基于相空间重构的Internet业务流量非线性动力学分析

39820058JOURNALOFXI'ANJIAOTONGUNIVERSITYVol.39№8Aug.2005Internet,,(,710049,):,L,TCP-RenoREDDropTail,TCPUDP.,.:,,Lyapunov,Hurst1,;,Lyapunov,.:;;:TP393:A:0253!987X(2005)08!0796!04AnalysisonNonlinearDynamicsofInternetServiceTrafficBasedonPhaseSpaceReconstructionWangLi,LiZengzhi,XueKe(InstituteofComputerSystemArchitectureandNetwork,Xi'anJiaotongUniversity,Xi'an710049,China)Abstract:ThevariabilityofTCP-Renocongestionwindow(CWND)undertheREDandDropTailmecha-nismandthetraffictraitofTCPandUDPwithsharinglinkswerestudiedbasedontheconceptofphasespacereconstructionwhichisamethodstudyingbehaviorsofdynamicsystemthroughLdimensionstimeseriesthatgainedfromthemeasurementfunction.Asinglescalartimeserieswasreconstructedintoahigh-dimensionphasespacebythephasespacereconstruction,thenthechaoticcharacteristicsofthehigh-dimensionphasespacewasfurtherresearched.TheresultsshowthatthecorrelationdimensionsofCWNDvariablevalueundercertainexperimentalconditionsarefractional,thelargestLyapunovindexispositive,thehighdimensionspacehaschaoticcharacteristicsanditsHurstparameterisapproximatedto1.Mean-while,thespacehasstrictsecondorderself-similarity.Thecorrelationdimensionoftrafficvalueisfrac-tional,thelargestLyapunovindexispositive,andthespacealsohaschaoticcharacteristics.Keywords:servicetraffic;phasespacereconstruction;chaoticcharacteristic,(QoS).[1!5],.Internet,[6!9]、TCP-Tahoe[10]、REDTCPUDP[11]、TCP!RED[12]、REDTCPUDP[13].,REDDropTailTCP-Reno.:2004!09!24.:(1975),,;(),,,.:(90304006);(20020698018).1[14]dSdt=F(S)(1):S=(s1(t),s2(t),…,sn(t))S,Sn.(1),,A,,.(1),.H=(h1,h2,…,hL),L(Ln)X=H(S)(2)(1)[15,16].L=1,(2),[16].H,x(t)=H(S),t=1,2,…,N(3)n=(x(n),x(n+τ),x(n+2τ),…,x(n+(d-1)τ))(4):τ,;n=1,2,…,N-(d-1)τ;d.,τd.[17]τ,Cao[18]d.、、、.GP(Grassberger-Procaccia)、Lyapunov.2,2,1,Lyapunov1;2,,Lyapunov2.21,100s,0.1s,NS-2,Matlab6.5OpenT-STOOL[19].R1、R2,R1,R2;LR11C=0.1Mb/s,τ=10ms,b=4,NS!2.2TCPLR,REDDropTailw,2TCP-RenoREDDropTailw2.2C=2Mb/s,τ=10ms,b=50,RED5TCP10UDPLR,NS!2.Tτ3.τ=2ms,d=3,4.(a)RED(b)DropTailw1:1TCP!Reno;w2:2TCP-Reno2TCP!RenowI5,II'6.7978,:Internet3T45633.111,REDDropTailTakens[20],Kantz[21]Lyapunov,1.11Lyapunovw1w2Lyapunovw1w2RED1.10931.10390.19350.1600DropTail1.14051.13010.19250.16001,w,Lyapunov.,1,TCP-RenoREDDropTailw.,[22]wHurst,2.21HurstHurstREDw1w2DropTailw1w20.88980.90000.91720.89172,wHurst1,,1w.3.224,,,Lyapunov,3.32LyapunovLyapunovRED2.03410.01303,,Lyapunov.,2,TCP-RenoRED.,56,,3,,.,89739TCP-RenoREDDropTail,TCPUDP.4TCP-RenoREDDropTail,TCPUDP.,,Lyapunov,,.,/,,,.:[1]DistributedManagementTaskForce.Commoninfor-mationmodel(CIM)specificationversion2.2[EB/OL].!02!11.[2]DistributedManagementTaskForce.Commoninfor-mationmodel(CIM)coremodelversion2.4whitepa-per[EB/OL].!2!11.[3]TB-GN.010-2.0-94,Managementarchitecturever-sion2.0[S].[4]GB910!2000,Telecomoperationsmapapprovedver-sion2.1[S].[5],,,.[J].,2004,38(6):571!574.[6]LelandW,TaqquM,WillingerW,etal.Ontheself-similarnatureofEthernettraffic(extendedversion)[J].IEEE/ACMTransactionsonNetworking,1994,2(1):1!15.[7]PaxsonV,FloydS.Wide-areatraffic:thefailureofPoissonmodeling[J].IEEE/ACMTransactionsonNetworking,1995,3(3):226!244.[8]BeranJ,ShermanR,TaqquMS,etal.Long-rangedependenceinvariable-bit-ratevideotraffic[J].IEEETransactionsonCommunications,1995,43(2!4):1566!1579.[9]CrovellaME,BestavrosA.Self-similarityinworldwidewebtraffic:evidenceandpossiblecauses[J].IEEE/ACMTransactionsonNetworking,1997,5(6):835!846.[10]VeresA,BodaM.ThechaoticnatureofTCPconges-tioncontrol[A].TheConferenceonComputerCom-munications,TelAviv,Israel,2000.[11]RanjanP,LaRJ,AbedEH.BifurcationsofTCPandUDPtrafficunderRED[A].10thMediterraneanCon-ferenceonControlandAutomation,Lisbon,Portugal,2002.[12]LaRJ,RanjanP,AbedEH.NonlinearinstabilitiesinTCP-RED[J].IEEE/ACMTransactionsonNetwor-king,2004,12(6):1079!1092.[13]RanjanP,AbedEH,LaRJ.NonlinearityofTCPandinstabilitywithRED[A].InternetPerformanceandControlofNetworkSystemsIII,Boston,USA,2002.[14].[D].:,1998.[15]PackardNH,CruchfieldJP,FarmerJD,etal.Ge-ometryfromatimeseries[J].PhysRevLett,1980,45(9):712!716.[16]TakensF.Lecturenotesinmathematics:detectingstrangeattractorsinturbulence[M].Berlin:Spring-er-Verlag,1980.366!381.[17]FraserAM,SwinneyHL.Independentcoordinatesfrommutualinformation[J].PhysRevA,1986,33(2):1134!1140.[18]CaoL.Practicalmethodfordeterminingtheminimumembeddingdimensionofascalartimeseries[J].Phys-icaD,1997,110(1!2):43!50.[19]DPIandUniversityofGöttingen.OpenTSTOOLsoftwareanddocumentationareavailable[EB/OL].!09!16.[20]TakensF.Lecturenotesinmathematics:dynamicalsystemsandbifurcations[M].Berlin:Springer-Ver-lag,1985.[21]KantzH.ArobustmethodtoestimatethemaximalLyapunovexponentofatimeseries[J].PhysLettA,1994,185(1):77!87.[22]TaqquM,TeverovskyV,WillingerW.Estimatorsforlong-rangedependence:anempiricalstudy[J].Frac-tals,1995,3(4):785!798.()9978,:Internet