workloads. Try extremes (lowest and highest) since may reveal bugs One CPU, Zero disk

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Consistency tests – similar inputs produce similar outputsEx: 2 sources at 50 pkts/sec produce same total as

1 source at 100 pkts/secSeed independence – random number

generator starting value should not affect final conclusion (maybe individual output, but not overall conclusion)

More Model Verification Techniques

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Ensure assumptions used are reasonable Want final simulated system to be like real system

Unlike verification, techniques to validate one simulation may be different from one model to another

Three key aspects to validate:1. Assumptions2. Input parameter values and distributions3. Output values and conclusions

Compare validity of each to one or more of:1. Expert intuition2. Real system measurements3. Theoretical results

Model Validation Techniques

9 combinations- Not all are always possible, however

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• Most practical, most common

• “Brainstorm” with people knowledgeable in area

• Present measured results and compare to simulated results (can see if experts can tell the difference)

Model Validation Techniques - Expert Intuition

Th

roughput

Packet Loss Probability

0.2 0.4 0.8

Which alternativelooks invalid? Why?

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Most reliable and preferred May be unfeasible because system does not exist or too

expensive to measure That could be why simulating in the first place!

But even one or two measurements add an enormous amount to the validity of the simulation

Should compare input values, output values, workload characterization Use multiple traces for trace-driven simulations

Can use statistical techniques (confidence intervals) to determine if simulated values different than measured values

Model Validation Techniques - Real System Measurements

Measurement

Three measurementMeasurement and simulationAnalytical model and simulationModel and measurement

Theoretical Results

Model and simulation are wrongAnalysis = SimulationUsed to validate analysis alsoBoth may be invalidUse theory in conjunction with experts'

intuition E.g., Use theory for a large configurationCan show that the model is not invalid

Exercise Imagine that you have been called as an expert to review a simulation study. Which of the following simulation results

would you consider non-intuitive and would want it carefully

validated: 1. The throughput of a system increases as its load increases. 2. The throughput of a system decreases as its load increases. 3. The response time increases as the load increases. 4. The response time of a system decreases as its load

increases. 5. The loss rate of a system decreases as the load increases.

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IntroductionCommon Mistakes in SimulationTerminologySelecting a Simulation LanguageTypes of SimulationsVerification and ValidationTransient RemovalTermination

Outline

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Most simulations only want steady stateRemove initial transient state

Trouble is, not possible to define exactly what constitutes end of transient state

Use heuristics:Long runsProper initializationTruncationInitial data deletionMoving average of replicationsBatch means

Transient Removal

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Use very long runsEffects of transient state will be amortizedBut … wastes resourcesAnd tough to choose how long is “enough”Recommendation … don’t use long runs alone

Long Runs

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Start simulation in state close to expected stateEx: CPU scheduler may start with some jobs in

the queueDetermine starting conditions by previous

simulations or simple analysisMay result in decreased run length, but still

may not provide confidence that are in stable condition

Proper Initialization

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• Assume variability during steady state is less than during transient state

• Variability measured in terms of range – (min, max)

• If a trajectory of range stabilizes, then assume that in stable state

• Method:– Given n observations {x1,

x2, …, xn} – ignore first l observations– Calculate (min,max) of

remaining n-l– Repeat for l = 1…n– Stop when l+1th

observation is neither min nor max

Truncation

(Example next)

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• Sequence: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 10, 11, 10, 9…

• Ignore first (l=1), range is (2, 11) and 2nd observation (l+1) is the min

• Ignore second (l=2), range is (3,11) and 3rd observation (l+1) is min

• Finally, l=9 and range is (9,11) and 10th observation is neither min nor max

• So, discard first 9 observations

Truncation Example

TransientInterval

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• Find duration of transient interval for:11, 4, 2, 6, 5, 7, 10, 9, 10,

9, 10, 9, 10

Truncation Example 2 (1 of 2)

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• Find duration of transient interval for:11, 4, 2, 6, 5, 7, 10, 9, 10,

9, 10, 9, 10• When l=3, range is

(5,10) and 4th (6) is not min or max

• So, discard only 3 instead of 6

Truncation Example 2

“Real” transient

Assumed transient

Replication

Change seed so you have replication in simulation

If the seed is the same, it is not.Do some replication to smooth the average

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Study average after some initial observations are deleted from sampleIf average does not change much, must be deleting

from steady stateHowever, since randomness can cause some

fluctuations during steady state, need multiple runs (w/different seeds)

Given m replications size n each with xij jth observation of ith replicationNote j varies along time axis and i varies across

replications

Initial Data Deletion

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Initial Data Deletion (cont)

Initial Data Deletion (cont)

Initial Data Deletion (cont)

35

Initial Data Deletion

xij

j

xj

j

xl

l

(xl –

x)

/ x

l

transientinterval

knee

Individual replicationMean Across replications

Mean of last n-l observationRelative Change

Batch Means

Run a long simulation and divide into equal duration part

Part = Batch = Sub-sample Study variance of batch means as a function

of the batch sizeR

esp

on

ses

Observation number

n 2n 3n 4n 5n

Batch Means (cont)

Batch Means (cont)

Batch Means

Ignore peaks followed by an upswing

Vari

ance

of

batc

h m

eans

transientinterval

Batch size n

(Ignore)