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Improving TCP Slow Start

Permanent Link: http://ufdc.ufl.edu/UFE0041219/00001

Material Information

Title: Improving TCP Slow Start
Physical Description: 1 online resource (116 p.)
Language: english
Creator: Yu, Inkwan
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: network, slow, start, tcp
Computer and Information Science and Engineering -- Dissertations, Academic -- UF
Genre: Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The TCP slow start algorithm tries to increase the initial congestion window size exponentially until the slow start threshold is reached. The initial TCP start-up performance depends on accurate estimation of these two parameters. However, due to lack of information on network states initially, the standard TCP uses default values for these parameters. If the initial congestion window size and the slow start threshold can be estimated accurately, it is possible for TCP to achieve higher initial bandwidth without congesting the network. For this purpose, we introduce a method to estimate the slow start threshold and the congestion window size using other TCP connections sharing the bottleneck links by taking advantage of fairness in TCP. Furthermore, when the information of other TCP connections sharing the same bottleneck links is not available, it is possible to approximate end-to-end available bandwidth with packet pair measurements which, in turn, is used to estimate the slow start threshold. The standard TCP slow start, when delayed acknowledgement is enabled, can be slow since the growth rate of the congestion window is lower than when the delayed acknowledgement is not used. By way of inverted packet pairs and counting duplicate acknowledgements to increase the congestion window size during slow start, the advantage of delayed acknowledgement is retained during the congestion avoidance stage of TCP, while achieving almost the same performance in slow start as when delayed acknowledgement is not used. Finally, our slow start algorithms can help to achieve higher initial bandwidth on a large delay bandwidth product path. This allows users of multimedia streaming applications or web browsers can have an improved user experience.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Inkwan Yu.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Newman, Richard E.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-06-30

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041219:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041219/00001

Material Information

Title: Improving TCP Slow Start
Physical Description: 1 online resource (116 p.)
Language: english
Creator: Yu, Inkwan
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: network, slow, start, tcp
Computer and Information Science and Engineering -- Dissertations, Academic -- UF
Genre: Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The TCP slow start algorithm tries to increase the initial congestion window size exponentially until the slow start threshold is reached. The initial TCP start-up performance depends on accurate estimation of these two parameters. However, due to lack of information on network states initially, the standard TCP uses default values for these parameters. If the initial congestion window size and the slow start threshold can be estimated accurately, it is possible for TCP to achieve higher initial bandwidth without congesting the network. For this purpose, we introduce a method to estimate the slow start threshold and the congestion window size using other TCP connections sharing the bottleneck links by taking advantage of fairness in TCP. Furthermore, when the information of other TCP connections sharing the same bottleneck links is not available, it is possible to approximate end-to-end available bandwidth with packet pair measurements which, in turn, is used to estimate the slow start threshold. The standard TCP slow start, when delayed acknowledgement is enabled, can be slow since the growth rate of the congestion window is lower than when the delayed acknowledgement is not used. By way of inverted packet pairs and counting duplicate acknowledgements to increase the congestion window size during slow start, the advantage of delayed acknowledgement is retained during the congestion avoidance stage of TCP, while achieving almost the same performance in slow start as when delayed acknowledgement is not used. Finally, our slow start algorithms can help to achieve higher initial bandwidth on a large delay bandwidth product path. This allows users of multimedia streaming applications or web browsers can have an improved user experience.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Inkwan Yu.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Newman, Richard E.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-06-30

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041219:00001


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First,Iwouldliketothankmyadvisor,Dr.RichardNewman,forhissupportandencouragementduringmygraduatestudy.Also,it'sbeenagreathonortoworkwithmyPh.D.advisorycommitteemembersincludingDr.ShigangChen,Dr.JonathanLiu,Dr.RickSmithandDr.YeXiainalphabeticalorder.ThankstodiscussionwithmyPh.D.committee,Icouldrealizenovelaspectsofmyresearchandimprovemyknowledgeonthesubject.Ialsohavetothankmyfamily,whohadtosufferbecauseofmyabsenceduringthepastfewyears.TheyenduredandmanagedfamilymattersthatIshouldhavehandled.Insteadofcomplaining,theyencouragedmeandhelpedme.Again,mygratitudetomyfamily. 4

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page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 12 CHAPTER 1INTRODUCTION ................................... 14 2TCPSLOWSTARTWITHFAIRSHAREOFBANDWIDTH ............ 19 2.1Introduction ................................... 19 2.2RelatedWork .................................. 21 2.3EstimatingCongestionWindowSizeforSlowStartThreshold ....... 24 2.4EstimatingInitialCongestionWindowSize .................. 26 2.5Simulation .................................... 28 2.5.1HomogeneousNetwork ........................ 30 2.5.2LargeNetwork ............................. 35 2.5.2.1Networktopologywith200nodes ............. 36 2.5.2.2Networktopologywith600nodes ............. 40 2.6Discussion ................................... 43 2.7Conclusion ................................... 43 3TCPSLOWSTARTWITHINVERTEDPACKETPAIRS .............. 46 3.1Introduction ................................... 46 3.2InvertedPacketPairMethod .......................... 49 3.3Simulation .................................... 52 3.3.1SingleFTPFlow ............................ 53 3.3.2MultipleFTPFlows ........................... 54 3.4Conclusion ................................... 59 4TCPSLOWSTARTWITHPACKETPAIRMEASUREMENTS .......... 60 4.1Introduction ................................... 60 4.2LinearityofPacketPairGaps ......................... 62 4.2.1Assumptions .............................. 63 4.2.2AnExample ............................... 64 4.2.3ProbingwithZero-sizedPacketPairs ................. 65 4.2.4ProbingwithNonzero-sizedPacketPairs ............... 67 4.3ApproximateEnd-to-endAvailableBandwidth ................ 71 4.4SimulationofPacketPairGapMeasurements ................ 73 5

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........................ 74 4.4.2SimulationofDumbbellModel ..................... 74 4.4.3SimulationofParkingLotModel .................... 84 4.4.4Remarks ................................. 87 4.5SlowStartwithPacketPairMeasurements ................. 92 4.6SimulationofSlowStartModels ....................... 95 4.6.1SimulationEnvironment ........................ 95 4.6.2SlowStartModelsforComparison .................. 97 4.6.3SimulationResults ........................... 100 4.7Conclusion ................................... 106 5CONCLUSION .................................... 107 5.1SlowStartwithInformation .......................... 107 5.2SlowStartwithPacketPairs .......................... 108 5.3FutureWork ................................... 109 REFERENCES ....................................... 111 BIOGRAPHICALSKETCH ................................ 116 6

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Table page 4-1AverageofestimatedssthreshvaluesanditsstandarddeviationforAstart-ERE,Astart-BWE,SPM,Hoe,andPaStwithvaryingBandwidth ............ 106 7

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Figure page 2-1cwndgraphsoftwoTCPowsF1andF2sharingthecommonbottlenecks. .. 27 2-2Homogeneousnetworktopology. .......................... 30 2-3ServerthroughputwithvaryingBandwidthinhomogeneoustopology. ..... 31 2-4ServerthroughputwithvaryingDelayinhomogeneoustopology. ........ 32 2-5Serverthroughputwithvaryingconnectioninter-arrivaltimeinhomogeneoustopology(20Mbpslink). ............................... 33 2-6Serverthroughputwithvaryingconnectioninter-arrivaltimeinhomogeneoustopology(10Mbpslink). ............................... 33 2-7Servernsecondthroughputinhomogeneoustopology. ............. 34 2-8ServerthroughputwithvaryingParetoshapeparameterinhomogeneoustopology. 35 2-9Randomtopologywith200nodes. ......................... 36 2-10Randomtopologywith600nodes. ......................... 37 2-11Serverthroughputwithvaryingbandwidthin200-nodetopology. ........ 37 2-12Servernsecondthroughputin200-nodetopology. ................ 39 2-13Serverthroughputwithvaryingexponentialinter-arrivaltimein200-nodetopology. 39 2-14Serverthroughputwithvaryingbandwidthin600-nodetopology. ........ 40 2-15Serverthroughputwithvaryingexponentialinter-arrivaltimein600-nodetopology. 41 2-16Servernsecondthroughputin600-nodetopology. ................ 42 3-1Simulationtopology. ................................. 53 3-2SingleFTPtransferthroughput. ........................... 54 3-3ThroughputofmultipleFTPtransferswithadrop-tailqueue. ........... 56 3-4GoodputofmultipleFTPtransferswithadrop-tailqueue. ............ 56 3-5AveragequeuesizeofmultipleFTPtransferswithadrop-tailqueue. ...... 56 3-6ThroughputofmultipleFTPtransferswithanREDqueue. ............ 58 3-7GoodputofmultipleFTPtransferswithanREDqueue. .............. 58 3-8AveragequeuesizeofmultipleFTPtransferswithanREDqueue. ....... 58 8

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............ 61 4-2Singlerouterqueuechangeovertime. ....................... 65 4-3Packetoutputfromtherouterovertime. ...................... 65 4-4Outputgaplessthaninputgap. ........................... 70 4-5Dumbbelltopologyforpacketpairmeasurements. ................ 75 4-6Inputgapsandmeanoutputgapswith1sourceofCBRcrosstrafcindumbbelltopology. ....................................... 76 4-7Inputgapsandmeanoutputgapswith2sourcesofCBRcrosstrafcindumbbelltopology. ....................................... 77 4-8Inputgapsandmeanoutputgapswith3sourcesofCBRcrosstrafcindumbbelltopology. ....................................... 77 4-9Inputgapsandmeanoutputgapswith4sourcesofCBRcrosstrafcindumbbelltopology. ....................................... 78 4-10Inputgapsandmeanoutputgapswith1sourceofPoissoncrosstrafcindumbbelltopology. ....................................... 78 4-11Inputgapsandmeanoutputgapswith2sourcesofPoissoncrosstrafcindumbbelltopology. .................................. 79 4-12Inputgapsandmeanoutputgapswith3sourcesofPoissoncrosstrafcindumbbelltopology. .................................. 79 4-13Inputgapsandmeanoutputgapswith4sourcesofPoissoncrosstrafcindumbbelltopology. .................................. 80 4-14Inputgapsandmeanoutputgapswith1sourceofParetocrosstrafcindumbbelltopology. ....................................... 80 4-15Inputgapsandmeanoutputgapswith2sourcesofParetocrosstrafcindumbbelltopology. ....................................... 81 4-16Inputgapsandmeanoutputgapswith3sourcesofParetocrosstrafcindumbbelltopology. ....................................... 81 4-17Inputgapsandmeanoutputgapswith4sourcesofParetocrosstrafcindumbbelltopology. ....................................... 82 4-18Inputgapsandmeanoutputgapswith1sourceofFTPcrosstrafcindumbbelltopology. ....................................... 82 4-19Inputgapsandmeanoutputgapswith2sourcesofFTPcrosstrafcindumbbelltopology. ....................................... 83 9

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................ 84 4-21Inputgapsandmeanoutputgapswith1sourceofCBRcrosstrafcinparkinglottopology. ...................................... 86 4-22Inputgapsandmeanoutputgapswith5sourcesofCBRcrosstrafcinparkinglottopology. ...................................... 86 4-23Inputgapsandmeanoutputgapswith10sourcesofCBRcrosstrafcinparkinglottopology. ...................................... 87 4-24Inputgapsandmeanoutputgapswith1sourceofPoissoncrosstrafcinparkinglottopology. ...................................... 87 4-25Inputgapsandmeanoutputgapswith5sourcesofPoissoncrosstrafcinparkinglottopology. ................................. 88 4-26Inputgapsandmeanoutputgapswith10sourcesofPoissoncrosstrafcinparkinglottopology. ................................. 88 4-27Inputgapsandmeanoutputgapswith2sourceofParetocrosstrafcinparkinglottopology(1Mbpscrosstrafcduringthebusyperiod). ............ 89 4-28Inputgapsandmeanoutputgapswith10sourcesofParetocrosstrafcinparkinglottopology(1Mbpscrosstrafcduringthebusyperiod). ........ 89 4-29Inputgapsandmeanoutputgapswith20sourcesofParetocrosstrafcinparkinglottopology(1Mbpscrosstrafcduringthebusyperiod). ........ 90 4-30Inputgapsandmeanoutputgapswith1sourceofFTPcrosstrafcinparkinglottopology. ...................................... 90 4-31Inputgapsandmeanoutputgapswith5sourcesofFTPcrosstrafcinparkinglottopology. ...................................... 91 4-32Inputgapsandmeanoutputgapswith20sourcesofFTPcrosstrafcinparkinglottopology. ...................................... 91 4-33Parkinglottopologymodelforslowstart. ..................... 96 4-34cwndduring[500,515]secondsinparkinglottopologywhenBandwidthis25Mbps. ......................................... 101 4-35cwndduring[500,515]secondsinparkinglottopologywhenBandwidthis50Mbps. ......................................... 101 4-36cwndduring[500,515]secondsinparkinglottopologywhenBandwidthis100Mbps. ....................................... 102 10

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....................................... 102 4-38cwndduring[500,515]secondsinparkinglottopologywhenBandwidthis400Mbps. ....................................... 103 11

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TheTCPslowstartalgorithmtriestoincreasetheinitialcongestionwindowsizeexponentiallyuntiltheslowstartthresholdisreached.TheinitialTCPstart-upperformancedependsonaccurateestimationofthesetwoparameters.However,duetolackofinformationonnetworkstatesinitially,thestandardTCPusesdefaultvaluesfortheseparameters. Iftheinitialcongestionwindowsizeandtheslowstartthresholdcanbeestimatedaccurately,itispossibleforTCPtoachievehigherinitialbandwidthwithoutcongestingthenetwork.Forthispurpose,weintroduceamethodtoestimatetheslowstartthresholdandthecongestionwindowsizeusingotherTCPconnectionssharingthebottlenecklinksbytakingadvantageoffairnessinTCP.Furthermore,whentheinformationofotherTCPconnectionssharingthesamebottlenecklinksisnotavailable,itispossibletoapproximateend-to-endavailablebandwidthwithpacketpairmeasurementswhich,inturn,isusedtoestimatetheslowstartthreshold. ThestandardTCPslowstart,whendelayedacknowledgementisenabled,canbeslowsincethegrowthrateofthecongestionwindowislowerthanwhenthedelayedacknowledgementisnotused.Bywayofinvertedpacketpairsandcountingduplicateacknowledgementstoincreasethecongestionwindowsizeduringslowstart,theadvantageofdelayedacknowledgementisretainedduringthecongestionavoidance 12

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Finally,ourslowstartalgorithmscanhelptoachievehigherinitialbandwidthonalargedelaybandwidthproductpath.Thisallowsusersofmultimediastreamingapplicationsorwebbrowserscanhaveanimproveduserexperience. 13

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TCPhasbeenthedominanttransportprotocolintheInternetfordecades.Consequently,theperformanceoftheInternetisinuencedbyTCPsignicantly.Inthisstudy,weespeciallyfocusonimprovingstart-upperformanceofTCPbymodifyingthestart-upalgorithmofTCPcalledslowstart.Initially,whenaTCPconnectionisestablished,theslowstartalgorithmincreasesthecongestionwindowsize(cwnd)ofTCPexponentiallyuntiltheslowstartthreshold(ssthresh)isreached,wheretheslowstartphaseofTCPterminatesandcongestionavoidanceofTCPinitiates.InthestandardTCP,thessthreshvalueisxedbydefaultat65536bytes. ConsideringthatcwndlimitsTCPconnectionbandwidth,theinitialstart-upperformanceofTCPlargelydependsonssthresh,asssthreshboundstheexponentialgrowthofcwnd.Thus,whenssthreshistoolarge,cwndwillgrowexponentiallyuntilmultiplepacketdropsaregenerated,wastingnetworkresources.Whenssthreshistoosmall,TCPcannotutilizethebandwidthfully,sinceTCPwillslowdownthegrowthofcwndprematurely.Unfortunately,estimatingagoodvalueforssthreshisnoteasy,sincelittlenetworkstateinformationisavailablefortheTCPconnectioninitially. Inthisstudy,twodifferentapproachesareexaminedtoestimatessthreshandalgorithmsbasedoneachapproachareevaluated.Astherstapproach,cwndofanewTCPconnectionisestimatedbasedonotherTCPconnectionssharingthesamebottlenecklinks.Previously,Zhangetal.[ 63 ]andSavageetal.[ 49 ]suggestedthatssthreshcanbeestimatedbyapassivenetworkmonitorthatcanidentifythenumberofconnectionssharingthesamesubnet,andthemonitorcandiscoverthebandwidthsharedbytheconnections.Consequently,ssthreshforanewconnectionsharingthesamesubnetcanbeestimatedeasilybydividingthebandwidthbythenumberofconnections.Obviously,thecomputationaloverheadforsuchpassivenetworkmonitorsmaybehigh.Balakrishnanetal.[ 6 ]placeamonitorintheOSkerneltokeeptrackof 14

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Thesecondapproachinestimatingssthreshusespacketpairmeasurements.Relatedtoourwork,Hoe[ 19 ]usesasinglepacketpairtoestimatessthresh.However,Hoe'salgorithmtendstooverestimatessthresh.HuandSteenkiste[ 21 ]estimaterelativelygoodssthreshvaluesbywayofpacedpacketpairs.Unfortunately,bothapproachesdonotconsiderthedelayedacknowledgementfeatureoftheTCPreceiversandthelatterapproachcanworkunderanunrealisticassumptionthatanumberofpacketsarealwaysavailabletobetransmitted.Incontrast,oursecondapproachintroducestheinvertedpacketpairmeasurementmethodofPerssonetal.[ 44 ]intoslowstarttoworkarounddelayedacknowledgementanddoesnotrequiretheassumptionofthelatterapproach.Inoursecondestimationmethod,packetpairscanbesentfromtheTCPsenderwithaspecictemporalgapbetweentherstandthesecondpacketofthepacketpairs.Whenpacketpairspassthrougharouter,thetemporalgapextendsorshrinksdependingoncrosstrafcandsamplingintervalofpacketpairs.Thesegapscanbeusedtoinferavailablebandwidthforanewconnection.Inparticular,bywayofalinearleastsquaremethod,wecanobtainagoodssthreshvalue.Thisssthreshvalueis 15

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Initially,ssthreshisgivenadefaultvalueandcwndincreasesuntilsshtreshisreached.Duringthisperiod,theTCPsendermeasurespacketpairgapsusingacknowledgements(ACKs)toestimateanewssthresh.However,whendelayedacknowledgementisenabledintheTCPsender,itsuppressesanACKforeveryotherpacketmakingitdifculttomeasurepacketpairgaps.Thisdifcultyissolvedusinginvertedpacketpairs.Infact,Perssonetal.[ 44 ]rstusedinvertedpacketpairpairstomeasurethebottlenecklinkcapacity.Here,weuseduplicateACKstoincreasecwndratherthantomeasurepacketpairgaps.Tobemorespecic,withinvertedpacketpairs,theTCPreceiverisforcedtogenerateanACKforeverypacketitreceivesimmediately.ThentheTCPsendermeasurespacketpairgapsusingduplicateACKsgeneratedbyinvertedpackets.Asthisalgorithmperformsbetterwhenthenumberofpacketsavailabletobetransmittediseven,thelimitedbytecountingalgorithmbyAllman[ 3 ]isadopted.OurslowstartalgorithmwithpacketpairmeasurementsislessaggressivethanthestandardTCPslowstartalgorithm,sinceouralgorithmpacespacketpairstoreducemeasurementbias.Asaresult,ouralgorithmmaynotperformwellonasmalldelaybandwidthproductpath.However,itshowsgoodperformanceonhighspeedlinks,especiallyapplicabletoTCPmultimediatrafctoreducetheinitialplay-outdelayofmultimediastreaming. Thelimitedbytecountingalgorithmwasintroducedtospeedupthecwndgrowth,toaddresstheproblemofslowcwndgrowthwhentheTCPreceiverisenabledwithdelayedacknowledgement.However,thelimitedbytecountingalgorithmtendstotransmitfourpacketsperACKcomparedtotwopacketsperACKinthecaseofthestandardTCPslowstartalgorithmwithoutdelayedacknowledgement.Astheburstofpacketsincreasestheaveragequeuelengthandpacketdropratewithlowerthroughput,weintroduceanewalgorithmcalledslowstartwithinvertedpacketpairs(SSIPP)that 16

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Therestofthisstudyisorganizedasfollows.InChapter 2 ,ssthreshandcwndestimationbasedonfairbandwidthofTCPisexplained.Thenfourvariantsofslowstartmodelsbasedonestimatedssthreshandcwndvalues,namely,LISS,ISS,MISS,andJSareintroduced.LISS,andISSarethesameastheoriginalTCPexceptthattheyuseestimatedssthreshvalues.Similarly,Hoe[ 19 ]reliesontheoriginalTCPslowstartalgorithmwithssthreshestimatedusingapacketpairmeasurementmethod.JSisanalogoustoZhangetal.[ 63 ]withadifferencethatJSusesssthreshasestimatedinLISS.Thesemodelsarecomparedtoeachotherinahomogeneousnetworktopology,alsoinasmallandalargeheterogenousnetworktopologythroughns-2simulations.Inaddition,itisshownthatourslowstartalgorithmscanprovidebetteruserexperienceofmultimediastreamingorwebbrowsing.Simulationresultsshowthatourschemesworkbestinahomogeneousandsmallnetwork. Chapter 3 explainshowSSIPPcanbeimplementedintheTCPsender.SSIPPiscomparedwiththelimitedbytecountingalgorithmandTCPRenowithdelayedacknowledgementenabled.Simulationwithns-2showsthatSSIPPworksbetterthanthelimitedbytecountalgorithmintermsofthroughput,goodput,andaveragequeueingbuffersizewhenthequeuemanagementalgorithmisdrop-tail. Chapter 4 beginswithanalysisofpacketpairgapmeasurementsanddenestheapproximateend-to-endavailablebandwidth.Then,simulationconrmstheanalysisisvalidwithCBR,Poisson,andParetocrosstrafcofns-2usingadumbbelltopologyandaparkinglottopology.Basedontheanalysis,anovelslowstartalgorithmcalledSPMisdevelopednext.ToevaluatetheperformanceofSPM,otherslowstartmodelssuch 17

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59 ]withBWE,AstartwithERE,Hoe'smethod[ 19 ]andPaSt[ 21 ]arecomparedinaparkinglottopologywithns-2simulation.Finally,Chapter 5 summarizescontributionsofthisstudy. 18

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53 ],slowstartusestheslowstartthreshold(ssthresh)asaparameterfortheupperboundofrapidcongestionwindowgrowth.ThevalueofssthreshsignicantlyimpactstheperformanceofTCP.Whenitistoosmall,theslowstartphaseterminatestooearly,losingtheopportunitytoutilizeavailablebandwidth.Whenitistoolarge,slowstartinducesmultiplepacketlossesbeforeitreachesssthresh.ItisobviousthatanaccurateestimateofthessthreshvalueearlyintheslowstartphasecansignicantlyimproveTCPperformance. Here,weintroduceanewmethodtoestimatessthresh.Thismethod,whichwecallLessInformedSlowStart(LISS),estimatesssthreshusingthecongestionwindow(cwnd)oftheoldestconnectionamongconnectionssharingcommonbottlenecks.AssumingfairnessofTCP[ 12 ],LISSisrelativelyaccurate,althoughitsapplicationisratherlimitedsinceitrequiressteadyandactiveTCPconnectionssharingbottlenecks.Inotherwords,ourschemeassumesthatanewTCPconnectionwillusethesamebandwidthasotherTCPconnectionssharingbottlenecklinksandassignsthessthreshvalueaccordingtothisbandwidth.ItshouldbenotedthatLISSimprovesTCPReno[ 23 ]withoutmodifyingtheTCPalgorithmitself,asitonlychangesaTCPparameter.IfitisallowabletomodifytheTCPalgorithm,furtherimprovementoverLISSisattainable.Whenestimatingssthresh,ExponentiallyWeightedMovingAverage(EWMA)ofcwndoftheoldestconnectionamongconnectionssharingcommonbottlenecks,canbeusedinsteadofcwnd,asinthens-2[ 22 ]simulator,tosmoothoutthetypicalcwndgrowthpatternthatfollowsthesaw-toothshapedcycles.WecallthisslowstartschemeInformedSlowStart(ISS).RelatedtoLISSandISS,Hoe[ 19 ]usestheoriginalTCPslowstartalgorithmwithssthreshestimatedwithapacketpair. 19

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Asyetanotherapproach,theinitialssthreshobtainedinLISSisalsousedastheinitialcwnd.WecallthisschemeJumpStart(JS),asitdoesnotinvolveexponentialgrowthofcwnd.JSissimilartotheworkofZhangetal.[ 63 ],astheiralgorithmalsoburstsinitialcwndpacketswithpacketpacing.However,intheiralgorithm,theinitialcwndvalueofanewconnectionistakenfromamovingaverageofcwndvaluesofotherconnectionssharingbottlenecklinksestimatedbyanetworkmonitor.InbothMISSandJS,inordertoreducetheimpactofovershootingpackets,packetpacingasinPadmanabhanetal.[ 38 ]isemployed. Alltheseapproachesapplytoaserverthathandlesmultipleclients.ByusingtheIPaddressprexestorelateconnections,theserverhastheopportunitytoobtaintheneededinformationaboutconnectionslikelytosharecommonbottlenecks. TheperformanceofourschemesisinuencedbyfairnessofTCP.Fairnessisachievedifeachconnectionwithcommonbottleneckshasthesamebandwidth.Itseemsthatfairnessishardertoobservewithgreatercrosstrafcandlargerheterogeneousnetworks.Ingeneral,TCPperformancedegradeswithalongdelaypaths.Consequentlyourschemeworksbetterwithasmallandhomogeneousnetwork. Inthisstudy,withoutlosingthegeneralprinciplesofTCP,weassumethatssthreshrepresentsthenumberofpackets,andslowstartterminatesifcwndreachesssthresh,whereas,withthestandardTCP,ssthreshisrepresentedinbytes. 20

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5 7 19 20 26 48 54 ]. AweaknessofthecurrentTCPslowstartmechanismbecomesapparent,whenthereisalargedelaybandwidthproduct(delaybandwidth)path.Inanetworkpathwithalargeroundtriptime(RTT)valueandhighbandwidth,slowstartisnotfastenough.Forexample,ittakesalongtimetoincreasecwndforatypicalsatellitenetwork[ 2 ].InTCPReno,self-clockingofpacketsisusedwhilecwndislimitedbyssthresh[ 15 ].Duetoself-clocking,thecwndsizedoesnotgrowfastenoughifRTTislarge,eventhoughthecongestionwindowgrowthrateisexponential. Iftheinitialssthreshvalueissmallinalargedelaybandwidthproductpath,theslowstartphaseterminatestooearly,andthenthecwndincreasesslowlyundertheAdditiveIncreaseandMultiplicativeDecrease(AIMD)phaseofTCPReno.Toalleviatethesmallinitialwindowsizeproblem,somemodicationshavebeensuggested[ 1 2 ].Nevertheless,thexedinitialwindowsizeisstillaproblem[ 59 ].Ifwehaveagoodestimateofavailablebandwidth,itisreasonabletoincreasecwndtotheavailablebandwidthquickerthanTCPReno.Forinstance,TCPFastStartintroducedinPadmanabhanetal.[ 38 ]usesapreviousconnection'scachedssthreshvalueforanewconnection,whereasVisweswariahetal.[ 57 ]investigatethereuseofpreviousssthreshvalueofanidleTCPconnectioninslowstart.BothstudiesadoptpacketpacingintroducedinAronetal.[ 5 ]. 21

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59 ].Whenthereismoreavailablebandwidth,morepacketsaresent.Severalwaysofincreasingcwndaresuggested[ 1 2 59 ]. SlowstartmayoccurinthreedifferentstagesofaTCPconnectionwhentheconnectionisinitiallyestablished,whentheconnectionisidleforawhile,andwhenthereisatimeout[ 1 ].Thesethreecasescanbehandleddifferentlysincetheconnectioninformationavailableforeachcaseisdifferent.Therehavebeeneffortstosolveeachcaseintheliterature[ 4 5 38 57 59 ].Amongthesethreecases,thelattertwohaveanadvantageinthattheycaneasilyacquirethestatesofthecurrentconnectionsuchasthecongestionwindowsize,RTT,anditsvariance. Fortheinitialslowstart,it'shardtoobtainanaccurateestimateofavailablebandwidth.Hoe[ 19 ]usesapacketpairmethodtoestimatetheinitialssthreshvalue.However,theinter-packetgapoftherstsinglepacketpairisnotaccurateenoughduetomultiplehopsinthepathandmeasurementerror.Furthermore,therstinter-packetgapcausesoverestimationofinitialcongestionwindowsize[ 14 35 42 48 ].MultiplepacketpairsareusedtoestimatethessthreshvalueinHuetal.[ 21 ]andAronetal.[ 5 ].InHuetal.[ 21 ],avariantoftheslowstartalgorithmdetectsthechangebetweeninter-packetgapswhenthetheconnectionreachesthepeakavailablebandwidth.Theauthorsalsousepacketpacingtoreducetheimpactofslowstartonrouters. Inanotherapproach,TCPWestwood[ 59 ]usesanimprovedbandwidthestimationmethodofTCPVegas[ 9 ].Thisapproachdynamicallyadjuststheslowstartpackettransmissionrate.Whenthereismoreavailablebandwidth,thesendingrateincreasesmorerapidlyandconversely,whenthereislessbandwidthavailable,thesendingratedecreases. Althoughnotdirectlyrelatedtoslowstart,therehavebeenanumberofstudiescalculatingavailablebandwidth[ 14 24 35 42 47 54 ].Mostoftheseschemesusetrainsofpacketstomeasurethebandwidthmoreaccurately.Closelyrelatedtoour 22

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38 ]usethepastTCPconnectionbandwidthasacachedvaluewithoutestimatingthecurrentavailablebandwidth.Inthisscheme,routerswithfairqueueingcapabilityareassumedtohandlethesituationwhenthecachedvalueisanoverestimatedone. Asfortheinitialcwnd,Allman[ 2 ]showsthatitisbenecialtousealargeinitialcwndforcertaincases.Zhangetal.[ 63 ]introduceaschemetospeedupthetransferofsmalllesusingTCP.Theytakeamovingaverageofcwndvaluesofotherconnectionssharingbottlenecklinksandthelesizetobetransferred,incalculatingtheinitialcwndvalue.ThisschemeissimilartoJSinthatitalsoburstscwndnumberofpacketswithpacketpacinginitially,however,itdiffersinthecwndestimationmethod. Theideaofusinginformationofotherconnectionssharingbottlenecklinkshasbeenaroundfornearlytwodecades.Savageetal.[ 49 ]showstrongevidenceoflocalityamongnetworkconnections.Thislocalityfacilitatesinformedcongestioncontrolofotherconnectionswiththesamelocality.Forthepurposeofcollectinginformationofconnectionswithsharedbottlenecks,apassivemonitorcanbeadopted.Then,thisinformationcanhelpotherconnectionsinmakingcongestioncontroldecisions. Balakrishnanetal.[ 6 ]introduceaschemecalledCongestionManager(CM)toaggregateconnectioninformationintheOSkernelresidinginbetweenTCPandIPstacks.Inaddition,CMbehavesasmediatorofTCPandUDPowstoprovidebettercongestioncontrolperformanceusingtheinformationfrommultipleowssharingthesamenetworkcharacteristics. Inthischapter,bywayofsimulation,theinitialslowstartperformanceismeasuredduringonesecondthroughtenseconds.Selvidgeetal.[ 50 ]mentionthatuserstendtoloseinterestiftheyhavetowaitmorethantensecondstodownloadawebdocument.Wang[ 58 ]alsondsthattheactualdelayaffectsuserexperiencesignicantly. 23

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whereboistheoldconnectionbandwidth,andbnisthenewconnectionbandwidthsharingthesamesourceanddestination.ThelatterequalityofEquation 2 occurswhenthecapacityofbottleneckislargerthantheadditionalbandwidthrequiredbythenewconnection.Togeneralizethis,deneCasthebottlenecklinkcapacity,Biasaconnectioncurrentlypassingthroughthebottlenecklink,andletbibethebandwidthofBi,wherei2f1,2,3,...g.LetBobetheoldconnectionandBnbethenewconnection.IfCPibi+bnwithfBogSfBigandfBng6SfBig,thenwithfairTCP,bn=bo.TherstequalityofEquation 2 canhappenwhenC=bo,andSfBig=fBog.Inthiscase,withadditionofBn,wehaveC=bo=2+bnandbn=bo=2.Moregenerally,ifC=Pibi,andanewconnectionisadded,itsbandwidthwillbeproportionaltothenumberofconnectionsinthebottlenecklink.Hence,ifthenumberofoldconnectionsisn,thentheminimumavailablebandwidthforthenewconnectionisbn=nbo 24

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IfnisthenewconnectionbandwidthfromaLANoranISPandoisoldconnectionbandwidthinthesameLANortheISPwithfairTCP,andthesourcecandetermineasetofdestinationspassingthroughthesharedbottlenecklinks,thentheminimumbandwidthofnewconnectionwillben=Ko Inpractice,anaccuratevaluefortheavailablebandwidthisnotreadilyavailable.ToavoidmakingchangestotheTCPRenoimplementation,wetakecwndofanexistingTCPconnectionintheAIMDphaseasanestimateofavailablebandwidth.Iftherearemultipleliveconnectionssharingbottlenecks,cwndoftheoldestconnectionistaken.SelectingtheoldestconnectioncanbeeasilyimplementedusingaqueueandgivesabetterbandwidthestimateasTCPconnectionstaketimetoreachsteadystate.Amongliveconnections,onesundertheslowstartphaseshouldbeseparatedfromthoseundertheAIMDphase.Connectionsintheslowstartstagearenotstableandshouldnotbeassumedtotakethesamebandwidthasother,steadyconnections. Now,inlightoftheabovediscussion,apracticalssthreshestimationschemecanbegiven.First,letwobethecongestionwindowsizeoftheoldeststeadyconnectionandwnbethessthreshvalueofthenewconnection.ThenumberofactiveTCPconnectionsintheAIMDphaseisrepresentedasLandthenumberofactiveTCPconnectionsintheslowstartphaseasM.DenecwndofasingleTCPconnectionundertheslowstartphaseassi,i2f1,2,3,...,MgandthesumofthemasS=PMi=1si.Then,thessthresh

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wo+1.(2) InEquation 2 ,S+LwoestimatesthesumofcwndsofTCPconnectionssharingthesamebottlenecks.Togetafaircongestionwindowsizeestimateforanewconnection,thesumisdividedbythenumberofTCPconnectionsplusone.However,TCPconnectionsundertheslowstartphasearenotinastablestateandtheircwndvaluesarenotfaircomparedtoothersteadyTCPconnections.Ifwoisafaircwndvalue,S wocanestimatethenumberofsteadyconnections,assumingSisusedforsteadyconnectionsinsteadofstart-upconnections. TheestimationofssthreshdescribedabovedependsonwoinEquation 2 .Ifwetakecwndoftheoldestconnectionaswo,slowstartwouldbeLISS.Instead,ifawndistakenforwoasgiveninthepseudocodebelow,thenslowstartwouldbeISS.awnd(1)awnd+cwnd 26

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[ 29 ],we'dliketoknowagoodinitialcwndvalueforanewconnectionthatsharesthesamesourceanddestination. Ifweknowthepacketdropintervaloftheexistingconnectionandthelasttimethatapacketdropoccurred,itispossibletoestimateagoodinitialcwndvalue.Letbethepacketdropintervalandthetimeoflastpacketdropbetl.Ifthecurrenttimewhenanewconnectionstartsistc,thentctlrepresentstheamountoftimesincethelastpacketdropuntilnowand(tctl)becomestheamountoftimeuntilthenextpacketdrop.AstheexistingTCPconnectionincreasescwndduringthisperiodwiththerateof1=R,(tctl) ThisideacanbegeneralizedforTCPconnectionswithsharedbottlenecklinks.LetT=ftiji=1,2,3,...,landtj
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Ifwedenethepacketdropintervalofconnectionswithsharedbottlenecksasti+1ti,whereti+1,ti2T,thenEWMAofsharedconnections'packetdropintervalwouldbe where2il,01and1=t2t1.Likewise,forui+1,ui2U,whenthepacketdropintervaloftheoldestconnectionamongconnectionswithsharedbottlenecksisui+1ui,EWMAoftheoldestconnectionpacketdropintervalwouldbe where2im,01and1=u2u1. Ifwetakem=lasthenumberofconnectionssharingbottlenecklinkswiththesamecwndgrowthrate,andeachconnectioncwndgrowthrateis1=R,then canbeacandidatecwndsizeforanewTCPconnectionsharingthesamebottlenecklinks.ThisisreasonableasthenumberofpacketsestimatedinEquation 2 istheamountofpacketswemayaddonthepathwithsharedbottleneckswithoutcausingapacketdrop.InMISS,wetakecwndforanewconnectionasestimatedaboveandssthreshasestimatedinLISS,andtobeconservativewhencwnd>ssthresh,wesetthessthreshvaluetocwnd.Furthermore,toreducetheimpactoftheinitialstart-upburstofpackets,therstcwndpacketsarepacedwiththepackettransmissionratecwnd=R. 28

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Ingeneral,networkswithlargedelaybandwidthproductpathsbenetfromLISSandISSintermsoftheserverthroughput.Dependingonthenetworktopologyandtrafccharacteristics,thedegreeofperformancegainofLISSandISSagainstTCPRenomaydiffersignicantly.Withahomogeneousnetwork,LISSandISSshowmuchhigherthroughputthanTCPRenosincefairnessofTCPiswellpreservedinsuchanenvironment.However,LISSandISSachieveonlyslightlybetterthroughputcomparedtoTCPRenoinalargeandheterogeneousnetwork. Incontrast,MISSandJSshowsignicantperformanceimprovementoverLISSandISSintermsofthensecondthroughput.However,asbandwidthincreases,MISSandJSperformslightlyworseintermsofthetotalthroughputeventhoughtheinitialnsecondthroughputshowsimpressiveimprovement,whentherouterqueuesizeislimited. Toevaluateeachmodel,wesimulateeachschemeusingns-2[ 22 ]version2.28onLinux.Asthereisnoteardownmechanismforone-wayTCPconnectioninns-2,resetOTCLcommandisaddedtotheTCPagentclass.TerminatedTCPconnectionsareresetandreusedlaterasanewconnectionneedstobeestablishedbetweenthesamesenderandthereceiver.Inns-2,thedefaultvalueofssthreshisinitializedtothedefaultadvertisedwindowsize,whichisundesirableforourpurpose.Hence,wedecouplethesetwoparametersbyinitializingthedefaultadvertisedwindowsizeto100andthedefaultslowstartthresholdvalueto10.Also,bydefault,cwndissettoone.AnewOTCLcommandinns-2isaddedtosetthessthreshvaluefortheTCPsendertousetheestimatedssthreshvalue.WhenthereisnootheractiveTCPconnectionssharing 29

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Homogeneousnetworktopology. bottlenecks,thedefaultssthreshvalueisused.awndispredenedinns-2wheretheEWMAweightparameterofawndissetto0.002bydefault.EWMAweightparametersofEquation 2 andEquation 2 aresetto23foreaseofimplementation. 2-2 .Thereisasingleserverandveclientseachlabeledwithsandwithcrespectively.Routersbetweenthemarelabeledasr1,r2,andr3.Togeneratecrosstrafcbetweenroutersr1andr2,vepairsofsourceanddestinationareused.Nodeslabeledwithxsarecrosstrafcsourcesandnodeswithxcarecorrespondingdestinationsinthegure.Delaylabeledonthelinksbetweenr1andr2,aswellasr2andr3isaparameterusedinthesimulationtoassigndifferentlinkdelays.Similarly,Bandwidthisaparameterforlinkbandwidth. Forcrosstrafc,FTPtrafcisgeneratedbetweenve(xs,xc)pairs.Toalleviatetheeffectofsimultaneousconnectionestablishments,FTPconnectionsarrivewiththeexponentialdistributionaverageofonesecond.Queueingdisciplineforroutersisdrop-tailwith50packetsasthemaximumqueuesize.Otherrouterparametersaredefaultvaluesinns-2.FTPconnectionsfromtheservertoclientsarrivewiththeexponentialdistributionaverageofvesecondswhileeachclientmayhavemultipleFTP 30

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BTotalthroughput. ServerthroughputwithvaryingBandwidthinhomogeneoustopology. connectionswiththeserver.Unlessmentioned,Delayissetto50msandBandwidthissetto20MbpsinFigure 2-2 .DurationofconnectionsbetweentheserverandclientsfollowstheParetodistributionwithameanof100secondsandshapeparameterof1.35.Thesimulationrunsfor3000seconds. Basedonthesimulationsetupgivenabove,werstevaluatehoweachmodelbehaveswithvaryingBandwidthvalues.InFigure 2-3 ,TCPReno,LISS,ISS,MISSandJSarecomparedintermsoftheserverthroughput.Figure 2-3B showsthetotalnumberofpacketsacknowledgedbytheserver,i.e.,thetotalthroughputwithvaryingBandwidth,whereasFigure 2-3A showstheinitial5secondthroughput.Clearly,thereissignicantdifferenceintheinitial5secondthroughputasBandwidthincreases.Eventhoughthereisnotsomuchdifferenceofthetotalthroughput,itisvisiblethatasBandwidthreaches18Mpbs,MISSandJSthroughputbecomesslightlyworse.ThiscanbeattributabletotheinitialbursttransmissionofpacketsinMISSandJSwithhighercapacitylinks,evenwhentheytrytoreducetheimpactbypacketpacing. InFigure 2-3A ,LISS,ISS,MISSandJSallshowbetterperformancethanTCPRenointermsoftheinitial5secondthroughputwithcomparableperformanceofthetotalserverthroughput.Withalinkspeedof16Mbps,TCPRenosuccessfullydelivers 31

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BTotalthroughput. ServerthroughputwithvaryingDelayinhomogeneoustopology. 84545packetstoclients,while124719,136307,187868,and187678packetsaredeliveredbyLISS,ISS,MISS,andJSrespectively.Thisimprovementamountstomorethan100%forMISSandJSagainstTCPReno. Figure 2-4 showstheinitial5secondthroughputandthetotalthroughputwithvaryingDelay.ItiswellknownthatTCPthroughputdecreasesasRTTincreasesandFigure 2-4B showsthistendencyclearly.NoticethatLISS,ISS,MISS,andJSoutperformTCPRenointermsofthetotalthroughputasDelayincreaseseventhoughthetotalthroughputofJSapproachesthatofTCPRenoasDelayincreases.WithlargeDelay,theinitialcwndandssthreshvalueshavegreaterinuenceonthetotalthroughputofTCP.Theinitial5secondthroughputshowsbetterperformancewhenDelayisrelativelysmallforLISSandISScomparedtoTCPReno,whileMISSandJSshowmuchbetterperformanceachievingmorethan30timestheinitial5secondthroughputofTCPRenoinsomecases.ThisimpliesthattheinitialcwndvalueimpactstheinitialthroughputofTCPsignicantlywithlongdelaypaths. GoodperformanceofLISS,ISS,andMISScomparedtoTCPRenoatsmalldelayisprobablyduetoself-clockingofTCPReno.Self-clockinglimitsthegrowthofcwndduringtheslowstartphase.Forexample,duringveseconds,therecan 32

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BTotalthroughput. Serverthroughputwithvaryingconnectioninter-arrivaltimeinhomogeneoustopology(20Mbpslink). BTotalthroughput. Serverthroughputwithvaryingconnectioninter-arrivaltimeinhomogeneoustopology(10Mbpslink). be10self-clockingcyclesforaconnectionwith500msRTTwhiletherecanbe100self-clockingcyclesforaconnectionwith50msRTT.Thisimpliesthattheconnectionwith50msRTThas10timesmoreopportunitiestoincreaseitscongestionwindowsizewhileintheslowstartphase. Figure 2-5 showstheinitial5secondthroughputandthetotalthroughputwithvaryingaverageFTPconnectioninter-arrivaltimebetweentheserverandclients.Theinter-arrivaltimefollowstheexponentialdistribution.Theinitial5secondthroughputis 33

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Servernsecondthroughputinhomogeneoustopology. apparentlysuperiorwithLISSandISStoTCPReno,whilethatofMISSandJSisevenmoresuperior.ThetotalthroughputshowsthatLISSandISSperformslightlyworsethanTCPReno,whileMISSandJSperformevenworse.Whenthelinkcapacityishigher,largecwndandssthreshvaluesfornewTCPconnectionscancausepacketdropsintherouterwithasmallqueuesize,decreasingthetotalthroughput.Asevidence,inFigure 2-6 ,theBandwidthvalueissetto10Mbpsinsteadofthedefaultvalueof20Mbps.Here,thetotalbandwidthofLISS,ISS,MISSandJSiscomparableagainstTCPReno,whilethe5secondthroughputshowssignicantimprovement. Figure 2-7 showstheinitialnsecondthroughputwherenrangesfrom1to10.ItisobservablethatthethroughputincreasesmuchfasterforLISSandISSachieving50%higherthroughputthanTCPRenoatthreeseconds,whereasMISSandJSstartwithmorethan10timesofthroughputatonesecondcomparedtoTCPReno.Thisisattributabletothefactthatthesetwoalgorithmsdonotwastetimereachingsteadycongestionwindowsize. Inoursimulation,theconnectiondurationbetweentheserverandaclientfollowstheParetodistribution.ThesmallertheshapeparameteroftheParetodistribution,theheaviertailtheParetodistributionhas.ForFTPconnectionswithlongduration,moreaccuratecwndandssthreshvaluescanbeobtainedaslongconnectionstendtobein 34

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BTotalthroughput. ServerthroughputwithvaryingParetoshapeparameterinhomogeneoustopology. steadystate.InFigure 2-8 ,LISS,ISS,MISSandJSachievehigherinitial5secondthroughputthanTCPRenoastheParetoshapeparametergetssmaller.MISSandJSshowslightlyworsetotalthroughputthanTCPRenoduetotheiraggressivecwndincrementpolicy.Theshapeparametervalues,1.05and1.95areratherextreme,andconsideringthatletransferswouldtakeaheavy-taileddistribution[ 36 39 56 ],thedefaultparametervalueof1.35isjustied. Tosummarize,itisshownthatLISS,ISS,MISS,andJSoutperformTCPRenoinasmallhomogeneousnetwork.Especiallywhenthebandwidthishigherandthelinkdelayissmall,thesefourmodelsshowsignicantimprovementoverTCPRenofortheinitialnthroughput.Goodperformanceoffourmodelsisobtained,sincefairnessofTCPiswellpreservedinthehomogeneousenvironment.However,whentherouterisnotequippedwithenoughqueueingbuffer,packetdropscanoccur,especiallywithJS,resultingintheslightlyreducedtotalthroughput.Forexample,inFigure 2-5B ,thetotalthroughputachievedbyJSforallaverageinter-arrivaltimesagainstthatofTCPRenois98.1%. 35

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Randomtopologywith200nodes. commonaddressprexessimilartosubnetsintheInternet.Inadditiontohierarchicaladdressing,atransit-stubbasedrandomtopologygeneratorisused.Forthispurpose,GeorgiaTechInternetworkTopologyModels(GT-ITM)[ 10 ]ischosen.Thens-2packageprovidesafewsamplecongurationsofGT-ITMandweslightlymodifytwoofthesamplecongurations,onefor200nodesandtheotherfor600nodes.Themodicationonthecongurationincreasesthesub-domainconnectivitytoformatopologywherethenodesinasub-domainsharethecommonbottlenecklinks.NetworktopologiesgeneratedbythesecongurationsareshowninFigure 2-9 andFigure 2-10 TheGT-ITMtopologyformatisconvertedintothens-2codeformatforhierarchicaladdressing,usingatoolprovidedbythens-2webpage[ 22 ].Theconvertedns-2codeassignsarandomdelaytoeachlinkwhilebandwidthiscongurableonlyasasinglevalueforalllinks.Forsimulation,weassignaservernearcorerouters. 2-9 ,thebandwidthforalllinksis10MpbsbydefaultandthelifetimeofFTPconnectionsbetweentheserverandclientsfollowtheParetodistributionwithanaverageof100secondsandshapeparameterof 36

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Randomtopologywith600nodes. BTotalthroughput. Serverthroughputwithvaryingbandwidthin200-nodetopology. 37

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Figure 2-11 showstheinitial5secondthroughputandthetotalthroughputwithvaryinglinkbandwidthvalues.Asthebandwidthincreases,theinitial5secondthroughputvaluesofLISS,ISSandMISSincreasegraduallyasshowninFigure 2-11A .However,thetotalthroughputofMISSforallBandwidthvaluesis95.9%ofthatofTCPReno.JSshowssignicantlybetterperformanceofthe5secondthroughputthanTCPReno,whileitstotalthroughputforallBandwidthvaluesis93.8%ofthatofTCPReno. OnenoticeabletendencyobservedinFigure 2-11B isthatthetotalthroughputofMISSandJSgetsworseagainstTCPRenoasbandwidthincreases.OnereasonforthismaybethattheinitialovershootingpacketsofTCPconnectionsnegativelyimpactsthetotalthroughputcausingpacketdrops.Also,withthe200-nodetopology,theaveragedelayislargerthanthehomogenoustopology,whichincreasestheinitialburstofTCPcausingmorepacketdropsattheroutersevenwithpacketpacing.Inaddition,withheterogeneousnetworks,itisnoteasytoobtaingoodestimatesofcwndandssthresh,asTCPfairnessisnotwellmaintained. InFigure 2-11A ,theinitial5secondthroughputisgreaterforLISS,ISS,MISS,andJSthanforTCPReno.Aslargeinitial5secondthroughputimpliesreducedinitialdownloadtimeformultimediaobjectsorwebdocuments,userswillhavebetterexperiencewiththesefourmodelsthanTCPReno. InFigure 2-12 ,theinitialnsecondthroughputisshownasnrangesfrom1to10forthetopologywith200nodesinFigure 2-9 .ParametersofsimulationarethesameasinFigure 2-11 .MISSandJSachievehigherinitialnsecondthroughputforsmalln,astheystartwithlargecwndvalues.Incontrast,theinitialnsecondthroughputofLISSand 38

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Servernsecondthroughputin200-nodetopology. BTotalthroughput. Serverthroughputwithvaryingexponentialinter-arrivaltimein200-nodetopology. ISSstartswithsmallvalues.Obviously,aggressivebehaviortoincreasecwndrapidlyinMISSandJShelpstoachievehigherthroughputinitially.However,thisisnotwithoutcost,asthetotalthroughputofMISSis94.2%ofTCPReno,andthetotalthroughputofJSis95.7%ofTCPReno,whenthetotalthroughputforallBandwidthvaluesareadded. Figure 2-13 showstheinitial5secondthroughputandthetotalthroughputwithvaryingaverageconnectioninter-arrivaltimebetweentheserverandclients.Astheaverageinter-arrivaltimeofexponentialdistributionrangesfrom5to0.5,LISS,ISS,MISS,andJSshowincreasinggainoverTCPRenointermsoftheinitial5second 39

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BTotalthroughput. Serverthroughputwithvaryingbandwidthin600-nodetopology. throughput.Thisisreasonableastherearemoreconnectionswithcommonbottlenecklinks,socwndandssthreshvaluescanbeestimatedmoreaccurately.However,alargeinitialcwndvaluecausesovershootingofpackets,inducingpacketdropsattherouterwithsmallbuffersize.Forthisreason,MISSandJSshowpoortotalthroughputperformancewhentheaverageinter-arrivaltimeissmall. Sincethetopologywith200nodesinFigure 2-9 haslargeraveragedelaythanthehomogenousnetworkinFigure 2-2 ,aggressivegrowthofcwndforanewconnectioncouldbedetrimentaltoTCPstart-upperformance,whereasgoodestimatesofcwnd,ssthreshandpacketpacingarebenecial.Evenwithpacketpacing,asuddenburstofpacketstendstogeneratepacketdropsintherouterwithsmallqueueforthetopologywith200nodes,aslargeaveragedelayofthetopologytendstointroducelargeinitialcwndvalues. 2-10 ,thedefaultbandwidthforalllinksis10Mbps.Thenumberofpairsofnodesusedforcrosstrafcis100.Crosstrafcconnectionarrivalsfollowtheexponentialdistributionwithaverageofonesecond.FTPconnectionsbetweentheserverandclientsterminatewiththeaveragelifetime 40

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BTotalthroughput. Serverthroughputwithvaryingexponentialinter-arrivaltimein600-nodetopology. of100seconds.ThislifetimedurationfollowstheParetodistribution,wheretheshapeparameterofParetodistributionis1.35.Theaverageinter-arrivaltimeofconnectionsbetweentheserverandclientsis0.5secondsbydefault. Forvaryinglinkbandwidthvalues,Figure 2-14 illustratesTCPReno,LISS,ISS,MISSandJSintermsoftheinitial5secondthroughputandthetotalthroughput.InFigure 2-14A ,itisnotclearwhichoneperformsbetterintermsoftheinitial5secondthroughputamongLISS,ISSandTCPReno,whereasMISSandJSsignicantlyoutperformTCPReno.However,MISSandJSachievethisbysacricingthetotalthroughput. Asshownearlier,estimationofssthreshbecomesmoredifcultasthenetworksizegrows,sincefairnessofTCPishardertoachieveinlargeandheterogeneousnetworks.LISS,ISS,MISS,andJSshowbetterperformanceinthenetworkwith200nodesinFigure 2-9 thaninthenetworkwith600nodesinFigure 2-10 ,sincethetopologywith600nodehaslargeraveragedelay. Figure 2-15 showstheinitial5secondthroughputandthetotalthroughput,astheaverageinter-arrivaltimeofconnectionsbetweentheserverandclientsrangesfrom1to0.1seconds.LISSandISSperformbetterthanTCPRenoinbothcasesbutthegain 41

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Servernsecondthroughputin600-nodetopology. isnottooimpressive.MISSandJSoutperformothersintermsoftheinitial5secondthroughputbutshowslightlyworseperformanceintermsofthetotalthroughputastheaverageinter-arrivaltimedecreases. TheinitialnsecondthroughputofFigure 2-16 illustrateshoweachmodelperformsasnincreases.ThethroughputgainofLISSandISSinFigure 2-16 ismorenoticeablewithlargenforthetopologywith600nodes,whereasrelativelysmallnisenoughtoseethedifferenceinFigure 2-12 forthetopologywith200nodes.Thereasonthatittakeslargerntoobservethroughputgainincaseof600-nodetopologyisprobablythelongeraveragedelayresultinginaslowerself-clockingcycle.Ontheotherhand,MISSandJSdonotrelyonACKstoincreasecwndinitially.Consequently,theyshowgoodperformanceevenwithsmallnwithsignicantdecreaseintermsofthetotalthroughputduetotheinitialburstofpackets.ThethroughputgainofLISS,ISSagainstTCPRenoissignicantonlywhennislargeintermsoftheinitialnsecondthroughputwiththelargeaveragelinkdelay.Also,asthenetworksizegrows,fairnessofTCPbecomeshardertoachieveduetoheterogeneityoftheenvironment,andcwndandssthreshestimatestendtobeinaccurate.Usually,MISSandJSstartwithlargeinitialcwndvalueswithanetworkwithlargedelaybandwidthproduct.Asaconsequence,whentherouterqueue 42

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57 ].Thisisbasedontheassumptionthatthenetworkconditionsmightbesteadyatleastforseveralminutes[ 40 62 ].Thesameassumptioncanbeappliedtoconnectionsterminatedafewminutesearlier.Ifwecanndthebandwidthofrecentlyterminatedconnectionsofthesamesubnet,anestimateofanewconnectionbandwidthcanbeobtained.Buthowabouttheconnectionsterminatedmorethanafewminutesearlier?ToanswerthisquestionitisnecessarytomeasureextensiveInternettrafcdynamicsforlongdurationsthatisnotinthescopeofthisstudy. Anotherissuethatshouldbeconsideredisamethodtoidentifysubnetswithcommonbottlenecks.TheAutonomousSystem(AS)prextablefromBorderGatewayProtocol(BGP)canbeusedinlocatingwebclientclusters[ 28 ].IftheASprextableisnotavailable,Internettomographycanbeconsidered[ 13 17 ].However,manyprobepacketsarenecessarytogetagoodestimateusingthistechnique.FlowMate[ 61 ]showsthatitispossibletondconnectionswithsharedbottlenecklinksintheOSkerneleffectively.Forsimplicity,wemaytaketheprexofsubnetmask/24assumingthatmostsubnetshavethesubnetmaskof/24. 63 ],whilethelatterreliesonanetworkmonitortoestimatessthresh. EachmodelestimatesaninitialssthreshvalueofanewTCPconnection.Inaddition,MISStriestoestimateanon-intrusiveinitialcwndvaluetoreducetheimpactonthe 43

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Bywayofsimulation,theinitial5secondthroughputandthetotalthroughputofourschemesarecomparedagainstTCPReno.Thefastramp-upofcwnduptotheestimatedssthreshvaluehelpstoachievehigherthroughput,whentherouterisequippedwithreasonablequeuesizeinahomogeneousnetworkwherefairnessofTCPiseasiertoobserve.Incontrast,whenanetworkislargeandheterogeneous,thetotalthroughputofourschemestendstobelowerthanthatofTCPReno,asitbecomeshardertoestimategoodcwndandssthreshvalues.Moreimportantly,astheinitialcwndandssthreshvaluesarelargewithlargedelaybandwidthproductpaths,packetdropsaremorelikelytooccurinarouterwithasmallqueue.ItisalsoevidentthattheinitialTCPstart-upperformancedependsoncwndincrementpolicy.Eventhoughitwasnotshowninthesimulation,JSwithoutpacketpacingisprohibitiveasitgeneratesmassivepacketdropswithlargenetworks.Infact,JSgeneratessizeablepacketdropsevenwhenpacketpacingisengagedonthelargedelaybandwidthproductpath.However,itshouldbenotedthatpacketdropsaresignicantlyreducedifroutershavelargequeueingbuffersforthelargedelaybandwidthproductpaths,achievingalmostthesametotalthroughputofISSandLISS. Consequently,webelieveourschemescanworkwellwithinanISPequippedwithmultimediaorwebservers,wheretheaveragedelaybetweenclientsandserversissmallwithoutrequiringthatroutershavelargebuffers.Inpractice,ContentDistributionNetworks(CDN)likeAkamai[ 27 ]useasimilararchitecturebyplacingdedicated(cache)serversatstrategiclocationsnearbyclients.Insuchcases,MISScanprovidecontenttouserswithmuchlessdelaythanTCPRenowithoutsacricingthetotalthroughput. Insituationswheresubscriberswithlargeandheterogeneousnetworksshouldbeconsidered,webelieveLISSisagoodchoice.LISSdoesnotrequiremodicationoftheTCPalgorithmandimprovestheTCPstart-upperformanceevenwithrouterswith 44

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45

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45 53 ],theTCPreceiversendsbacktotheTCPsenderanacknowledgement(ACK)packetforeveryin-orderpackettheTCPreceiverreceivesfromtheTCPsender.EventhoughACKsaresmallinsize,theyarestillpacketsandcannotbeignoredifwetakeintoaccountthatTCPisthedominantInternetprotocol.ToreducetheloadonthenetworkgeneratedbyACKs,RFC1122[ 8 ]introducedthedelayedacknowledgementalgorithm. Whendelayedacknowledgementisenabled,theTCPreceiverdoesnotacknowledgeeverypacket.Instead,theTCPreceiverstartsadelaytimerwhenitreceivesanin-orderpacketifthedelaytimerisnotyetrunning.Thedelaytimerrunsforaspecicdurationlessthanorequalto500ms.Whennopacketarrivesbeforethedelaytimerexpires,thenthepacketisacknowledged.IfthenextpacketarrivesattheTCPreceiverwhilethedelaytimerisrunning,thenewlyarrivedpacketisacknowledged,implicitlyacknowledgingthepreviousone.WhentheTCPreceiverreceivesanout-of-orderpacket,itshouldacknowledgethepacketimmediatelyregardlessofdelaytimerstate. Asaresult,ifthereisaconstantfeedofincomingpackets,theTCPreceiverwouldacknowledgeeverytwopackets,reducingtheACKtrafcalmostbyhalf.Thereductionofthenumberofacknowledgementsmaycauseslowgrowthofcongestionwindowsize(cwnd)andlowerbandwidth.However,Johnson[ 25 ]ndsthatdelayedacknowledgementimprovesbulkdatatransferperformanceincertainsituations. Earlier,Paxson[ 41 ]reportedthatvariantsofUnixoperatingsystemincludingearlyversionsofLinuxsupporteddelayedacknowledgement.Now,MicrosofthasimplementeddelayedacknowledgementfordesktopWindowsproducts[ 37 ]andmostcurrentLinuxdistributionssupportdelayedacknowledgement.Consideringthatthese 46

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WhiledelayedacknowledgementhelpsinreducingthenetworkloadbycuttingdownACKtrafc,itmaynotbedesirableforslowstart.Duringslowstart,theTCPsenderincreasescwndbyoneforeveryACK.Whenpacketsaretransmittedconstantly,delayedacknowledgementreducesthenumberofACKsbyhalf,losingopportunitiestoincreasecwnd.Tobemoreprecise,letWabetheadvertisedwindowsizeofTCPreceiverandWsthecongestionwindowsizewhentheslowstartthreshold(ssthresh)isreached.Asmentionedin[ 3 ],toreachssthresh,slowstartwithoutdelayedacknowledgementtakesRlog2W, Toimprovethisinefciency,Allman[ 3 ]showshowtoimproveinitialslowstartperformancebybytecounting.TheauthorsuggeststheLimitedByteCounting(LBC)algorithm.WithLBCenabled,theTCPsenderincreasescwndbytwoinsteadofone,whenthelatestACKisforthepacketmorethanonepacketaheadofthelastacknowledgedpacket. Withthisimprovement,however,LBCbecomesratheraggressive.Tobespecic,assumethatanACKarrivesattheTCPsenderandtheACKcorrespondstoasequencenumbergreaterthanthelastacknowledgedsequencenumberbytwo,thencwndisincreasedbytwo.Inaddition,asthearrivaloftheACKacknowledgestwopackets,twomorepacketscanbetransmitted.Inotherwords,arrivalofoneACKletstheTCPsendertransmitfourpackets.Forslowstartwithoutdelayedacknowledgement,each 47

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ForthesakeofsimplerargumentbutwithoutlosingthegeneralprincipleofTCP,weassumethattheTCPsenderassignssequencenumbersintermsofpacketsratherthanintermsofbytesasinrealimplementations.Also,aduplicateACKcorrespondstothepacketsequencenumberofthelastsuccessfullydeliveredoracknowledgedpacketandwhoseACKisobservedagainbytheTCPsender.WhentheTCPconnectionisestablishedtheinitialpacketsequencenumberbeginswithzeroinsteadofarandomsequencenumber. Withtheseassumptions,theLBCalgorithmcanbeimplementedeasilyintheTCPsenderwhenittriestoincreasecwndasinthefollowingpseudocode,wherehighest ackrepresentsthelatestpacketsequencenumberalreadyacknowledged,andackisthesequencenumberthatthenewlyarrivingACKisacknowledging. ack:thelatestpacketsequencenumberacknowledgedbytheTCPsenderg fack:thesequencenumberthattheTCPreceiverisacknowledgingg fcwnd:thecongestionwindowsizeoftheTCPsenderg ack=1then ack>=2then 4 ],itisnotedthatLBCdisplaysratheraggressivegrowthofcwndduringpacketlossrecoveryofslowstart,andtoamelioratethisproblem,bytecountingterminatesafterapacketdropinslowstart.Toaccountforthisidea,bytecountingisnotengagedafterapacketdropwhenwesimulateLBClater. 48

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Toachievealmostthesameperformanceasslowstartwithoutdelayedacknowledgement,wenoticethattheTCPreceiverisrequiredtosendbackanACKforeachout-of-orderpacketimmediately.Then,whentheTCPsendertransmitsinvertedpacketpairs,theTCPreceiverrespondsimmediatelyforeveryincomingpacketsinceinvertedpacketsareconsideredasout-of-orderpackets.Forinstance,ifaseriesofpacketpairswithsequencenumbers,n+1,n,n+3,n+2,...forapositiveintegernaresenttotheTCPreceiver,theTCPreceiversendsbackanACKforeverypacketitreceiveswithoutdelay.InvertedpacketpairsinaTCPconnectionareusedtomeasureinter-packetgapsinPerssonetal.[ 44 ].Here,weapplythistechniquenottomeasurepacketpairgap,buttocausetheTCPreceivertogenerateanACKperpacketduringtheslowstartphaseofTCP.OurslowstartmechanismreliesonthisbehaviorandwillbecalledSlowStartwithInvertedPacketPairs(SSIPP). Forthepurposeofillustration,assumethattheTCPsenderdenesavariablet seqtokeeptrackofnextpacketsequencenumbertobetransmitted,andalsodenesalinkedlistiv dup packetstoaddorremovepacketsequencenumbersinthelist.Also,assumethatthefunctionoutput()takesapacketsequencenumberasanargumentandtransmitsthepacketcorrespondingtothepacketsequencenumber. WhentheTCPsenderisreadytosendpackets,itinvokesthefunctioniv output()asshowninAlgorithm 1 .Theniv output()checksifthepackettobetransmittedistheinitialpacket.Rememberthattheinitialsequencenumberoft seqnostartsfromzero.Iftheinitialsequencenumberisrequestedtobesent,iv output()transmitstheinitialpacketandincreaset seqnobyone. 49

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seqnoisoddandmorethanonepacketisreadytobetransmitted,thepacketwiththesequencenumbert seqno+1istransmitted.Asthenextin-orderpacketsequencenumberist seqno,thepacketjusttransmittedisout-of-order.Next,t seqnoissavediniv seqno.Notethein-orderpacketsequencenumberisnowiniv seqno.Then,t seqno1isaddedtothelistiv dup packetsandt seqnoisincreasedbyone.Noticethatthevaluesiniv dup packetsrepresentsequencenumberswhichtheTCPsenderreceivesasduplicateACKscorrespondingtoout-of-orderpacketstransmittedwhent seqnoisodd.Whent seqnoisevenandiv seqno+1=t seqno,thepacketwiththesequencenumberiv seqnoistransmitted.Notethativ seqnohasthepreviousvalueoft seqnowhent seqnowasodd.Therefore,twoconsecutiveinvocationsofiv output()resultinaninvertedpacketpairtransmission. Finally,ifnoneoftheaboveconditionsaremet,andapacketisreadytobetransmittedwiththesequencenumbert seqno,thenthepacketwiththesequencenumbert seqnoistransmittedandt seqnoisincrementedbyone.Asiv output()iscalledduringslowstartonly,inversionofpacketsoccursuntilssthreshisreachedorwhenapacketisdropped.Careshouldbetaken,eventhoughslowstartterminates.Ifthepacketofsequencenumberiv seqnoisnotyettransmitted,itshouldbetransmittedevenafterslowstartterminates.Then,iv seqnoisresetandpacketsaresentinorderafterthat. ToillustratewhathappensintheTCPreceiver,assumethattheTCPsendertransmittedpacketswithsequencenumbersn+1andnconsecutively.Then,theTCPreceiverreturnsaduplicateACKforthesequencenumbern1,whenn1isthelastsequencenumberthatthereceiverhassuccessfullyreceivedcumulatively.Next,whentheTCPreceiverreceivesthepacketwiththesequencenumbern,itreturnsanACKforthesequencenumbern+1asn+1becomesthesuccessfullyreceivedsequencenumberaccumulatively.NotethatbothACKsaresentimmediatelyastheyareforout-of-orderpackets. 50

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output() seqno:invertedpacketsequencenumbertobetransmittedatthenextinvocationofiv output()g ift seqno=0then output(t seqno) seqnot seqno+1 seqnoisoddandmorethanonepacketisavailablethen seqnot seqno seqno+1) addt seqno1toiv dup packets t seqnot seqno+1 seqnoisevenandiv seqno+1=t seqnothen output(iv seqno) seqnot seqno+1 output(t seqno) seqnot seqno+1 endif dup packets,thenitcorrespondstotherstpacketofaninvertedpacketpairandshouldnotbecountedasavalidduplicatepacketsequencenumber.Instead,weincreasecwndbyonefortheduplicateACKiniv dup packets.Afterincreasingcwndbyone,theduplicateACKsequencenumberisremovedfromiv dup packets.FurtherduplicateACKsofthesamesequencenumberaretreatedasrealduplicateACKs. Tobemorespecic,inthefollowingpseudocode,ifack=highest ack,ackisaduplicateACK.Ifackisforthepacketsequencenumbern1anditisfoundiniv dup packets,thentheTCPsenderprobablyhassentaninvertedpacketpairwithpacketsequencenumbersn+1andn.Then,ackcanbeusedtoincreasecwndbyone,anditisnottreatedasanactualduplicateACK. WhentheTCPsenderreceivesanactualduplicateACK,thesenderstillneedstotransmitapacket,unlessthreeduplicatepacketsarereceived.Thefunction 51

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ackandackisiniv dup packetsthen dup packets cwndcwnd+1 iv send one()isinvokedtotransmitonepacketiftheTCPreceiverreceivesaduplicatedACKnotfoundiniv dup packetsasshowninAlgorithm 2 .FortheactualduplicateACK,westopinvertingpacketsexceptforonesalreadysentout-of-order.Forthisreason,iv send one()doesnothavetotestift seqnoisodd. send one() seqnoisevenandiv seqno+1=t seqnothen output(iv seqno) resetiv seqno output(t seqno) seqnot seqno+1 22 ]version2.28.ThetopologyforsimulationshowninFigure 3-1 isthesameastheoneusedinAllman[ 3 ].Therouterqueuebuffersizeis50packets.TheTCPadvertisedwindowsizeandthessthreshvalueare20.TheTCPreceiverdelaytimerissettoexpirein100ms.Thepacketsizeis1000bytesexcluding40-byteTCPheaderinns-2.LBCandSSIPPareimplementedonTCPRenoAgentinns-2.Whensimulationresultsareshowningures,thelabelDelAckrepresentsTCPRenoslowstartwithdelayedacknowledgement,whilethelabelSSIPPisfor 52

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Simulationtopology. SSIPPwithdelayedacknowledgementandthelabelLBCrefersLBCwithdelayedacknowledgement. ThroughputforthreeslowstartmodelsarecomparedinFigure 3-2 .xaxisshowsthenumberofpacketstransmittedforeachFTPtransferandyaxisrepresentsthroughputobservedbythesender.ObviouslySSIPPshowsthebestperformancefollowedbyLBCandslowstartwithdelayedacknowledgement. InFigure 3-2 ,asthenumberofpacketsincreases,throughputofeachFTPtransferincreases.Thisisreasonablebecausewhenthereisenoughlinkcapacityandqueueingbufferintherouter,throughputshouldincreaseascwndgrows.Interestingly,throughput 53

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SingleFTPtransferthroughput. inFigure 3-2 increasepiecewiselinearlyasthenumberofpacketsincreases.ThispiecewiselineargrowthisnotobservedinAllman[ 3 ].Webelieveeventhoughitisnotclearlystatedhowmeasurementisdoneintheauthor'sstudy,thedifferenceisprobablyduetothedifferenceinmeasurementmethod.Forexample,ifthroughputismeasuredattheTCPreceiver,thebandwidthgrowthwillbesmoother.Inourmeasurement,ifthelastpackettransmittedisdelayedintheTCPreceiver,itextendsthetransfercompletiontimeby100msattheTCPsender.Ontheotherhand,ifthelastpackettransmittedisout-of-order,thentheTCPreceivergeneratesanACKimmediatelywithoutextendingthetransfercompletiontimeobservedattheTCPsender.Therefore,whenthenumberofpacketsareeven,bandwidthishigherthansomeofthelargerbutoddnumberedtransfersizes. 3-1 generatesmultipleinstancesofFTPconnections.Eachtransfersizeintermsofthenumberofpacketsispickedupintheinterval[5,100]usingtheuniformrandomdistribution.EachFTPtransferstarttimeintermsofsecondsischosenintheinterval[0,100]withtheuniformrandomdistribution.ThenumberofFTPconnectionsvariesfrom50to500with50astheinterval,throughoutthesimulation. 54

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ThroughputofeachFTPtransferiscalculatedasBi=Ail ThesamplemeanofqueuesizeismeasuredforthelinkfromthenodeRtothenodeTinFigure 3-1 ,wherethesamplingrateis102seconds.Goodputisthenumberofpacketsdeparteddividedbythenumberofpacketsarrivedatthequeueuntilthesimulationterminates. Twocommonqueuemanagementalgorithmsareconsidered,namely,drop-tailandRandomEarlyDrop(RED).OursimulationusestheautomaticREDparametersettingsasimplementedinns-2,whileAllman[ 3 ]usesspecicparameters. First,throughputismeasuredasshowninFigure 3-3 withadrop-tailqueueattherouter.SSIPPshowsthebestperformancefollowedbyLBCandslowstartwithdelayedacknowledgementforallscenarios.Here,itisalsoworthmentioningthatwhenSSIPPrunswiththeTCPreceiverwithdelayedacknowledgementenabled,itisalmostidenticaltoslowstartwithoutdelayedacknowledgementintermsofthroughput,aswellasgoodputandaveragequeuesize.ThisimpliesSSIPP'smodicationofTCPdoesnotdegradeperformancecomparedtotheoriginalTCP. 55

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ThroughputofmultipleFTPtransferswithadrop-tailqueue. Figure3-4. GoodputofmultipleFTPtransferswithadrop-tailqueue. Figure3-5. AveragequeuesizeofmultipleFTPtransferswithadrop-tailqueue. 56

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3-4 showsthegoodputoftransmittedpacketsamongthethreemodelswithadrop-tailqueue.Notethattheverticalscaledoesnotstartatzero,inordertomagnifythedifferences,sincetheseareveryslight.Slowstartwithdelayedacknowledgementshowsslightlybettergoodput,eventhoughitshowedpoorperformanceintermsofthroughput.Thisisduetoslowerincreaserateofcwnd.SSIPPshowsconsistentlybetterperformancethanLBCintermsofgoodputandisalmostidenticalatcongestedstateswithslowstartwithdelayedacknowledgement. Figure 3-5 illustratestheaveragequeuesizeformultipleFTPtransferswithadrop-tailqueue.ForsmallnumbersofFTPows,slowstartwithdelayedacknowledgementshowsthebestperformancefollowedbySSIPPandLBC.ForlargenumbersofFTPows,slowstartwithdelayedacknowledgementshowsasteeperincreaseinaveragequeuesize.Infact,theaveragequeuesizeforlargenumbersofFTPowsuctuatesrathersharplyinoursimulation.ThisobservationisdifferentfromAllman[ 3 ],whereaveragequeuesizechangesaresmootherthanourresult.Webelievethisdifferencecouldbeattributabletomeasurementmethodology. Figure 3-6 showsthroughputofthreemodels,whentherouterisenabledwithREDqueuemanagement.ThebestthroughputisobtainedwithSSIPP,followedbyLBCandslowstartwithdelayedacknowledgement.Forallthreemodels,throughputwithREDqueueisworsethanthatwithdrop-tailqueue.ForgoodputshowninFigure 3-7 ,slowstartwithdelayedacknowledgementshowsthebestperformance,whileSSIPPandLBCshowsimilarperformance.GoodputwithREDqueueisalsoworsethanthatwithdrop-tailqueue.Finally,Figure 3-8 showstheaveragequeuesizeofeachmodel.Slowstartwithdelayedacknowledgementshowsthebestperformanceinmostcases,followedbySSIPPandLBC.TheaveragequeuesizewithREDqueueissignicantlysmallerthanthatwithdrop-tailqueue.Howeverthiscomesatthepriceofdegradedperformanceofthroughputandgoodputcomparedtothedrop-tailqueuescenarios. 57

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ThroughputofmultipleFTPtransferswithanREDqueue. Figure3-7. GoodputofmultipleFTPtransferswithanREDqueue. Figure3-8. AveragequeuesizeofmultipleFTPtransferswithanREDqueue. 58

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OnedisadvantageofusingourschemeversusLBCistheextraduplicateACKsgeneratedbyinvertedpacketpairs.However,consideringthatslowstartusuallyisshortinduration,andtheperformancegainoutweighstheoverhead,ouralgorithmisabetteralternativetoLBC. 59

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2 ,wehaveseenthatgoodssthreshestimatesplayanimportantroleinachievinggoodstart-upperformanceofTCP.AstheschemesintroducedinChapter 2 assumethattheinformationofconnectionssharingthecommonbottlenecklinksisavailable,theirapplicationisratherlimited.Inthischapter,weintroduceaschemetoestimatessthresh,evenwhentheinformationofotherconnectionsisnotaccessible,basedonpacketpairmeasurements.Infact,toestimatessthresh,manyalgorithmshavebeenproposed[ 19 21 59 ],butnoneofthemissatisfactory,astheyhaveperformanceproblemsortechnicalproblems.Forexample,whendelayedacknowledgementisenabledattheTCPreceiver,theTCPsenderreceivesoneACKforeveryotherpacketthatthesenderhastransmitted.Asaresult,ACKscannotbeusedtomeasureoutputgapsatthesender.Toworkaroundthisdifculty,weadopttheinvertedpacketpairmeasurementmethodintroducedinPerssonetal.[ 44 ]forslowstart. Indeed,therehavebeenconsiderableresearcheffortsinestimatinglinkcapacityandend-to-endavailablebandwidth[ 14 24 35 52 ].Amongthese,weareespeciallyinterestedinestimatingend-to-endavailablebandwidthwithasinglebottleneckhoporrouter,usingpacketpairsasshowninFigure 4-1 .Inthegure,therearetwoinputsources,onefromthesenderofpacketpairorprobinghostandtheotherfromthecrosstrafcsource.Theprobinghostsendspacketsinpairswithtemporaldistancetermedasgap.Thegapbeforeapacketpairenterstherouterisittheinputgapandthegapafterthepacketpairexitstherouteristheoutputgap.Theoutputgapisusedinterchangeablywiththetimeaveragedoutputgap,ifitisclearfromthecontext.Therouterisequippedwiththequeueorbuffermemory.Notethat,inpractice,whilethesendercanmeasuretheinputgapaccurately,itisonlyabletoapproximatetheoutput 60

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Singlerouterwithcrosstrafcinputandpacketpairinput. gapbymeasuringthetimebetweentheacknowledgementsofthepacketpairitreceivesfromthereceiver. Forasinglehopbottleneckmodel,ithasbeenshownanalyticallythatavailablebandwidthcanbeaccuratelyestimatedusingpacketpairsinKangetal.[ 48 ],whereavailablebandwidthisdenedastheresiduebandwidthofbottlenecklinkcapacityoccupiedbycrosstrafc.However,theapplicationoftheirestimationmethodislimitedastheirmethodassumes,foraccurateestimation,thattheprobinghostcansendpacketsatahigherratethantherouterservicerate.Obviously,therearesituationsthatthesenderhaslowerpackettransmissionratethantherouterservicerate. Toberealistic,itshouldbepossibletoestimateavailablebandwidthwithpacketpairseveniftheprobinghosthasalimitedpackettransmissionrate.However,iftheprobinghosthasalowertransmissionratethantherouterservicerate,theoutputgapofapacketpairmayincludetherouteridletimeaswellasthecrosstrafcasdescribedin 61

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31 ],Machirajuetal.[ 33 ],andSharmaetal.[ 51 ].Furthermore,whentherearemultiplebottlenecksonthepathbetweenthesenderandthereceiverofpacketpairs,itbecomesevenmoredifculttointerpretwhattheoutputgaprepresentsasanalyzedinLiuetal.[ 32 ].Consequently,itisnoteasytoestimateavailablebandwidthaccuratelywithapacketpairmethod,inthepresenceofrouteridletimeintheoutputgap. Forthisreason,wedonotattempttomeasureexactavailablebandwidth.Instead,wedeneanapproximatelinearrelationshipbetweentheinputgapandtheoutputgapofapacketpairandthenstudyhowthislinearitycanbeusedinestimatingapproximateend-to-endavailablebandwidth.Then,bywayoftheapproximateend-to-endavailablebandwidth,weexaminehowtheTCPslowstartalgorithmcanbeimproved. InTCPReno[ 53 ],slowstartincreasesthecongestionwindow(cwnd)exponentiallyuntiltheslowstartthreshold(ssthresh)isreached,withself-clockingonacknowledgement(ACK)packets.Eventhoughtheperformanceofslowstartlargelydependsonssthresh,usuallytheoptimalvalueisnotknownwhenaTCPconnectionisestablished.Therefore,itisbenecialtoestimateanssthreshvaluelargeenoughthatwillnotcausepacketdropsduringslowstart. 48 ]andLiuetal.[ 31 ],exactlinearityisobservableonlyinlimitedenvironments,e.g.,whenPoissonArrivalsSeeTimeAverage(PASTA)[ 60 ]samplingisused.Ingeneral,exactlinearityisnotobservable,astheidletimeoftheroutertendstobecapturedintheoutputgap.Nevertheless,westillcanndapproximatelinearitybetweeninputgapsandoutputgapsandthisapproximatelinearitycanleadustoestimateapproximateend-to-endavailablebandwidth. 62

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<1,whereistheinputarrivalrateandistheservicerateofthequeue. Itisassumedthattheprobinghostcancontroltheinputpacketpairgap,whilethereceiverofapacketpaircanmeasuretheoutputpacketpairgap.Morespecically,iftiandti+1arepacketarrivaltimesoftherstandthesecondpacketatthequeue,theinputgapisti+1ti.Likewise,ifcorrespondingsiandsi+1arepacketdeparturetimesoftherstandthesecondpacketfromthequeue,theoutputgapbecomessi+1si.Toavoidatechnicalproblem,whenapacketfromcrosstrafcandapacketfromapacketpairarriveattheroutersimultaneously,assumethatthepacketfromthepacketpairenterstherouterrst.Forthemoment,assumethatthepacketsizeofpacketpairsiszero. Tobeginouranalysis,letX(t)bethenumberofpacketarrivalsattherouterbytimet0.Assumethenumberofpacketarrivalsin[t,t+)fort0and0<<1beA(t)=X(t+)X(t)<1. Then,whenthepacketsizeofpacketpairiszero,denetheidletimeduringtheinterval[t,t+)asI(t)=Zt+tI()d.

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4-2 representthesemarkers,withthemarkerontheleftinthegurerepresentingtherstpacketofthepacketpairarrivalattimet,andtheoneontherightarrivingattimet+isthesecondpacketmarker.TheheightofthequeueattisH(t)=3.Duringthetimeinterval[t,t+1),onepacketofcrosstrafcarrivesandbytimet+3,fourmorepacketsarrive.Ifnomorepacketsarriveuntilt+8,thequeuebecomesemptyatt+8andwedenotethistimeasS(t).AstherightarrowontherightofFigure 4-2 shows,thereisonepacketinthequeueatthearrivalofsecondpacketattimet+andthiscanberepresentedasH(t+)=1. Figure 4-3 showsthetimewhenpacketsareservedbytherouterfromH(t)+tuntilt++1.H(t)+tiswhentherstmarkerofpacketpairgetstransmitted,andt++H(t+)=t++1iswhenthesecondpacketmarkerdepartsfromthequeue.InFigure 4-3 ,thesetimepointsaremarkedbytheup-arrows(").AtS(t),thequeuebecomesempty.Therouteralternatesidleandbusystatessincethen.Notethatthedifferenceofsecondmarkerdeparturetimeandrstmarkertransmissiontime,(t++H(t+))(H(t)+t),istheoutputgap,andthecorrespondinginputgapisthedifferenceofsecondmarkerarrivaltimeandtherstmarkerarrivaltime,(t+)t. 64

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Singlerouterqueuechangeovertime. Packetoutputfromtherouterovertime. ItisevidentfromFigure 4-3 ,theexactcrosstrafcpacketsarecapturedin[H(t)+t,S(t)),withouttherouteridletime.NotethatH(t)(S(t)t),hence,iftheinputgapislessthanH(t),theexactcrosstrafciscapturedintheoutputgap.Forexample,ifinFigure 4-2 weretwo,byt+2,thesecondpacketmarkerwouldarriveontopoftwopacketsofcrosstrafc.Theoutputgapwillbe(H(t)+t+2)(H(t)+t). 31 ]showsthat 65

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Also,byLemma5inLiuetal.[ 31 ],itcanbeinferredthatlimt!11 4-3 ,whatiscapturedintheoutputgapfortheinputgapinterval[t,t+)isA(t)+I(t).Thisoutputgapisequivalentto(t++H(t+))(t+H(t)),if<.Hence,thetimeaverageoftheoutputgapwouldbelimt!11 4 andEquation 4 arevalidforany.Then,foranitepositivek,wehavelimt!11 tZt0D0()d=limt!11 Equation 4 showsthatthetimeaverageofoutputgapD0k(t)fortheinputgapkisktimesofD0(t)forthecorrespondinginputgap. Inordertoobservethislinearrelationshipbypacketpairsamples,thePASTAtheoremisapplicable.Initially,inWolff[ 60 ],thePASTAtheoremisonlyconsideredfor 66

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34 ].TwoconditionsinordertoapplythePASTAtheoremareLackofAnticipationAssumption(LAA)andtheconvergenceoftimeaverageoftheobservedprocess.AsfA(t)gandfI(t)ghaveconvergenttimeaverages,fD0(t)galsohastheconvergenttimeaverage.Ifzero-sizedpacketpairsarriveattherouterindependentoffX(t)g,itispossibletoobtainthetimeaverageoffD0(t)g. AsthePASTAtheoremstatesthattheaverageofPoissonsamplesbecomesthetimeaverageofthesampledprocessinthelimit,wehavelimt!11 4 ,wehavelimN!1k NNXi=0D0(ti)=limM!11 However,thisresultisnotimpressivesinceonlytrivialinformationcanbeobtainedastheaverageoutputgapwillbethesameastheinputgap.Probablytheonlyinformationofinterestcanbewhen>,wherethetimeaverageoftheoutputgapwillbegreaterthan.Fortunately,ifweincreasethepacketsizeofprobingpackets,moreinformationisobtainedaswillbeillustratedshortly. 31 ].Forthemoment,assumethatweusealowenoughsamplingratetobeabletoignorethe 67

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Forthefollowinganalysis,rememberthatfI(t)gisfortheidletimewhentherearenoprobingpackets.Then,ifaprobingpacketpairwithsizeentersthequeueattimetwiththeinputgap,theoutputgapwillbe8>><>>:A(t)+I(t)ifI(t),A(t)+I(t)+(I(t))ifI(t)<. If,thesecondpacketofthepacketpairarrivesatthequeuebeforetherstonedeparts.Inthiscase,A(t)+isalwayscapturedastheoutputgapfortheinputgapinterval[t,t+),andasKangetal.[ 48 ]analyze,theavailablebandwidthcanbedeterminedusingthelinearityoftheinputgapandtheoutputgap. When>,theoutputgapisdependentonthedistributionofI(t).However,asthedistributionofI(t)isnotknowningeneral,wetakeaqualitativeapproachtodescribetherelationshipoftheinputgapandtheoutputgap.Assumethatisxed.Then,ifismuchsmallerthan,ortherouterservicerateishigh,theoutputgapissimilartothecaseofzero-sizedprobepackets.Inotherwords,theoutputgapwillbenearlythesameastheinputgapandthiscanbeinterpretedtomeanthattheprobingpacketsarenotcausingcongestionattherouter,oreveniftheyare,theimpactontherouterwouldbenegligiblysmall.Eventhoughisnotsmall,ifPfI(t)giscloseto1ortherouterhaslittleload,theinputgapandtheoutputgapwouldbealmostthesame. 68

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IfPfI(t)
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Outputgaplessthaninputgap. Withtheintroductionof-sizedprobingpacketfor>0,therelationshipnolongerholds.Instead,thefollowinginequalitycanbeobserved:limN!11 4-1 .Morespecically,inFigure 4-4 ,packetsinCrossTrafcandpacketpairsinPacketPairsarrivesattherouter,andthecorrespondingoutputfromtherouterisshownasOutputfromQueue.Theinputgapsizeisfortwopacketpairs.TherstpacketpairiscomposedofP1andP2,andthesecondpacketpairconsistsofP3andP4.Betweenthesetwopacketpairsistheinterpacketpairgap.AssumingthatthequeueisemptywhenP1arrives,the 70

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4-4 ,D1=,however,D2<.ThecompressionofD2comparedtoisduetothequeuelengthP3discovers.ItishigherthanthequeuelengthwhenP1arrives.Thisobservationimplieswhenissmall,itispossibletoseethattheaverageoutputgapislessthantheinputgap. Packetpairsalsocanbeusedforestimatinglinkcapacity.IftheprobinghostOScanschedulepacketsfasterthanthetransmissionrateoftheconnectedlink,thelinkcapacitycanbeestimatedasfollows.First,assumethattheminimumgapwiththelinkisnfortheprobingpacketsize>0.Let0=0<1<2<...
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When>0,weusuallyhave wherexminx10.Thedifferencebetweenxandyissmallifissmall,ortherouterservicerateishigh.Obviously,whenissmall,thechanceof 72

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Onceanappropriateischosen,needstobefound.Insteadoftryingtoobtaintheexact,asequenceofsamplepoints(xi,yi)arepartitionedintosubsequencesindexedas(xi,k,yi,k)tondavaluenear,wherexi,k=xi,lfor1k,lniandniisthenumberofsamplepointsinthepartitionedsubsequence.Alsoxi,1
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22 ]version2.28isused.TheUDPAgentofns-2ismodiedtogeneratepacketpairswithsequencenumbersandtimestamps.AlsoamodiedUDPAgentgeneratesanACKforeachpacketofapacketpairimmediately.TheUDPpacketsizeofprobingpacketsis1000bytes.However,otherUDPtrafcandTCPtrafcusethedefaultpacketsizesofns-2.CBRcrosstrafcandParetocrosstrafcgeneratorsareprovidedinns-2.APoissoncrosstrafcagentisimplementedandaddedinns-2basedonPentikousis[ 43 ].Therouterparametersusedaredefaultvaluesofns-2unlessmentionedotherwise,whilethequeuemanagementalgorithmisdrop-tail.Thedefaultrouterqueuesizeis50packets.Themeantimeintervalbetweenpacketpairsisonesecondandeachsimulationruns1000seconds.Forarangeofinputgaps,packetpairsaregeneratedandcorrespondingACKsaremeasuredtoobtainoutputgapsignoringdroppedpackets.Outputgapsareaveragedasstatisticalmean.Notethat1Kis103inns-2parlance. WhenPASTAsamplingisconsidered,thetimeintervalbetweenpacketpairsmaybetoocloseandpacketpairsmayoverlap.Inthissituation,thesecondpacketpairisscheduledrightaftertherstpair.ThereforeourPASTAsamplingisnotstrictlyPASTA. 4-5 ,adumbbelltopologyisshown.Inthegure,nodeslabeledwithxsarecrosstrafcsenderswhilenodeslabeledwithxcarereceivers.Thenumberofcrosstrafcsendersandcorrespondingreceiversisacongurableparameterandweassumethatthenumberofcrosstrafcsourcesreferstothenumberofxsnodes.Routersarelabeledwithr1andr2.Thepacketpairsenderislabeledwithsanditscorrespondingreceiverwithc.Thelinkbetweenr1andr2has1Mbpscapacitywith100msdelay.Allotherlinksareequippedwith1Mbpscapacityand10msdelay. 74

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Dumbbelltopologyforpacketpairmeasurements. First,onesourceofCBRcrosstrafcwith250Kbpsisconsidered.InFigure 4-6 ,xaxisrepresentstheinputgapofpacketpairwhileyaxisrepresentsthemeanoutputgapvaluesofcorrespondinginputgap.InputgapsandoutputgapsformtheinputgapandoutputgapgraphlabeledwithCBRinFigure 4-6 .Thelinelabeledwithy=xisforreference,whereinputgapsandcorrespondingoutputgapsareidentical.Notethatinputgapvalues0.004secondsand0.008secondshavealmostthesameaverageoutputgapvaluesandformahorizontalline.Astheprobinghostsisconnectedtothelinkwith1Mbpscapacity,itcansenda1000bytepacketper0.008secondsatmaximum.Therefore,evenifpacketsarescheduledwiththetransmissionintervalof0.004seconds,theyaretransmittedwiththeintervalof0.008seconds.Observethattheinputgapandtheoutputgapmeetsy=xat0.012secondsorearlier.Thisimpliesthatpacketswith1000bytesinsizecanbesent,atleast,withthetransmissionintervalof0.012seconds,equivalentof8000=0.012667Kbpswithoutcongestingtherouter. 75

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Inputgapsandmeanoutputgapswith1sourceofCBRcrosstrafcindumbbelltopology. Alsonotethattheoutputgapfortheinputgapvalueof0.04secondsislessthan0.04seconds.Thismeansthattheoutputgapisslightlycompressedfromtheinputgapbecauseofthesamplingrate. Next,twosourcesofCBRcrosstrafc,eachonewithtransmissionrate250Kbps,areconsideredinFigure 4-7 .Theinputgapandoutputgapgraphisstraightandstartstomeety=xat0.016seconds,equivalentof8000/0.016=500Kbpsintermsofbandwidth.Notethatbetweeninputgaps0.008secondsand0.016seconds,thereisastraightlinesegment. Thecaseforthreesourcesof250KbpsCBRcrosstrafcisshowninFigure 4-8 .Theinputgapsstartingfrom0.008secondsuntil0.032secondsformastraightlineuntilitmeetsy=x.Attheinputgap0.032seconds,therate8000/0.032=250Kbpscanbeestimatedasavailablebandwidth.Thisisaquiteaccuratemeasurement,asthe1Mbpslinkissharedbythree250KbpsCBRtrafc,leaving250Kbpsforuse. Withfour250KbpsCBRcrosstrafcsources,1Mbpslinkissaturatedandpacketdropsareobserved.Asaresult,inputgapsandoutputgapsformanotsostraightlineasshowninFigure 4-9 .Also,thislinealmostparallelsy=xindicatingthatthereisnomorebandwidthavailableforanotherconnection.Theoutputgapvaluedoesnotexceed 76

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Inputgapsandmeanoutputgapswith2sourcesofCBRcrosstrafcindumbbelltopology. Figure4-8. Inputgapsandmeanoutputgapswith3sourcesofCBRcrosstrafcindumbbelltopology. morethan0.008secondsfromy=x,implyingthatourobservationconrmsthethemaximumoutputgaptoinputgapratioinSection 4.2 Asweaddrandomnesstocrosstrafc,theoutputgapstartstocontaintherouteridletime.InFigure 4-10 ,theinputgapandoutputgapgraphmeetsy=xat0.016secondswithonePoissoncrosstrafcsourcewiththeaveragetransmissionrateof250Kbps.RememberingthatinthecaseofoneCBRcrosstrafc,theinputgapandoutputgapgraphmetat0.012seconds,0.016secondsisanoverestimation. 77

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Inputgapsandmeanoutputgapswith4sourcesofCBRcrosstrafcindumbbelltopology. Figure4-10. Inputgapsandmeanoutputgapswith1sourceofPoissoncrosstrafcindumbbelltopology. Similarly,theinputgapandoutputgapgraphwithtwo250KbpsPoissoncrosstrafcsourcesisshowninFigure 4-11 .WecanobservethattheinputgapandoutputgapgraphinFigure 4-11 isnotastraightlineastheoutputgapsincludetherouteridletimewithPoissoncrosstrafc.ThecasewiththreesourcesofPoissoncrosstrafcshowsthesametendencyinFigure 4-12 .Withfour250KbpsPoissoncrosstrafcsources,therouterstartstodroppackets,andinputgapsandoutputgapsformalineparalleltoy=x,eventhoughthelineisnotstraightasinFigure 4-13 78

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Inputgapsandmeanoutputgapswith2sourcesofPoissoncrosstrafcindumbbelltopology. Figure4-12. Inputgapsandmeanoutputgapswith3sourcesofPoissoncrosstrafcindumbbelltopology. WhencrosstrafcisParetocrosstrafcwiththe500msaverageidleperiodandthe500msaveragebusyperiod,500Kbpstransmissionrateduringthebusyperiodmakes250Kbpstrafcinaverage.AsParetocrosstrafcuctuatesmorethanCBRorPoissoncrosstrafc,packetdropsstarttobeobservedwithtwoParetotrafcsources,andquiteafewpacketdropsappearwiththreeandfourParetocrosstrafcsources. TheinputgapandoutputgapgraphwithoneParetocrosstrafcsourceisshowninFigure 4-14 .Thegraphintersectsy=xataround0.016seconds.Thisamountsto 79

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Inputgapsandmeanoutputgapswith4sourcesofPoissoncrosstrafcindumbbelltopology. Figure4-14. Inputgapsandmeanoutputgapswith1sourceofParetocrosstrafcindumbbelltopology. roughly8000/0.016=500Kbps.Apparently,thisisanoverestimationoftheoutputgapwithoneCBRcrosstrafcsourceshowninFigure 4-6 TheinputgapandoutputgapgraphsshowninFigure 4-15 andFigure 4-16 areforthreeandfourParetocrosstrafcsources.ThegraphsoverestimateoutputgapscomparedtoFigure 4-7 andFigure 4-8 respectively.AlsotheyoverestimateoutputgapsofFigure 4-11 andFigure 4-12 .ConsideringthatCBRcrosstrafcismoststationaryfollowedbyPoissoncrosstrafcandthenParetocrosstrafc,wecanverifythatthe 80

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Inputgapsandmeanoutputgapswith2sourcesofParetocrosstrafcindumbbelltopology. Figure4-16. Inputgapsandmeanoutputgapswith3sourcesofParetocrosstrafcindumbbelltopology. moreburstythecrosstrafcis,thelargeroutputgapsitgeneratesforagivenrate.ThisillustratesthattheidletimecapturedintheoutputgapisgreaterwithmoreirregularcrosstrafcasouranalysispredictedinSection 4.2 .WhentherearefourParetocrosstrafcsources,theinputgapandoutputgapgraphparallelsy=x,eventhoughthelineisnotstraightduetopacketdropsinFigure 4-17 Figure 4-18 showstheinputgapandoutputgapgraphforoneFTPtrafc.Thegraphisconvexbutnotastraightline.WhentherearetwoFTPcrosstrafcsources, 81

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Inputgapsandmeanoutputgapswith4sourcesofParetocrosstrafcindumbbelltopology. Figure4-18. Inputgapsandmeanoutputgapswith1sourceofFTPcrosstrafcindumbbelltopology. thebottlenecklinkbecomescongested.However,fewerpacketdropsareobservedwithFTPcrosstrafccomparedtoCBR,Poisson,andParetocrosstrafc,asTCPadaptivelythrottlesthetrafcitgenerates.Consequently,thegraphinFigure 4-19 isstraightandparallelsy=x. 82

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Inputgapsandmeanoutputgapswith2sourcesofFTPcrosstrafcindumbbelltopology. 83

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Parkinglottopologyforpacketpairmeasurements. 4-20 ,aparkinglottopologyisillustrated.Thedefaultrouterqueuesizeofns-2isnotenoughforthepackinglottopologyaslinkcapacitybetweenroutersis10Mbps.Toreducemassivepacketdrops,therouterqueuesizeissetto300packets.AsinFigure 4-5 ,nodeslabeledwithxsarecrosstrafcsenderswhilenodeslabeledwithxcarereceivers.Thenumberofxsnodesisacongurableparameterandthenumberofcrosstrafcsourcesreferstothenumberofxsnodes.Nodeslabeledfroms1tos5arealsocrosstrafcsenders.Correspondingreceiversarefromc1toc5respectively.Inthegure,s1andc1hasadirecteddottedlineinbetweenthemtosignifythecrosstrafcowgeneratedbys1.Thecrosstrafctypethatnodess1throughs5generateisthesametypeaseachxsgenerates.Thepacketpairsenderislabeledwithsanditscorrespondingreceiverwithc,androutersarelabeledfromr1tor5.Thelinksbetweenroutershave10Mbpscapacitywith10msdelay.Allotherlinksareequipped 84

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Fortheparkinglottopology,CBRandPoissoncrosstrafcisgeneratedwiththeaveragerateof1Mbps.Paretocrosstrafchas500msbusyperiodand500msidleperiodandgeneratesanaveragetrafcrateof1Mbpsduringthebusyperiod,whichamountsto500Kbpsonaverage.Therefore,forParetocrosstrafc,thenumberofcrosstrafcconnectionsistwicethenumberofconnectionsofCBRorPoissoncrosstrafctohavethesameaveragetransmissionrate. First,Figure 4-21 ,Figure 4-22 ,andFigure 4-23 showinputgapandoutputgapgraphsofone,ve,andtensourcesofCBRcrosstrafc.InFigure 4-21 ,theinputgapandoutputgapgraphisslightlybelowy=xafter0.012seconds,conrmingtheanalysisofSection 4.2 thattheoutputgapcanbelessthantheinputgap,evenwiththeparkinglotmodel.Figure 4-21 lookssimilartoFigure 4-22 ,whileFigure 4-23 showsthattheinputgapandoutputgapgraphparallelsy=x.ItisworthmentioningthattheinputgapandoutputgapgraphofFigure 4-23 isslightlyabovey=x,whereasinFigure 4-9 ,theinputgapandoutputgapgraphislocatedevenhigherabovey=x.Thishastodowiththehighlinkspeedbetweenroutersintheparkinglottopology.Also,thisconrmsthattheoutputgaptoinputgapratioissmallerwhentheprobingpacketsizeissmallorthelinkspeedisfast. Figure 4-24 ,Figure 4-25 ,andFigure 4-26 showinputgapandoutputgapgraphsofone,ve,andtensourcesofPoissoncrosstrafc.TheyshowbehaviorsimilartoCBRcrosstrafc.ForParetocrosstrafc,differentnumbersofcrosstrafcsourcesareused.Figure 4-27 ,Figure 4-28 ,andFigure 4-29 showinputgapandoutputgapgraphsoftwo,ten,andtwentysourcesofParetocrosstrafcsources.TheinputgapandoutputgapgraphsofParetocrosstrafcshowsbehaviorsimilartoCBRandPoissoncrosstrafcscenarios. 85

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Inputgapsandmeanoutputgapswith1sourceofCBRcrosstrafcinparkinglottopology. Figure4-22. Inputgapsandmeanoutputgapswith5sourcesofCBRcrosstrafcinparkinglottopology. Figure 4-30 ,Figure 4-31 ,andFigure 4-32 showinputgapandoutputgapgraphsofone,ve,andtwentysourcesofFTPcrosstrafc.FTPcrosstrafcinputandoutputgraphsshowbehavioranalogoustoothercrosstrafctypes.EvenwithtwentysourcesofFTPcrosstrafc,theinputgapandoutputgapgraphshowsastraightlineparallelwithy=x,asTCPisadaptivetocongestionandreducespacketdrops. 86

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Inputgapsandmeanoutputgapswith10sourcesofCBRcrosstrafcinparkinglottopology. Figure4-24. Inputgapsandmeanoutputgapswith1sourceofPoissoncrosstrafcinparkinglottopology. 4.2 isvalidusingdifferentsimulationscenarios.Notably,whencrosstrafcundulates,therouteridletimeiscapturedintheoutputgap.Also,ifcrosstrafcuctuates,thechanceofpacketdropsincreases.Consequently,itisprudenttotransmitpacketsslowlytopreventpacketdropswhencrosstrafcisnotstationary.Accordingly,itmaybebenecialtooverestimatethe 87

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Inputgapsandmeanoutputgapswith5sourcesofPoissoncrosstrafcinparkinglottopology. Figure4-26. Inputgapsandmeanoutputgapswith10sourcesofPoissoncrosstrafcinparkinglottopology. outputgapforsuchcrosstrafc,astheoverestimationofoutputgapwouldresultinanon-aggressivepackettransmissionrate. SimulationresultsinthissectionarebasedonPASTAsampling.However,asTariqetal.[ 55 ]shows,itispossibletouseperiodicsamplingwithoutlosingtoomuchprecisioninmanysituations.ThesamescenariossimulatedwithPASTAsamplingalsohavebeensimulatedwithperiodicpacketpairsampling.Resultsaresimilarforalltrafctypes.However,periodiccrosstrafcmaycausephaselockingwiththeperiodic 88

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Inputgapsandmeanoutputgapswith2sourceofParetocrosstrafcinparkinglottopology(1Mbpscrosstrafcduringthebusyperiod). Figure4-28. Inputgapsandmeanoutputgapswith10sourcesofParetocrosstrafcinparkinglottopology(1Mbpscrosstrafcduringthebusyperiod). sampling,resultinginbiasedsamplepoints.Tomitigatethephaseeffect,boundedrandominterpacketpairintervalscanbeusedforprobing. 89

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Inputgapsandmeanoutputgapswith20sourcesofParetocrosstrafcinparkinglottopology(1Mbpscrosstrafcduringthebusyperiod). Figure4-30. Inputgapsandmeanoutputgapswith1sourceofFTPcrosstrafcinparkinglottopology. 90

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Inputgapsandmeanoutputgapswith5sourcesofFTPcrosstrafcinparkinglottopology. Figure4-32. Inputgapsandmeanoutputgapswith20sourcesofFTPcrosstrafcinparkinglottopology. 91

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Tobeginwith,wedenotexiastheinputgapofaprobingpacketpairwithpacketsize>0.Assumethattherstpacketandthesecondpacketofthispacketpairaresentattiandti+xi,respectively.Theoutputgapcorrespondingtoxiisdenotedbyyi.Alsoitisassumedthatcrosstrafcandprobingpacketsdonotcausecongestionintherouter. TodescribealinearleastmethodinCasellaetal.[ 11 ],letx=1

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11 ].Inotherwords,thevarianceofslopeaisminimized,whenxiareeither0orxminforxi2[xmin,0],andsampleoutputgapsdonotcontainrouteridletime,where0andxminareasdenedinSection 4.3 .However,inourcase,measurementerrorsarebiased,sincemorerouteridletimeisincludedintheoutputgapwhentheinputgapislarge,andxminand0arenotknownapriori. Instead,considery0asasampleoutputgapwhentheinputgapis0and(xi,k,yi,k)arepartitionedsubsequencesaswehaveseeninSection 4.3 .Letx1,1=y0,x2,1=3 2y0,x3,1=2y0andx4,1=4y0.Accordingly,y1=1 where1.If0=x1,1,wetake=0.Otherwise,thelinearleastsquaremethodisappliedtosamplepoints(xi,k,yi,k)forxi,0,togety=ax+basdescribedearlier.If(^,^)istheintersectionofy=xandy=ax+b,wetake=minf0,^g.Then,thecongestionwindowsizethatwouldnotcausecongestioncanbeestimatedasR=,whereRistheroundtriptime(RTT)ofanewTCPconnection.Thiscongestionwindowsizecanbeusedforssthresh. Inaddition,notewhenthenetworkisnotcongested,a<1.However,itispossibletohavea1.Whena1,itcanbeinferredthatthenetworkiscongestedandnoextrabandwidthisavailableforanewconnection.Inthiscase,wedonotreadjustthessthreshvalue. TheabovealgorithmcanbeimplementedintheTCPsender.Forinstance,iftheTCPreceiverimmediatelyrespondswithanACKforeachpacketitreceivesfromtheTCPsender,ACKscanbeusedbytheTCPsendertomeasuresampleoutputgaps, 93

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2y0,2y0,4y0inroundrobintogetyirespectivelyuntilenoughsamplepointsarecollected.ThesamplingintervaliscalculatedbyR 46 ]isadoptedtoestimatessthresh,whencwndreaches32. However,therearetechnicalissuesinobtainingoutputgapsamples.WhentheTCPreceiverisenabledwithdelayedacknowledgement,itisdifculttoobtainoutputgapmeasurementsjustusingACKpackets,sincetheTCPsenderusuallyreceivesoneACKforeveryotherpacketitgenerates.Toworkaroundthisproblem,twopacketsofapacketpaircanbeinvertedinorder.AsdescribedinChapter 3 ,theTCPreceivergeneratesACKsforout-of-orderpacketsimmediately,evenifdelayedacknowledgementisenabled.Then,theTCPsendercanuseACKstomeasuretheoutputgap.ThistechniqueisusedinPerssonetal.[ 44 ]tomeasurethebottlenecklinkcapacityusingaTCPconnection. Anotherproblemisthenumberofpacketsavailabletobetransmitted.Withself-clocking,theTCPsendertransmitsonlyasmanypacketsasthecurrentcongestionwindowallows.Assumethatthecongestionwindowisusedupandthelastpacketsequencenumberacknowledgedisn1.Usually,whendelayedacknowledgementisnotinvolved,thenextACKisforthesequencenumbern.WhentheACKforthesequencenumbernarrives,theTCPsendercantransmittwopackets,sincetheACKincreasesthelastacknowledgedpacketsequencenumberbyoneandcwndisincreasedbyoneduringslowstart. Whendelayedacknowledgementisinvolved,oneACKacknowledgestwopacketsusually.Forexample,ifthelastsequencenumberacknowledgedisn2,thenextexpectedACKisforthesequencenumbern.ThisimpliesthatoneACKarrivaltriggers 94

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ThisdifcultycanbeovercomeifweadopttheLBCalgorithmbyAllman[ 3 ].LBCallowscwndtogrowbytwo,ifanACKarrivalacknowledgesmorethanonepacket.Duringslowstart,withaconstantfeedofpacketsfromthehost,theTCPsenderwouldacknowledgetwopacketsperACKandcwndincreasesbytwoduetoLBC.Asaresult,fourpacketscanbetransmittedforeachACK,makingitpossibletogeneratetwopacketpairs. Ourslowstartalgorithmterminateswhencwndreaches32orapacketdropisdetected.ssthreshisestimatedwhenatleast12sampleoutputgapsarecollectedandtheslopeaislessthanone.Itispossible,whencwndreaches32,aninsufcientnumberofsampleoutputgapshavebeenobtained.Inthiscase,wemaywaitformoreACKsofpacketpairsoutstandinginthenetworktoestimatessthresh.Itisnotedthattheparameter1ofEquation 4 shouldnotbelarge,orwemayoverestimatessthreshinducingpacketdrops.Forsimulationinlatersections,issetto1.05. 4.6.1SimulationEnvironment 4-33 issimilartothatinFigure 4-20 .OnedifferenceisthelabelBandwidthinFigure 4-33 .Bandwidthisacongurableparameterforlinkcapacitybetweenrouters,r1,r2,r3,r4,andr5.Betweenrouters,thelinkdelayis50ms,whileotherlinkshave10msdelaywith50Mbpsbandwidth.Thenumberofxsnodesandthenumberofxcnodesarexedat5.FiveFTPcrosstrafcconnectionsareestablishedbetweenxsandxcnodes.Also,FTPcrosstrafcowsfroms1toc1,s2toc2,s3toc3,s4toc4,ands5toc5.Finally,theTCPsendersestablishesanFTPconnectionwiththeTCPreceiverc 95

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Parkinglottopologymodelforslowstart. usingmodiedslowstartalgorithms.TheTCPconnectionbetweensandciswithoutdelayedacknowledgementwhileotherTCPconnectionsareenabledwithdelayedacknowledgement.TheTCPpacketsizebetweenthenodesandthenodecis1040bytes.Whenthesimulationinitiates,eachcrosstrafcFTPconnectionarrivesfollowingtheExponentiallydistributedinterarrivaltime.Theaverageinterarrivaltimeisonesecond.TheFTPconnectionbetweensandcbeginsat500seconds. Theinitialssthreshvalueofsissetto32andthecrosstrafcTCPadvertisedwindowsizeissetto1000asthetopologyisequippedwithalargedelaybandwidthproductpath.Also,therouterbuffersizeissetto500packetstoaccountforthehighspeedlinks.Eventhoughouralgorithmcanperformwellwithdelayedacknowledgment,delayedacknowledgementisdisabled,sincesomeslowstartmodelscomparedinthisstudymaynotrunproperlywhendelayedacknowledgementisenabled. 96

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19 ].ThessthreshvalueobtainedbyHoe'smethodusuallyisanoverestimation,sincetheoutputgapcorrespondingtotheinputgapvalue0maycongestthenetworkifitisusedforthepackettransmissionintervalofanewconnectionaswehaveseeninSection 4.2 .AlsoHoe'smethodisnotdesignedwithdelayedacknowledgementinmind,andmaynotworkproperlywiththeTCPreceiverswithdelayedacknowledgementenabled. Wecanestimatessthreshmoreaccuratelyusingmultiplepacketpairs.PacedslowStart(PaSt)[ 21 ]isattractiveinthisrespect.PaStdependsontheassumptionthattheoutputgapwillbegreaterthantheinputgap,ifthereisnotenoughavailablebandwidthintherouter.WithPaSt,slowstartrunsinrounds.Eachroundconsistsof2,4,8,16,and32inputpacketsrespectively.EachroundterminateswhenalltheACKsarereceivedforagivennumberofpacketsoftheround.WhenthePaStalgorithmterminates,theestimatedssthreshisusedforfurtherslowstart. Toparaphrase,therstroundofPaStstartswithaback-to-backpacketpairoftwopackets,fromwhichweobtaintheinitialoutputgap.Then,thesecondroundrunswithfourpacketsfollowedbythethirdroundofeightpackets,etc.PaStusesatrainofpacketsincalculatingoutputgaps.Forinstance,whenpacketsn,n+1,n+2,n+3aretransmittedinorderwithaspeciedintervalbetweenthem,outputgapscorrespondingpairsnandn+1,n+1andn+2,n+2andn+3aremeasuredandthenaveraged.Inessence,PaStgoesthroughanitestatemachineinAlgorithm 3 adjustinginputgapsbetweenroundsbasedontheaveragedoutputgapofpreviousround.Thestatemachineterminateswhenterminateisreached,wherethegapvalueisdetermined. 97

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AsinHoe'smethod,PaStdoesnotconsiderdelayedacknowledgement,whichmakesitdifculttousePaStwiththeTCPreceiverswithdelayedacknowledgementenabled.Also,therealwaysshouldbepacketstotransmitintheTCPsender.Forexample,32packetsshouldbeavailableduringthelastroundofPaSt.Otherwise,correctmeasurementofoutputgapsisnotfeasible. Wangetal.[ 59 ]suggestAdaptivestart(Astart)forTCPslowstartwithabandwidthestimationmethodforTCPWestwoodcalledEligibleRateEstimate(ERE).Originally,TCPWestwood[ 18 ]introducedadifferentbandwidthestimationmethod,calledBandWidthEstimate(BWE).Tobespecic,lettkbethetimeofk-thACKarrivalanddkbetheamountdatabitsacknowledgedbetweentk1andtk.Thenbk=dk=(tktk1)isthesamplebandwidthmeasuredintheinterval[tk1,tk].Eachbkisusedtogetalow-passlteredestimate^bk,i.e.,BWEas^bkk^bk1+(1k)bk+bk1 2+(tktk1)and1=isthecutofffrequencyforthelter. Incontrast,EREdeterminesthesamplingintervalkbykRw=Rmin IntheoriginalAstartalgorithm,ssthreshisestimatedwithEREasssthresh^kRmin=,

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fin gap:theinputgapforthenextroundg fprev in gap:theinputgapofthepreviousroundg fout gap:theaverageoutputgapofthepreviousroundg fgap:thenalgapforestimatingssthreshg gap0fInitialinputgapis0g gapout gap2 ifprev in gap
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Forsimulation,wemodiedthens-2implementationofBWEavailablefromtheWestoodhomepage[ 30 ],whereasEREisimplementedwithtwotimersinns-2.OnetimerexpiresinthelatestRTTwhenthetimerstarted,andisrescheduledrightaftertheexpirationwiththelatestRTT.Theamountofdataacknowledgedbetweenthestartandtheexpirationtimeofthetimerisusedtocalculate.HereisnotlteredasintheoriginalAstartalgorithm,asitdoesnotmakemuchdifferenceinestimatingssthreshinoursimulation.Theothertimerexpiresinthelatestkandisrescheduled.TheamountofdataacknowledgedduringkisusedtoobtainERE.ForbothBWEandERE,thecutofffrequencyi.e.,1=issettoone. 4-34 ,Figure 4-35 ,Figure 4-36 ,Figure 4-37 ,andFigure 4-38 showtypicalsimulationresultswhenBandwidthvariesamong25Mbps,50Mbps,100Mbps,200Mbpsand400Mbps.Inthegures,thelabelAstart-BWErepresentsslowstartwithAstart,whenthebandwidthestimationmethodisBWE.Similarly,thelabelAstart-EREdenotesslowstartwithAstart,whenthebandwidthestimationmethodisERE.ThelabelRenoisforTCPReno.OurschemeislabeledwithSPMtostandforSlowstartwithPacketpairMeasurements,whilethelabelHoeisforHoe'smethodandPaStrepresentsPaSt.Eachslowstartalgorithmstartsat500secondsandcwndvaluesaresampledwiththeintervalof0.1secondsstartingfrom500secondsuntil515seconds. 100

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101

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102

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InFigure 4-34 ,allmodelssufferfrompacketdropsasthenetworkisseverelycongested.InFigure 4-35 Hoe'smethodapparentlyoverestimatesssthreshandgeneratespacketdrops.AstartwithBWEandPaStalsooverestimatessthreshandstarttodroppackets.Incontrast,SPMdoesnotgeneratepacketdropswithitsssthreshestimation.TCPRenoandAstartwithEREalsodonotcausepacketdropsinthisscenario.Notably,TCPRenoandAstartwithEREoverlapeachotherasAstartwithEREtypicallyestimatesssthreshlessthan32. WhenBandwidthis100MbpsasshowninFigure 4-36 ,Hoe'smethodisstillaggressiveinestimatingssthreshandstartstodroppackets.AstartwithBWEdoesnotdroppacketswithalargessthresh.NextfollowsSPMwithoutcausingpacketdrops.AstartwithERE,PaStandTCPRenoalldonotcausepacketdropswithsmallssthreshvalues.Asbefore,TCPRenoandAstartwithEREoverlapeachother.Figure 4-37 showsthesimulationresultwhenBandwidthis200Mbps.Allslowstartmodelsdonotdroppackets,whileHoe'smethodisthemostaggressivefollowedbyPaSt,SPM,Astart 103

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Whenthenetworkisleastcongestedwith400MbpslinksinFigure 4-38 ,allslowstartmodelsmayuseupto50Mbpscapacity.Hoe'smethodalmostfullyutilizestheavailablebandwidth,whilessthreshisunderestimatedforPaSt,AstartwithBWE,TCPReno,andAstartwithERE.SPMshowsalmostthesameperformanceasHoe's,asSPM'scwndvaluesalmostoverlapwiththoseofHoe's.Also,TCPRenoandAstartwithEREshowthesamecwndgrowthpatternandoverlapeachother. Table 4-1 showstheaverageandthestandarddeviationof100samplesforeachscenariowhenBandwidthvaluerangesfrom25Mbpsto400Mbps.ThecaseofTCPRenoisnotshownasitinvariablyhas32asssthresh.Asitisnotknownwhatvaluesofssthreshareoptimal,weconsideraveragesofcwndsamplestakenfromxsnodesat500seconds.Theseaveragesare62.8,218.9,581.5,584.1,and584.1forBandwidthof25Mbps,50Mbps,100Mbps,200Mbps,and400Mbpsrespectively.Inoursimulationenvironment,sampledcwndvaluesareboundedabovearound600.Infact,aseachxsnodehasaminimumRTTof0.44secondswhenthereisnocrosstrafc,cwndincreasesbyoneper0.88secondswhendelayedacknowledgementisusedduringthecongestionavoidancephaseofTCP. Inoursimulationenvironment,xsnodescongestthenetworkwhenBandwidthis25Mbpsand50Mbps,andssthreshofthenodesshouldnotexceed62.8for25Mbpsand218.9for50Mbps,ifTCPfairnessisconsidered.Thisisreasonableasssthreshistheupperboundofcwndduringslowstart.Forthe400Mbpsscenario,thereisenoughbandwidthforeveryconnection,andthenodesmayincreasecwndupto(0.44seconds)=((10408bits)=50Mpbs)2644,where0.44secondsisRTT,and1040istheTCPpacketsizeinbytes.WhenBandwidthis100Mbps,itisnotclearwhatcwndvaluethenodesshouldhave,ascwndofthenodexsprobablyisnotfullyincreasedtoutilizethebandwidth.Atleast,thenodesmayuse581.5as 104

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Overall,Hoe'smethodtendstooverestimatessthreshwhenthereiscrosstrafcinthenetwork.ThisisexpectedbecauseHoe'smethodusesoneoutputgapofback-to-backinputpacketpairthatisusuallylessthan0fromourearlieranalysis.Incontrast,AstartwithEREunderestimatesssthreshinallcases.WithAstartwithERE,thedatabitssamplingintervalistoolongforasmallcwndvalueinitially.Consequently,itmayunderestimatessthreshwithalargedelaybandwidthproductpath.AstartwithBWEdoesnothavethisproblem.However,itislesssensitivetocrosstrafcduringslowstart,estimatingssthreshtooaggressivelywhenthereisseverecongestioninthenetworkandunderestimatingssthreshwhenthereisampleavailablebandwidth.PaStshowsreasonableperformance,butduetolimitedterminalstatesofitsstatemachine,estimationofssthreshisbounded.Also,forpracticalreasons,PaStisunlikelytobedeployed.Incontrast,SPMachievesgoodperformanceexceptforthe100Mbpsscenario,whenitsuffersfromratherhighvariance.Thevarianceofssthreshestimatesofourschememaybeduetosmallsamplesizecomparedtoothermodels. Oneissueworthmentioningisthattherouterqueuesizeplaysanimportantroleinslowstartwithalargedelaybandwidthproductpath.Evenifwegetagoodbutlargeestimateofssthresh,itstillcangeneratepacketdropsiftheroutersarenotequippedwithlargequeueingbuffersforahighspeednetwork.Therefore,whentherouterqueueingbuffersizeisnotknown,thereshouldbealimitoncwndgrowth.ActuallythisobservationisinaccordancewithwhatRFC3742[ 16 ]recommends. 105

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AverageofestimatedssthreshvaluesanditsstandarddeviationforAstart-ERE,Astart-BWE,SPM,Hoe,andPaStwithvaryingBandwidth B/W ERE BWE SPM Hoe PaStMbps AvgDev AvgDev AvgDev AvgDev AvgDev 25 15.56.1 214.0113.6 57.055.0 683.6382.5 39.539.150 15.24.9 418.5153.6 98.8106.4 1205.4725.9 46.476.8100 16.44.1 694.2175.1 88.7107.9 1475.6455.9 54.223.7200 19.42.2 1027.7218.7 1668.4948.2 2493.3478.4 1095.0564.4400 19.52.6 1071.3183.8 2528.9520.1 2563.9447.9 1321.1592.8 Here,weintroducedaslowstartalgorithmbasedonpacketpairmeasurements.Ourslowstartalgorithmtakesadvantageofapproximatelinearityofinputgapsandoutputgapsofpacketpairstoestimateanon-intrusiveslowstartthresholdvalue.Also,ouralgorithmsolvestheproblemofobtainingpacketpairmeasurementswhendelayedacknowledgementisenabled. Simulationresultsshowthatouralgorithmestimatesgoodslowstartthresholdvalueswithoutcongestingrouters.ItisalsoshownthatthedefaultslowstartthresholdvalueinTCPRenomaybetoosmalltoachievegoodinitialperformanceinanetworkwithalargedelaybandwidthproduct.Incontrast,Hoe'smethodistooaggressiveinslowstartgeneratingmassivepacketdrops.Astartbasedalgorithmshaveperformanceproblemsduetotheirbandwidthestimationmethods.PaStshowsreasonableperformance,butitonlyworkswhendelayedacknowledgementisnotusedandthereshouldalwaysbethespecicnumberofpacketsavailabletobetransmitted. 106

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Asnetworkspeedincreases,theneedforimprovingTCPperformancebecomesapparent.Forinstance,withalargedelaybandwidthproductpath,aTCPconnectionmaytakealongwhiletoincreasecwnduptotheavailableend-to-endbandwidthinitiallyduetothexedssthreshvalueat65535bytesduringslowstart.However,improvingTCPslowstartperformanceisnottrivial,ingeneral,asinsufcientnetworkstateinformationisavailablewhenaTCPconnectionisestablished. Sincessthreshplaysanimportantroleinachievinggoodperformanceduringslowstart,itiscrucialtoestimateagoodssthreshtoimprovetheTCPstart-upperformance.Asoneattempt,thechangeofRTTvaluesmaybeusedtoestimatessthreshasinAstartwithEREorBWE.EventhoughAstartcanadaptivelyestimatessthreshvaluesuntilapacketdropoccurs,initialestimatesusingonlyafewmeasurementsamplesareusuallyunsatisfactory,asAstartwithBWEisratherinsensitivetotheavailablebandwidth,andAstartwithEREtendstounderestimatessthresh. Asanotherattempt,packetpairgapscanbeusedtoestimatessthreshasinPaStorHoe'smethod.However,ifpacketpairgapsaremeasuredusingACKsandwhentheTCPreceiverisenabledwithdelayedacknowledgement,desiredoutputgapscannotbemeasured.Toaddresstheseproblems,weintroducedthepacketpairinversionmethodinPerssonetal.[ 44 ]attheTCPsenderduringslowstart.Then,duplicateACKscanbeusedtoincreasecwndmorerapidlyanditalsobecomespossibletomeasurepacketpairoutputgaps.Indeed,givingtemporalgapsinbetweenpacketsmayslowdowncwndgrowthslightlyduetoself-clocking,butthebenetismuchhigherifwecanestimatessthreshvaluescorrectlyinhighspeednetworks. 2 ,thehistoryof 107

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Inprovidingmultimediaobjectsorwebdocumentstonearbyendhostsinahomogenousnetworkenvironment,MISSandJSexhibitreasonablygoodperformanceintermsoftheinitial5secondthroughputandthetotalthroughputwhentheroutercapacityissufcient.Eventhoughwecanestimategoodssthreshandcwndvalues,packetdropsstillcanoccuriftheroutersonthepatharenotequippedwithenoughqueueingcapacity.Consequently,forhighspeednetworks,theperformanceofslowstartdependsontheroutercapacityevenwhenpacketpacingisused.Alsothedelaybetweentheserverandclientsisasignicantfactorinachievinggoodinitialnthroughput. Infact,therehavebeenattemptstondafairshareofbandwidthforanewconnectionusingpassivenetworkmonitors.Evidently,withhighspeednetworks,thepassivemonitorcapabilitybecomesquestionableasthemonitorhastokeeptrackofamassivenumberofpacketstocollectconnectionstateinformation.Instead,theservercandetermineafairshareofbandwidthsharingthesamebottlenecklinks,usingthestateinformationofeachTCPconnectionalreadyexistingintheserver. 3 examineshowinvertedpacketpairsareusedinslowstartwhendelayedacknowledgementisenabled.Byreducingsegmentbursts,theSSIPPalgorithmachieveshigherthroughputthanTCPRenoortheLBCalgorithm.SSIPPalsooutperformsLBCintermsofgoodputandtheaveragequeuelengthwithdrop-tailqueuemanagementorREDqueuemanagement.However,SSIPPhastokeeptrackof 108

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InChapter 4 ,slowstartwithpacketpairmeasurements(SPM)isintroduced.First,usingalinearleastsquaremethod,theapproximateend-to-endavailablebandwidthisdeterminedusinginputgapsandoutputgaps.Tosampleoutputgaps,theTCPsendertransmitsinvertedpacketpairswithinputgaps.SimulationresultsshowthatSPMobtainsagoodestimateofssthreshonaverage.However,thevarianceisratherhighduetolimitedsamplepoints.Also,whenthenetworkismoderatelycongested,SPMtendstounderestimatessthreshduetoidletimecapturedinoutputgaps. PerformancegainofSPMwouldbehighwithalargedelaybandwidthproductpath,asthereismoreroomforcwndtogrowuptossthresh.Withtheimprovedinitialslowstatperformance,userscanhavesignicantlyenhancedexperience. ItwouldbeinterestingtoanalyzewhyLISSandISSdidnotshowmuchdifferenceinslowstartperformance.IfanEWMAofcwndisnotagoodestimateofstablecwndvalueovertime,whatwouldbeagoodestimate?Insomecases,theremaybenocurrent,stable,activeconnections.LISSandISScanusearecentconnectioncwndvalueastheinitialvalueinthissituation.Measuringthestabilityofcwndandssthreshovertimewouldbedesirabletodeterminetheirvalidityforbothidleconnectionsandnewconnectionswhenthereisnocurrentinformationavailable. Also,whenestimatingssthresh,therouterqueuesizecanbeconsideredalongwithavailablebandwidth.EvenwhenSPMcanestimatessthreshvaluescorrectly,packetdropsstillcanoccuriftherouterbuffercapacityisnotenoughtoabsorbpacketbursts. 109

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InChapter 4 ,SPMwascomparedwithotherslowstartmodelsonlyinaparkinglotmodelwithFTPcrosstrafc.SPMmaybesimulatedindifferenttopologieswithcrosstrafcotherthanFTP.Alsoitwouldbeinterestingtoaddrandomnessinpacketpairsamplingintervalsandseehowtherandomnessinuencestheestimationofssthresh.SPMmayalsoincreasethenumberofprobesamplesbasedonthevarianceofmeasurements. Bysimulation,itwasshownthatSPMunderestimatesssthreshwhenthenetworkismoderatelycongested,andAstartwithBWEperformsratherunsatisfactorywhenthennetworkisuncongestedorheavilycongested.ItwouldbegreatifwecanndawaytocombineSPMandAstartwithBWEtousessthreshofAstartwithBWEwhenthenetworkismoderatelycongested,andssthreshofSPMwhenthenetworkisseverelycongestedoruncongested. 110

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[1] M.Allman,S.Floyd,andC.Partidge.RFC3390:Increasingtcp'sinitialwindow,2002. [2] MarkAllman.Improvingtcpperformanceoversatellitechannels.Master'sthesis,OhioUniversity,1997. [3] MarkAllman.Onthegenerationanduseoftcpacknowledgments.SIGCOMMComput.Commun.Rev.,28(5):4,1998. [4] MarkAllman.Tcpbytecountingrenements.ACMSIGCOMMConmputerCommunicationReview,29(3):14,July1999. [5] MohitAronandPeterDruschel.Tcp:Improvingstartupdynamicsbyadaptivetimersandcongestioncontrol.Technicalreport,RiceUniversity,1998. [6] HariBalakrishnan,HariharanS.Rahul,andSrinivasanSeshan.Anintegratedcongestionmanagementarchitectureforinternethosts.SIGCOMMComput.Commun.Rev.,29(4):175,1999. [7] Jean-ChrysotomeBolot.End-to-endpacketdelayandlossbehaviorintheinternet.ACMSIGCOMMComputerCommunicationReview,23(4):289,1993. [8] R.Braden.RFC1122:Requirementsforinternethosts-communicationlayers,October1989. [9] LawrenceS.BrakmoandLarryL.Peterson.TCPvegas:Endtoendcongestionavoidanceonaglobalinternet.IEEEJournalonSelectedAreasinCommunica-tions,13(8):1465,1995. [10] KennethL.Calvert,MatthewB.Doar,AscomNexion,EllenW.Zegura,GeorgiaTech,andGeorgiaTech.Modelinginternettopology.IEEECommunicationsMagazine,35:160,1997. [11] GeorgeCasellaandRogerL.Berger.StatisticalInference.Duxbury,secondedition,2002. [12] Dah-MingChiuandRajJain.Analysisoftheincreaseanddecreasealgorithmsforcongestionavoidanceincomputernetworks.Comput.Netw.ISDNSyst.,17(1):1,1989. [13] M.Coates,A.Hero,R.Nowak,andB.Yu.Internettomography.SignalProcessingMagazine,19(3),May2002. [14] C.Dovrolis,P.Ramanathan,andD.Moore.Whatdopacketdispersiontechniquesmeasure?InProceedingsofIEEEINFOCOM'01,volume2,pages905,2001. [15] KevinFallandSallyFloyd.Simulation-basedcomparisonsoftahoe,renoandsacktcp.ACMSIGCOMMCompututerCommunicationReview,26(3):5,July1996. 111

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S.Floyd.RFC3742:Limitedslow-startfortcpwithlargecongestionwindows,March2004. [17] MichaelFreedman,MythiliVutukuru,NickFeamster,andHariBalakrishnan.Geographiclocalityofipprexes.InInternetMeasurementConference(IMC),2005. [18] MarioGerla,M.Y.Sanadidi,RenWang,andAndreaZanella.Tcpwestwood:Congestionwindowcontrolusingbandwidthestimation.InIEEEGlobecom2001,pages1698,2001. [19] J.Hoe.Improvingthestart-upbehaviourofacongestioncontrolschemefortcp.InACMSIGCOMM'96:ConferenceproceedingsonApplications,technologies,architectures,andprotocolsforcomputercommunications,pages270,NewYork,NY,USA,August1996.ACM. [20] NingningHuandPeterSteenkiste.Evaluationandcharacterizationofavailablebandwidthprobingtechniques.IEEEJournalonSelectedAreainCommunications,21(6):879,2003. [21] NingningHuandPeterSteenkiste.Improvingtcpstartupperformanceusingactivemeasurements:Algorithmandevaluation.InIEEEICNP'03:Proceedingsofthe11thIEEEInternationalConferenceonNetworkProtocols,Washington,DC,USA,2003.IEEEComputerSociety. [22] ISI/USC.Thenetworksimulator-ns-2.[cited2008November1].Availablefrom:http://www.isi.edu/nsnam/ns/. [23] VanJacobson.Congestionavoidanceandcontrol.InACMSIGCOMM'88:SymposiumproceedingsonCommunicationsarchitecturesandprotocols,pages314,August1988. [24] ManishJainandConstantinosDovrolis.End-to-endavailablebandwidth:measurementmethodology,dynamics,andrelationwithtcpthroughput.InACMSIGCOMM'02:Proceedingsofthe2002conferenceonApplications,technologies,architectures,andprotocolsforcomputercommunications,pages295,NewYork,NY,USA,2002.ACM. [25] StacyJohnson.Increasingtcpthroughputbyusinganextendedacknowledgementinterval.Master'sthesis,OhioUniversity,June1995. [26] SrinivasanKeshav.Acontrol-theoreticapproachtoowcontrol.ACMSIGCOMMComputerCommunicationReview,21(4):3,1991. [27] LeonidasKontothanassis,RameshSitaraman,JoelWein,DukeHong,RobertKleinberg,BrianMancuso,DavidShaw,andDanielStodolsky.Atransportlayerforlivestreaminginacontentdeliverynetwork.ProceedingsofIEEE,92(9):1408,September2004. 112

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BalachanderKrishnamurthyandJiaWang.Onnetwork-awareclusteringofwebclients.InACMSIGCOMM'00:ProceedingsoftheconferenceonApplications,Technologies,Architectures,andProtocolsforComputerCommunication,pages97,NewYork,NY,USA,2000.ACM. [29] J.F.KuroseandK.W.Ross.ComputerNetworking:ATop-DownApproachFeaturingtheInternet.Addison-Wesley,thirdedition,2002. [30] HighPerformanceInternetLab.Tcpwestwoodhomepage.[updated2003October27;cited2009November11].Availablefrom:http://www.cs.ucla.edu/NRL/hpi/tcpw/. [31] XiliangLiu,KaliappaRavindran,andDmitriLoguinov.Aqueueing-theoreticfoundationofavailablebandwidthestimation:single-hopanalysis.IEEE/ACMTrans.Netw.,15(4):918,2007. [32] XiliangLiu,KaliappaRavindran,andDmitriLoguinov.Astochasticfoundationofavailablebandwidthestimation:multi-hopanalysis.IEEE/ACMTrans.Netw.,16(1):130,2008. [33] SridharMachiraju,DarrylVeitch,FrancoisBaccelli,andJeanC.Bolot.Addingdenitiontoactiveprobing.SIGCOMMComput.Commun.Rev.,37(2):17,2007. [34] BenjaminMelamedandDavidD.Yao.Theastaproperty.InJ.H.Dshalalow,editor,AdvancesinQueueing:Theory,MethodsandOpenProblems,chapter7,pages195.CRCPress,1995. [35] B.Melander,M.Bjorkman,andP.Gunningberg.Anewend-to-endprobingandanalysismethodforestimatingbandwidthbottlenecks.InIEEEGLOBECOM'00,volume1,pages415,2000. [36] ArtMenaandJohnHeidemann.Anempiricalstudyofrealaudiotrafc.InProceedingsofIEEEINFOCOM'00,volume1,pages101,2000. [37] Microsoft.Microsoftdevelopernetworkmsdnlibrary.[cited2009November10].Availablefrom:http://msdn.microsoft.com/en-us/library/. [38] VenkataN.PadmanabhanandRadyH.Katz.Tcpfaststart:Atechniqueforspeedingupwebtrasfers.InIEEEGlobecom,1998. [39] KihongPark,GitaeKim,andMarkCrovella.Ontherelationshipbetweenlesizes,transportprotocols,andself-similarnetworktrafc.TechnicalReportBU-CS-96-016,ComputerScienceDepartment,BostonUniversity,1996. [40] VernPaxson.End-to-endroutingbehaviorintheinternet.InACMSIGCOMM'96:ConferenceproceedingsonApplications,technologies,architectures,andprotocolsforcomputercommunications,pages25,NewYork,NY,USA,1996.ACM. 113

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VernPaxson.Automatedpackettraceanalysisoftcpimplementations.InSIG-COMM'97:ProceedingsoftheACMSIGCOMM'97conferenceonApplications,technologies,architectures,andprotocolsforcomputercommunication,pages167,NewYork,NY,USA,1997.ACM. [42] VernPaxson.End-to-endInternetpacketdynamics.InProceedingsoftheACMSIGCOMM'97conferenceonApplications,Technologies,Architectures,andProtocolsforComputerCommunication,volume27,pages139.ACM,September1997. [43] KostasPentikousis.Application/trafc/poisson-poissontrafcgeneratorforns-2.[cited2009November11].Availablefrom:http://ipv6.willab./kostas/src/Application-Trafc-Poisson/. [44] AndersPersson,CesarA.C.Marcondes,Ling-JyhChen,LiLao,M.Y.Sanadidi,andMarioGerla.Tcpprobe:Atcpwithbuilt-inpathcapacityestimation.InIEEEGlobalInternetSymposium,2005. [45] J.Postel.RFC793:Transmissioncontrolprotocol,September1981. [46] WilliamH.Press,BrianP.Flannery,SaulA.Teukolsky,andWilliamT.Vetterling.NumericalRecipesinC:TheArtofScienticComputing.CambridgeUniversityPress,secondedition,1992. [47] RolfRiedi,JiriNavratil,RichBaraniuk,andLesCottrell.pathchirp:Efcientavailablebandwidthestimationfornetwork.InPassiveandActiveMeasurementWorkshop'03,2003. [48] SeongryongKang,XiliangLiu,MinDai,andDmitriLoguinov.Packet-pairbandwidthestimation:Stochasticanalysisofasinglecongestednode.InIEEEInternationalConferenceonNetworkProtocols,volume0,pages316,LosAlamitos,CA,USA,2004.IEEEComputerSociety. [49] StefanSavage,NealCardwell,andTomAnderson.Thecaseforinformedtransportprotocols.InHOTOS'99:ProceedingsoftheTheSeventhWorkshoponHotTopicsinOperatingSystems,page58,Washington,DC,USA,1999.IEEEComputerSociety. [50] PaulaR.Selvidge,BarbaraS.Chaparro,andGregoryT.Bender.Theworldwidewait:effectsofdelaysonuserperformance.InternationalJournalofIndustrialErgonomics,29(1):1520,2002. [51] VinodSharmaandRaviMazumdar.Estimatingtrafcparametersinqueueingsystemswithlocalinformation.Perform.Eval.,32(3):217,1998. [52] AlokShriram,MargaretMurray,YoungHyun,NevilBrownlee,AndreBroido,MarinaFomenkov,andKcClaffy.Comparisonofpublicend-to-endbandwidthestimationtoolsonhigh-speedlinks.InPAM,2005. 114

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W.RichardStevens.TCP/IPIllustrated(Vol.1):TheProtocols.Addison-WesleyProfessional,1993. [54] JacobStrauss,DinaKatabi,andFransKaashoek.Ameasurementstudyofavailablebandwidthestimationtools.InIMC'03:Proceedingsofthe3rdACMSIGCOMMconferenceonInternetmeasurement,pages39,NewYork,NY,USA,2003.ACM. [55] MuhammadMukarramBinTariq,AmoghDhamdhere,ConstantinosDovrolis,andMostafaAmmar.Poissonversusperiodicpathprobing(or,doespastamatter?).InIMC'05:Proceedingsofthe5thACMSIGCOMMconferenceonInternetMeasurement,pages10,Berkeley,CA,USA,2005.USENIXAssociation. [56] EvelineVeloso,VirglioAlmeida,Jr.WagnerMeira,AzerBestavros,andShudongJin.Ahierarchicalcharacterizationofalivestreamingmediaworkload.IEEE/ACMTransactiononNetworking,14(1):133,2006. [57] VikramVisweswaraiahandJohnHeidemann.Improvingrestartofidletcpconnections.TechnicalReportUSCTR97-661,USC,November1997. [58] EnlieWang.Human-computernetworkinteraction:Delayeffectsanditsmediators.PhDthesis,2005. [59] RenWang,GiovanniPau,KenshinYamada,M.Y.Sanadidi,andMarioGerla.Tcpstartupperformanceinlargebandwidthdelaynetworks.InProceedingsofIEEEINFOCOM'04,volume2,pages796,2004. [60] RonaldW.Wolff.Poissonarrivalsseetimeaverages.OperationsResearch,30(2):223,March1982. [61] OssamaYounisandSoniaFahmy.Flowmate:scalableon-lineowclustering.IEEE/ACMTrans.Netw.,13(2):288,2005. [62] Y.Zhang,N.Dufeld,VernPaxson,andS.Shenker.Theconstancyofinternetpathproperties.InIMW'01:Proceedingsofthe1stACMSIGCOMMWorkshoponInternetMeasurement,pages197,NewYork,NY,USA,2001.ACM. [63] YinZhang,LiliQiu,andSrinivasanKeshav.Speedingupshortdatatransfers:Theory,architecturalsupport,andsimulationresults.InNOSSDAV'00,2000. 115

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InKwanYureceivedhisB.A.degreeinphilosophyin1992andM.Sdegreeincomputersciencein1994fromKoreaUniversity,Seoul,RepublicofKorea.In2003,hecametotheDepartmentofCISE,UniversityofFlorida,Gainesville,Florida,USA.HegraduatedfromUniversityofFloridain2009withhisPh.D.degreeincomputerengineering.InKwanYualsoworkedatKoreaInstituteforDefenseAnalysisduring1994andSoftforumCo.Ltd.during1999. 116