现代网络业务流的几个基本定律

(自然科学版)355JournalofSouthChinaUniversityofTechnologyVo.l35No.520075(NaturalScienceEdition)May2007文章编号:1000565X(2007)05005406收稿日期:20060314*基金项目:(3139)作者简介:(1961),,,,.Emai:[e-mail]现代网络业务流的几个基本定律*陈云龙叶梧冯穗力(,510640)摘要:为了采用有物理意义的参数,在多个时间尺度下对现代网络业务流进行建模,考察了网络流量长相关(LRD)的基本特征,提出了业务流中满足的几个基本定律,揭示了在流量中描述LRD定量关系的参数c(或cf)流量聚集级m平均到达率l之间的基本关系,并通过实际测量的数据加以验证.所提出的定律表明:(1)流量确实存在LRD行为;(2)平均到达率(TCP和IP流等)与参数c(或cf)存在一定的统计定量关系.关键词:因特网;业务流;自相似;长相关;流量模型中图分类号:TP393文献标识码:A()(EthernetLANs,CCSN/SS7,ISDNVideooverATM):[18]..(LRD),(SRD);,LRD([9][1012][13][14])[15].,,.Weibull,(QoS),,..[16].-,.,.,QoS[14,1718],[1920].[21],,,.,,.,,,.,,().LRD,,,,.:.1现代网络流量与长相关X={Xn,n!Z+},n(T,)()Xn=N[nT]-N[(n-1)T].tN(t)=∀t0dN(x),dN(t).Xn,:=E[Xn];2=Var[Xn]=E[(Xn-)2];Cov(Xn,Xn+k)=E[(Xn-)#(Xn+k-)]=X(k,T);()(ACF,)!(k,T)=Cov(Xn,Xn+k)/2;(PSD)f(∀)=12p∃k=-∃X(k)e-jk∀,∀![-p,p]X(k)=∀p-pf(∀)ej∀kd∀,,∀=2pf.,f(0)=12p∃k=-∃X(k).,,,;,()(WSS),(2).,,2;!(k,T)k();,n%n+k,X1,X2,&,Xn,!(k,T)=0,k%0.LRDm,[2225]:X={Xn,n!Z+}mX(m)=X(m)n,n!Z+,X(m)n=1mnmi=(n-1)m+1Xi.X(m):Xnm,,.X(1)=Xn,1Xn.,X(m)(m1)X(1)().X(m)Xn.,X(m):(m)2(m)(m)X(k)!(m)(k,T).X,X(m),2(m)=2m+2m2mk=1(m+k)X(k)2(m)=2m+2m2m-1s=1sk=1X(k).X,.N,X=E[Xn]=1NNi=1Xi=;Var[X]=E[(X-EX)2]=2/N.Xn,mm.,0[24],Var(!X)=2[1+#N(!)]N,#N(!)=k%0!(k,T)N.X∃(0∋∃∋1),m!Z+,[26]:(()Var[X(m)]=Var[X]m∃;())!(m)(k,T)=!(k,T);(∗)∃H∃=2(1-H),HHurst.,,∃=10;,.X∃(0∋∃∋1),k(()Var[X(m)]=Var[X]m∃(1)())!(m)(k,T)+!(k,T),m+∃(2),m+∃,X(m)1m.1mm+∃0(,).,m+∃,,.XLRD,T,(),∃k=0X(k)=∃,555:,,,X.,LRD:Cov(Xn,Xn+k)~k-∃,k+∃0∃1;(SRD):Cov(Xn,Xn+k)~ak,k+∃,0a1;,SRD,∃k=0X(k)∃.,k,X(k),LRD,SRD.LRD,X(k)~ck-∃,k,0∃1(3)fX(∀)~cf∀∃-1,∀+0,0∃1(4)2(m)~2m-∃,m,0∃1(5)∃=2(1-H),(3)~(5),.∃=2(1-H),,H;c,LRD,.,.2实际流量测量,T,{Xn}n!Z+,,m{X(m)n}n!Z+.,3h,n=3,3600/T.,,X(m),mX(m),S(m)n=mX(m)=nmi=(n-1)m+1Xi,m.,LRD.1km,c(m)S∀cm2H(6)LRD,(2),km!(m)(k)∀!(k),(m)X(k)(m)X(0)∀X(k)X(0)(7)(1)(m)X(0)=X(0)m-∃,S(m)=mX(m),(m)S(k)=m2(m)X(k),(7)(m)S(k)m∃-2∀X(k).k+∃,(m)S(k)∀c(m)Sk-∃m,,∃m,c(m)Sk-∃mm∃-2∀ck-∃([2728],).k,c(m)S∀cm2-∃=cm2H.1:mc(m)Sc.HurstH=0#5SRD.2l,ml(m)l(m)∀ml(8)l.Xn=N[nT]-N[(n-1)T],l=limT+∃XnT,T,ml(m)=limT−+∃mX(m)nT−=limT−+∃mk=1X(n-1)m+kT−=mk=1limT−+∃X(n-1)m+kT−=mi=1l=ml.2:ml(m)lm.3m(m!Z+)S(m),(m)S(k)c(m)SS(m)l(m)c(m)S∀(l(m))2Hb(9):b=cl-2H.(8)m(7)(9).56(自然科学版)353c(m)Sl(m).3定律的检验及应用说明[29](12).12[29]c^fc^,c^=2c^f%(1-^&)Sin(p^&/2)[30],^&=2H^-1;N1sN100msN10ms1s100ms10ms.34(6)(8)(9).1~4,∃,,1s,LRD,.:(1)LRD,;(2)H(∃),,H,H,AV,http:.~darryl/;(3),,,,;(4)[31],,,1Table1MeasuringresultsofflowtracePeak/01Night/01Peak/00Night/00H^fc^l^fH^fc^l^fH^fc^l^fH^fc^l^fN1s0.76159.806049.900.764.4662.7900.7571.188225.900.784.77773.68N100ms0.755.03834.990.730.15230.2800.741.84502.530.760.16140.37N10ms0.740.16350.490.800.00360.0280.750.03760.250.780.00310.042Table2MeasuringresultsofpackettracePeak/01Night/01Peak/00Night/00H^pc^l^pH^pc^l^pH^pc^l^pH^pc^l^pN1s0.8835830.0001113.00.73995.910040.060.862935.000444.750.83605.023063.51N100ms0.88643.396111.30.7233.62004.000.8792.58044.490.8316.31006.35N10ms0.8810.55911.10.760.80710.400.881.6194.450.870.25540.633Table3CalculatingresultsofflowtracebylawsprovedinthispaperPeak/01Night/01Peak/00Night/00H^fc^l^fH^fc^l^fH^fc^l^fH^fc^l^fN1s0.74149.114049.000.805.70562.8000.7537.600025.000.784.08664.00N100ms0.744.93764.900.800.14330.2800.751.18902.500.780.11260.40N10ms0.740.16350.490.800.00360.0280.750.03760.250.780.00310.044Table4CalculatingresultsofpackettracebylawsprovedinthispaperPeak/01Night/01Peak/00Night/00H^pc^l^pH^pc^l^pH^pc^l^pH^pc^l^pN1s0.8834964.0001110.00.73884.970040.00.885361.000445.000.87771.300063.00N100ms0.88607.607111.00.7226.73004.00.8893.16444.500.8714.04006.30N10ms0.8810.55911.10.760.80710.40.881.6194.450.870.25540.63575:H;(5)(6)k∃,.cLRD,,,,;,,,c.[32].4结语LRD,HurstHLRDc,.c,.,.参考文献:[1]WillingerW.Thediscoveryofselfsimilartraffic[J].PerformanceEvaluation,2000,1769:493505.[2]LelandWE,TaqquMS,WillingerW,eta.lOntheselfsimilarnatureofEthernettraffic(extendedversion)[J].IEEE/ACMTransactionsonNetworking,1994,2(1):115.[3]PaxsonV,FloydS.Wideareatraffic:thefailureofpoissonmodeling[J].IEEE/ACMTransactionsonNetworking,1995,3(3):226244.[4]CrovellaME,BestavrosA.SelfsimilarityinWorldWideWebtraffic:evidenceandpossiblecauses[J].IEEE/ACMTransactionsonNetworking,1997,5(6):835846.[5]WillingerW,PaxsonV,TaqquMS.Selfsimilarityandheavytails:structuralmodelingofnetworktraffic[M].AdlerR,FeldmanR,TaqquMS.APracticalGuidetoHeavyTails:StatisticalTechniquesforAnalyzingHeavyTailedDistributions.Boston:Birkhauser,1998:2753.[6]RiediRH,VehelLJ.MultifractalpropertiesofTCPtraffic:anumericalstudy[EB/OL].[20051019].http:.~riedi/.[7]ParkK,WillingerW.Selfsimilarnetworktrafficandperformanceevaluation[M].NewYork:Wiley&Sons,2000.[8]RollsDA.Limittheoremsandestimationforstructuralandaggregateteletrafficmodels[D].Kingston,Canada:DepartmentofMathematicsandStatistics,Queen/sUniversityatKingston,2003.[9]ErramilliA,WangJL.Monitoringpackettrafficlevels[C].ProceedingsofGLOBECOM/94.SanFrancisco:IEEE,1994:274280.[10]DuffieldNG,O/ConnellN.Largedeviationsandoverflowprobabilitiesforthegeneralsingleseverque