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Performance, Reliability, and Availability Evaluation of Computational Systems PDF

841 Pages·2023·22.377 MB·English
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Performance, Reliability, and Availability Evaluation of Computational Systems, Volume 1 This textbook intends to be a comprehensive and substantially self-contained two-volume book covering performance, reliability, and availability evaluation subjects. The volumes focus on computing systems, although the methods may also be applied to other systems. The first volume covers Chapter 1 to Chapter 14, whose subtitle is “Performance Model- ing and Background”. The second volume encompasses Chapter 15 to Chapter 25 and has the subtitle “Reliability and Availability Modeling, Measuring and Workload, and Lifetime Data Analysis”. This text is helpful for computer performance professionals for supporting planning, de- sign, configuring, and tuning the performance, reliability, and availability of computing systems. Such professionals may use these volumes to get acquainted with specific sub- jects by looking at the particular chapters. Many examples in the textbook on computing systems will help them understand the concepts covered in each chapter. The text may also be helpful for the instructor who teaches performance, reliability, and availability evalua- tion subjects. Many possible threads could be configured according to the interest of the audience and the duration of the course. Chapter 1 presents a good number of possible courses programs that could be organized using this text. Volume 1 is composed of the first two parts, besides Chapter 1. Part I gives the knowledge required for the subsequent parts of the text. This part includes six chapters. It covers an introduction to probability, descriptive statistics and exploratory data analysis, random variables, moments, covariance, some helpful discrete and continuous random variables, Taylor series, inference methods, distribution fitting, regression, interpolation, data scal- ing, distance measures, and some clustering methods. Part II presents methods for perfor- mance evaluation modeling, such as operational analysis, Discrete-Time Markov Chains (DTMC), and Continuous Time Markov Chains (CTMC), Markovian queues, Stochastic Petri nets (SPN), and discrete event simulation. Performance, Reliability, and Availability Evaluation of Computational Systems, Volume 1 Performance and Background Paulo Romero Martins Maciel First edition published 2023 by CRC Press 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742 and by CRC Press 4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN CRC Press is an imprint of Taylor & Francis Group, LLC © 2023 Taylor & Francis Group, LLC Reasonable efforts have been made to publish reliable data and information, but the author and pub- lisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information stor- age or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, access www.copyright.com or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. For works that are not available on CCC please contact mpkbook- [email protected] Trademark notice: Product or corporate names may be trademarks or registered trademarks and are used only for identification and explanation without intent to infringe. ISBN: 978-1-032-29537-4 (hbk) ISBN: 978-1-032-30639-1 (pbk) ISBN: 978-1-003-30601-6 (ebk) DOI: 10.1201/9781003306016 Typeset in Nimbus font by KnowledgeWorks Global Ltd. Publisher’s note: This book has been prepared from camera-ready copy provided by the authors. Dedication TotheOneandTriuneGod,theHolyMysterythatisWhollyLove. Contents Preface.....................................................................................................................xiii Acknowledgement...................................................................................................xv Chapter1 Introduction.....................................................................................1 1.1 AnOverview...........................................................................1 1.2 AGlanceatEvaluationPlanning............................................9 PART I Fundamental Concepts Chapter2 IntroductiontoProbability............................................................25 2.1 SetsandAlgebraofSets.......................................................25 2.2 Probability.............................................................................29 2.3 ConditionalProbability.........................................................34 2.4 Independence........................................................................39 2.5 Bayes’RuleandtheLawofTotalProbability......................40 2.6 Counting...............................................................................45 2.6.1 N-Permutation.........................................................45 2.6.2 KoutofNPermutationwithReplacement.............47 2.6.3 KoutofNPermutationwithoutReplacement.......48 2.6.4 KoutofNCombinationwithoutReplacement......48 2.6.5 KoutofNCombinationwithReplacement...........49 Chapter3 ExploratoryDataAnalysis............................................................55 3.1 DiagramsandPlots...............................................................55 3.2 StatisticsofCentralTendency.............................................62 3.3 MeasuresofDispersion........................................................66 3.4 StatisticsofShape(AsymmetryandKurtosis).....................68 3.5 Outliers.................................................................................70 Chapter4 IntroductiontoRandomVariables.................................................79 4.1 DiscreteRandomVariables...................................................79 4.2 ContinuousRandomVariables.............................................90 4.3 Moments...............................................................................98 4.4 JointDistributions...............................................................110 4.4.1 JointDiscreteRandomVariables..........................111 4.4.2 JointContinuousRandomVariables.....................115 4.4.3 Convolution...........................................................120 4.4.4 Expect.andVar.ofProd.ofRand.Variab............124 4.4.5 Expect.andVar.ofSumsofRand.Variab............128 4.5 SummaryofPropertiesofExpectationandVariance.........131 4.6 Covariance,Correlation,andIndependence.......................132 vii viii Contents Chapter5 SomeImportantRandomVariables.............................................139 5.1 SomeDiscreteRandomVariables......................................139 5.1.1 Bernoulli...............................................................139 5.1.2 Geometric............................................................141 5.1.3 Binomial..............................................................144 5.1.4 NegativeBinomial...............................................147 5.1.5 Hypergeometric...................................................150 5.1.6 Poisson.................................................................152 5.2 SomeContinuousRandomVariables.................................156 5.2.1 Uniform................................................................156 5.2.2 Triangular.............................................................158 5.2.3 Normal.................................................................160 5.2.4 Chi-Square...........................................................165 5.2.5 Student’st............................................................168 5.2.6 FDistributions.....................................................171 5.2.7 Exponential..........................................................174 5.2.8 Gamma.................................................................178 5.2.9 Phase-Type...........................................................181 5.2.10 Erlang...................................................................181 5.2.11 Hypoexponential..................................................185 5.2.12 Hyperexponential.................................................190 5.2.13 Cox.......................................................................193 5.2.14 Weibull.................................................................197 5.3 FunctionsofaRandomVariable.........................................202 5.4 TaylorSeries.......................................................................207 Chapter6 StatisticalInferenceandDataFitting..........................................219 6.1 ParametricConfidenceIntervalforMean...........................219 6.1.1 ConfidenceIntervalwhenVarianceisKnown......221 6.1.2 ConfidenceIntervalwhenVarianceisUnknown..225 6.2 ParametricConfidenceIntervalforSD2andSD.................228 6.3 ParametricConfidenceIntervalforProportion...................231 6.3.1 ParametricConfid.Interv.for pbasedonb(n,k).231 6.3.2 ParametricConfid.Interv.for pbasedonN(µ,σ)235 6.4 ParametricConfidenceIntervalforDifference...................237 6.4.1 ConfidenceIntervalforPairedComparison.........237 6.4.2 Conf.Interv.forNon-Corresp.Measurements.....241 6.5 Bootstrap.............................................................................246 6.5.1 BasicBootstrap.....................................................246 6.5.2 Bootstrap-t............................................................249 6.5.3 Semi-ParametricBootstrap...................................252 6.6 GoodnessofFit...................................................................255 6.6.1 Probability–ProbabilityPlotMethod....................255 6.6.2 χ2Method.............................................................258 6.6.3 Kolmogorov-SmirnovMethod..............................262 Contents ix 6.7 DataFitting.........................................................................268 6.7.1 LinearRegression.................................................268 6.7.2 PolynomialRegression.........................................276 6.7.3 ExponentialRegression........................................279 6.7.4 Lagrange’sPolynomial.........................................282 Chapter7 DataScaling,Distances,andClustering......................................295 7.1 DataScaling........................................................................295 7.2 DistanceandSimilarityMeasures......................................313 7.3 ClusterDistances................................................................318 7.4 Clustering:anintroduction.................................................323 7.5 K-Means.............................................................................330 7.6 K-MedoidandK-Median...................................................337 7.7 HierarchicalClustering.......................................................341 PART II Performance Modeling Chapter8 OperationalAnalysis...................................................................365 8.1 UtilizationLaw...................................................................367 8.2 ForcedFlowLaw................................................................368 8.3 DemandLaw.......................................................................369 8.4 Little’sLaw.........................................................................372 8.5 GeneralResponseTimeLaw..............................................376 8.6 InteractiveResponseTimeLaw..........................................378 8.7 BottleneckAnalysisandBounds........................................382 Chapter9 DiscreteTimeMarkovChain......................................................393 9.1 StochasticProcesses...........................................................393 9.2 Chapman-KolmogorovEquation........................................398 9.3 TransientDistribution.........................................................404 9.4 SteadyStateDistribution....................................................407 9.5 ClassificationofStates,MRTandMFPT...........................408 9.6 HoldingTime(SojournTimeorResidenceTime).............421 9.7 MeanTimetoAbsorption...................................................423 9.8 SomeApplications..............................................................425 Chapter10 ContinuousTimeMarkovChain.................................................439 10.1 RateMatrix.........................................................................439 10.2 Chapman-KolmogorovEquation........................................442 10.3 HoldingTimes....................................................................448 10.4 StationaryAnalysis.............................................................450 10.4.1 GaussElimination.................................................452 10.4.2 Gauss-SeidelMethod............................................458 10.5 TransientAnalysis..............................................................463 10.5.1 IntervalSubdivision..............................................464

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