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1、EvolutionoftheInternetMapandLoadDistributionK.-I.Goh,B.Kahng,andD.KimSchoolofPhysicsandCenterforTheoreticalPhysics,SeoulNationalUniversity,Seoul151-747,KoreaAbstract.WetracktheevolutionaryhistoryoftheInternetattheau-tonomoussystems(ASes)levelandprovidetheevidenceth
2、atitcanbedescribedintheframeworkofthemultiplicativestochasticprocess.Itisfoundthatthefluctuationsarisingintheprocessofdiversifyingconnec-tionsofeachnodeplayanessentialroleinformingthestatusquooftheInternet.ExtractingrelevantparametersforthegrowthdynamicsoftheInternet
3、topology,weareabletopredicttheconnectivity(degree)expo-nentγoftheInternetASmapsuccessfully.Wealsointroduceaquantitycalledtheloadasthecapacityofnodeneededforhandlingthecommu-nicationtrafficandstudyitsdistributionovertheInternetacrossyears.Theloaddistributionfollowsapow
4、erlawwiththeexponentδ≈2.0and1.8theloadatthehubscaleswiththenetworksizeash∼N.1IntroductionDuringrecentyears,theInternethasbecomeoneofthemostinfluentialmediainourdailylife,goingbeyondinitsroleasthebasicinfrastructureinthetechnolog-icalworld.Explosivegrowthinthenumbero
5、fusersandhencetheamountoftraf-ficposesanumberofproblemswhicharenotonlyimportantinpracticefor,e.g.,maintainingitfreefromanyundesiredcongestionandmalfunctioning,butalsooftheoreticalinterestsasaninterdisciplinarytopic[1].Suchinterests,alsostim-ulatedbyotherdisciplinesli
6、kebiology,sociology,andstatisticalphysics,haveblossomedintoabroaderframeworkofnetworkscience[2,3,4].TheInternetisaprimaryexampleofcomplexnetworks.Itconsistsofalargenumberofveryhet-erogeneousunitsinterconnectedwithvariousconnectionbandwidths,however,itisneitherregula
7、rnorcompletelyrandom.Intheirlandmarkpaper,Faloutsosetal.[5]showedthattheInternetattheautonomoussystems(ASes)levelisascale-free(SF)network[6],meaningthatitfollowsapower-lawdistributionp(k)∼k−γ(1)dinnodedegreek,thenumberofconnectionsanodehas.ThedegreeexponentγoftheASm
8、apissubsequentlymeasuredbyanumberofgroupstobeγ≈2.1.Emergenceofsuchpower-lawdegreedistributioncallsforexplanationandunderstandingofthebasic
