The Network Calculus Part1

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1、NETWORKCALCULUSATheoryofDeterministicQueuingSystemsfortheInternetJEAN-YVESLEBOUDECPATRICKTHIRANOnlineVersionoftheBookSpringerVerlag-LNCS2050VersionJanuary16,20022AAnneliesAJoana,Maelle,AudraineetElias¨Amamere`-JLAmesparents-PTPoureviterlesgrumeaux´Quiencombrentlesreseaux´Il

2、fallait,cestcomplique,´Maıtriserlesseauxperces´Branle-basdanslescampusOnpourradorenavant´CalculerplussimplementGracealalg`ebreMin-Plus`FoindesobscuresastucesPourestimerlesdelais´EtlagiguedespaquetsPlaceaNetworkCalculus`-JLviSummaryofChanges2002Jan14,JLChapter2:addedabetterc

3、overageofGRnodes,inparticularequivalencewithservicecurve.FixedbuginProposition1.4.12002Jan16,JLChapter6:M.Andrewsbroughtconvincingproofthatconjecture6.3.1iswrong.RedesignedChapter6toaccountforthis.Removedredun-dancybetweenSection2.4andChapter6.AddedSETFtoSection2.4ContentsI

4、ntroductionxiiiIAFirstCourseinNetworkCalculus11NetworkCalculus31.1ModelsforDataFlows........................41.1.1CumulativeFunctions,DiscreteTimeversusContinuousTimeModels.........................41.1.2BacklogandVirtualDelay..................61.1.3Example:ThePlayoutBuffer.

5、...............71.2ArrivalCurves.............................81.2.1DefinitionofanArrivalCurve................81.2.2LeakyBucketandGenericCellRateAlgorithm.......121.2.3Sub-additivityandArrivalCurves..............171.2.4MinimumArrivalCurve...................201.3ServiceCurves.

6、...........................221.3.1DefinitionofServiceCurve.................221.3.2ClassicalServiceCurveExamples..............251.4NetworkCalculusBasics.......................281.4.1ThreeBounds.........................281.4.2AretheBoundsTight?....................331.4.3Concat

7、enation........................341.4.4ImprovementofBacklogBounds..............361.5GreedyShapers............................371.5.1Definitions..........................371.5.2Input-OutputCharacterizationofGreedyShapers......381.5.3PropertiesofGreedyShapers.................40

8、1.6MaximumServiceCurve,VariableandFixedDelay.........421.6.1MaximumServiceCurves..