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CloudSim Plus: A modern, highly extensible and easier-to-use Java 8 Framework for Modeling and Simulation of Cloud Computing Infrastructures and Services
/*
* CloudSim Plus: A modern, highly-extensible and easier-to-use Framework for
* Modeling and Simulation of Cloud Computing Infrastructures and Services.
* http://cloudsimplus.org
*
* Copyright (C) 2015-2021 Universidade da Beira Interior (UBI, Portugal) and
* the Instituto Federal de Educação Ciência e Tecnologia do Tocantins (IFTO, Brazil).
*
* This file is part of CloudSim Plus.
*
* CloudSim Plus is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* CloudSim Plus is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with CloudSim Plus. If not, see optionalErrorMargin = errorMargin(stats);
this.stdDev = stats.getStandardDeviation();
this.samples = stats.getN();
this.value = stats.getMean();
if(optionalErrorMargin.isPresent()) {
this.criticalValue = computeCriticalValue(samples);
this.errorMargin = optionalErrorMargin.get();
this.lowerLimit = stats.getMean() - errorMargin;
this.upperLimit = stats.getMean() + errorMargin;
//System.out.printf("95%% Confidence Interval: %.4f ∓ %.4f, that is [%.4f to %.4f]%n", ci, intervalSize, lowerLimit, upperLimit);
return;
}
/* When the number of simulations runs is not greater than 1,
* there is no way to compute the confidence interval.
* Therefore, it will just store the mean value for a given metric
* as the ci and all other attributes will be zero,
* indicating there is no confidence interval in fact. */
this.criticalValue = 0;
this.errorMargin = 0;
this.lowerLimit = 0;
this.upperLimit = 0;
}
/**
* Computes the Confidence Interval error margin for a given set of samples
* in order to enable finding the interval lower and upper bound around a
* mean value.
*
*
* To reduce the confidence interval by half, one have to execute the
* experiments 4 more times. This is called the "Replication Method" and
* just works when the samples are i.i.d. (independent and identically
* distributed). Thus, if you have correlation between samples of each
* simulation run, a different method such as a bias compensation,
* batch means or regenerative method has to be used.
*
* NOTE: How to compute the error margin is a little confusing.
* The Harry Perros' book states that if less than 30 samples are collected,
* the t-Distribution has to be used to that purpose.
*
* However, this
* Wikipedia
* article
* says that if the standard deviation of the real population is known, it
* has to be used the z-value from the Standard Normal Distribution.
* Otherwise, it has to be used the t-value from the t-Distribution to
* calculate the critical value for defining the error margin (also called
* standard error). The book "Numeric Computation and Statistical Data
* Analysis on the Java Platform" confirms the last statement and such
* approach was followed.
*
* @param stats the statistic object with the values to compute the error
* margin of the confidence interval
* @return the error margin to compute the lower and upper bound of the
* confidence interval
*
* @see
* Critical
* Values of the Student's t Distribution
* @see
* t-Distribution
* @see Harry
* Perros, "Computer Simulation Techniques: The definitive introduction!,"
* 2009
* @see Numeric
* Computation and Statistical Data Analysis on the Java Platform
*/
public static Optional errorMargin(final SummaryStatistics stats) {
final long samples = stats.getN();
if(samples <= 1) {
return Optional.empty();
}
try {
final double criticalValue = computeCriticalValue(samples);
return Optional.of(criticalValue * stats.getStandardDeviation() / Math.sqrt(samples));
} catch (final MathIllegalArgumentException e) {
return Optional.empty();
}
}
/**
* Computes the Confidence Interval critical value for a given
* number of samples and confidence level.
* @param samples number of collected samples
* @return
*/
private static double computeCriticalValue(final long samples) {
/* Creates a T-Distribution with N-1 degrees of freedom
* since we are computing the sample's confidence interval
* instead of using the entire population. */
final double freedomDegrees = samples - 1;
/* The t-Distribution is used to determine the probability that
the real population mean lies in a given interval. */
final var tDist = new TDistribution(freedomDegrees);
final double significance = 1.0 - CONFIDENCE_LEVEL;
return tDist.inverseCumulativeProbability(1.0 - significance / 2.0);
}
/**
* Gets the Confidence Interval value,
* which is the mean value for an arbitrary metric
* from multiple simulation runs.
* This value is usually referred as just CI.
*
* @see #CONFIDENCE_LEVEL
*/
public double getValue() {
return value;
}
public double getStdDev() {
return stdDev;
}
/**
* Gets the number of samples used to compute the Confidence Interval.
*/
public long getSamples() {
return samples;
}
/**
* Gets the t-Distribution critical value.
*/
public double getCriticalValue() {
return criticalValue;
}
/**
* Gets the CI error margin, which defines the size of the interval in which
* results may lay between.
* The interval is between {@link #getLowerLimit()} and {@link #getUpperLimit()}.
*/
public double getErrorMargin() {
return errorMargin;
}
/**
* Gets the lower limit of the Confidence Interval,
* based on the {@link #getErrorMargin()}.
*/
public double getLowerLimit() {
return lowerLimit;
}
/**
* Gets the upper limit of the Confidence Interval,
* based on the {@link #getErrorMargin()}.
*/
public double getUpperLimit() {
return upperLimit;
}
/**
* Gets the name of the metric for which the Confidence Interval is computed.
*/
public String getMetricName() {
return metricName;
}
/**
* Check if the CI was actually computed, if the number of samples is greater than 1.
* Otherwise, the CI {@link #value} is just the mean for the experiment metric,
* not the CI in fact.
* In that case, {@link #criticalValue}, {@link #errorMargin},
* {@link #lowerLimit} and {@link #upperLimit}
* will be zero (corroborating there is no CI).
*
* @return
*/
public boolean isComputed(){
return samples > 1;
}
}