互联网中的标准结构熵的时间演化分析

:2006203228:(2002EB010154):(1965-),,,;(1959-),,,,2712200612()JournalofNortheasternUniversity(NaturalScience)Vol127,No.12Dec.2006:100523026(2006)1221324203,,,(,110004):Internet,Internet,rieslingInternet,Internet20004013792004501318,0112%,Internet:Internet;;;:TP393.03;TN915.05:A,,,,,,[13]1,,,(),,(),,,,,[4,5],,,,,,;,,,,,,,,,,,,,,,,,[6],,,[7,8],,[9],,,,,,,,,,,,,,,,,,,,,,,,,;,,,,H(X)X,p(xi),i=1,2,,q,p=(p1,p2,,pq),H(P)H(X)=-6qi=1pilnpi=H(p1,p2,,pq)=H(P)(1),6qi=1pi=1,H(p)(q-1),q=2,p1+p2=1,p,(1-p)21998A.L.Barabasi2004Internet[10]:H=-6nk=1p(k)lnp(k),,p(k)Internet;nInternet;HInternetInternet,Internet,H=lnn,n,,,d,,6nv=1dv=nd,,1/nInternet,Hmax=-6nk=11nln1n=-n1nln1n=lnn(2)Internet,,,H=lnn-[n(n-1)]ln(n-1)(3),,1/n,(n-1)/nHmin=-1nln1n+n-1nlnn-1n=lnn-[(n-1)/n]ln(n-1)(4),Internet,Internet,,Internet:Hs=H-HminHmax-Hmin(5)Internet,,Internet,InternetInternet,Internet3CAIDArieslingapan-jp2000420045Internet,Internet,,1,01992,01984,rieslingapan-jp,20004,Internet(InternetStandardEntropy),Internet2000420045,,riesling200040.3792004501318,0112%apan-jp20004013882004501297,0118%,4,Internet,,InternetInternet523112:,,Internet,Internet1InternetFig.1RelationofInternetstandardentropyandtime,Internet,,,Internet,,,Internet,Internet,4(1)Internet,,(2)Internet,Internet,(3)Internet,,,,,:[1]OlbrichE,HeggerR,KantzH.Localestimatesforentropydensitiesincoupledmaplattices[J].PhysicalReview,2000,84:2132-2135.[2],,WebEmbeddedWebServer[J](),2002,23(11):1021-1024(HanGJ,WangJD,LinT.Designandrealizationofembeddedwebserverbasedonwebmanagement[J].JournalofNortheasternUniversity(NaturalScience),2002,23(11):1021-1024.)[3]CoverTM,ThomasJA.Elementsofinformationtheory[M].NewYork:JohnWiley&Sons,1991.21-42.[4]DavidP,JamesP.Structuralinformationintwo2dimensionalpatterns:entropyconvergenceandexcessentropy[J].PhysicalReview,2003,67:251-264.[5]ClitonD.Informationentropyofcomplexstructures[J].PhysicalReview,1997,56:5211-5215.[6]LiW.OntherelationshipbetweencomplexityandentropyforMarkovchainsandregularlanguages[J].ComplexSystems,1991,5(4):381-399.[7]BeongkuA,SymeonP.Anentropy2basedmodelforsupport2ingandevaluatingroutestabilityinmobileadhocwirelessnetworks[J].IEEECommunicationsLetters,2002,6(8):328-330.[8]ArnoldD.Information2theoreticanalysisofphasetransitions[J].ComplexSystems,1996,(10):143-155.[9]VinkRLC,BarkemaGT.Configurationalentropyofnetwork2formingmaterials[J].PhysRevLett,2002,89:1-4.[10],[J],2004,(6):1-3(TanYJ,WuJ.Networkstructureentropyanditsapplicationtoscale2freenetworks[J].SystemsEngineeringTheoryandPractice,2004,(6):1-3.)ResearchontheChangingPrincipleoftheInternetStandardStructureEntropyXUFeng,ZHAOHai,HATie2jun,ZHANGYong2qing(SchoolofInformationScience&Engineering,NortheasternUniversity,Shenyang110004,China.Correspondent:XUFeng,E2mail:[e-mail])Abstract:AccordingtothetheoryofShannonentropy,theInternetstandardentropywasdefined.ByusingtheglobalInternetmonitordataprovidedbyCAIDASkitterproject,thechangeoftheInternetstandardentropywithtimewerecomputedandtheresultsusingthemonitordatagotbyrieslingshowedthattheInternetstandardentropywasreducedfromthemaximum01379inApril2000to01318inMay2004,i.e.,thereductionpermonthwas0112percent.Ontheotherhandthecomputingresultsusingthemonitordatagotbyapan-jpshowedthattheInternetstandardentropywasreducedfromthemaximum01388inApril2000to01297inMay2004,i.e.,thereductionpermonthwas0118percent.ThedifferencebetweenthemrevealedthattheInternetstandardentropytendstoreduction.ItimpliesthatthereisaninformationmetabolismintheevolutionprocessofInternetsmacrotopologicalstructure.Keywords:Internet;smallworld;scalefree;routingalgorithmwithlinkpriority(ReceivedMarch28,2006)6231()27