Matthew N.O. Sadiku · Sarhan M. Musa Performance Analysis of Computer Networks Performance Analysis of Computer Networks Matthew N.O. Sadiku (cid:129) Sarhan M. Musa Performance Analysis of Computer Networks MatthewN.O.Sadiku SarhanM.Musa Roy.G.PerryCollegeofEngineering Roy.G.PerryCollegeofEngineering PrairieViewA&MUniversity PrairieViewA&MUniversity PrairieView,TX,USA PrairieView,TX,USA ISBN978-3-319-01645-0 ISBN978-3-319-01646-7(eBook) DOI10.1007/978-3-319-01646-7 SpringerChamHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2013947166 ©SpringerInternationalPublishingSwitzerland2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerpts inconnectionwithreviewsorscholarlyanalysisormaterialsuppliedspecificallyforthepurposeofbeing enteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthework.Duplication ofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheCopyrightLawofthe Publisher’s location, in its current version, and permission for use must always be obtained from Springer.PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter. ViolationsareliabletoprosecutionundertherespectiveCopyrightLaw. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) To my late dad, Solomon, late mom, Ayisat, and my wife, Kikelomo. To my late father, Mahmoud, mother, Fatmeh, and my wife, Lama. Preface Modeling and performance analysis play an important role in the design of computercommunicationsystems.Modelsaretoolsfordesignerstostudyasystem before it is actually implemented. Performance evaluation of models of computer networks during the architecture design, development, and implementation stages provides means to assess critical issues and components. It gives the designer the freedomandflexibilitytoadjustvariousparametersofthenetworkintheplanning ratherthanintheoperationalphase. The major goal of the book is to present a concise introduction to the perfor- mance evaluation of computer communication networks. The book begins by providing the necessary background in probability theory, random variables, and stochastic processes. It introduces queueing theory and simulation as the major tools analysts have at their disposal. It presents performance analysis on local, metropolitan,andwideareanetworksaswellasonwirelessnetworks.Itconcludes withabriefintroductiontoself-similarity. The bookisdesignedforaone-semestercourseforsenior-yearundergraduateand graduate engineering students. The prerequisite for taking the course is a background knowledgeofprobabilitytheoryanddatacommunicationingeneral.Thebookcanbe usedingivingshortseminarsonperformanceevaluation.Itmayalsoserveasafingertip reference for engineers developing communication networks, managers involved in systemsplanning,andresearchersandinstructorsofcomputercommunicationnetworks. We owe a debt of appreciation to Prairie View A&M University for providing theenvironmenttodevelopourideas.Wewouldliketoacknowledgethesupportof the departmental head, Dr. John O. Attia, and college dean, Dr. Kendall Harris. SpecialthanksareduetoDr.Sadiku’sgraduatestudent,NanaAmpah,forcarefully going through the entire manuscript. (Nana has graduated now with his doctoral degree.) Dr. Sadiku would like to thank his daughter, Ann, for helping in many ways especially with the figures. Without the constant support and prayers of our families,thisprojectwouldnothavebeenpossible. PrairieView,TX,USA MatthewN.O.Sadiku PrairieView,TX,USA SarhanM.Musa vii Contents 1 PerformanceMeasures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 ComputerCommunicationNetworks. . . . . . . . . . . . . . . . . . . . . 1 1.2 TechniquesforPerformanceAnalysis. . . . . . . . . . . . . . . . . . . . 2 1.3 PerformanceMeasures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 ProbabilityandRandomVariables. . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1 ProbabilityFundamentals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 SimpleProbability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.2 JointProbability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.3 ConditionalProbability. . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.4 StatisticalIndependence. . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 RandomVariables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.1 CumulativeDistributionFunction. . . . . . . . . . . . . . . . . . 12 2.2.2 ProbabilityDensityFunction. . . . . . . . . . . . . . . . . . . . . 13 2.2.3 JointDistribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 OperationsonRandomVariables. . . . . . . . . . . . . . . . . . . . . . . 20 2.3.1 ExpectationsandMoments. . . . . .. . . . . . . .. . . . . . . .. 20 2.3.2 Variance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3.3 MultivariateExpectations. . .. . . . .. . . . .. . . . .. . . . .. 22 2.3.4 CovarianceandCorrelation. . . . . . . . . . . . . . . . . . . . . . 23 2.4 DiscreteProbabilityModels. . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4.1 BernoulliDistribution. . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4.2 BinomialDistribution. . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4.3 GeometricDistribution. . . . . . . . . . . . . . . . . . . . . . . . . 30 2.4.4 PoissonDistribution. . . . . .. . . . . . .. . . . . .. . . . . . .. . 31 2.5 ContinuousProbabilityModels. . . . . . . . . . . . . . . . . . . . . . . . . 33 2.5.1 UniformDistribution. . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.5.2 ExponentialDistribution. . . . . . . . . . . . . . . . . . . . . . . . 34 2.5.3 ErlangDistribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 ix