RESULTSON N-DIMENSIONALDISCRETESPACESELF-SIMILARITY Seungsin Lee$, Rajesh Narasimha*, Raghuveer MRao# $SamsungInstitute
Georgia Tech · 2006
Inthecurrent work, wediscuss thevarious classes of self-similar processes thatcanbegenerated bymatrix New formulations andmodels wereproposed for scaling operation andtheconditions under whichthey exist. describing statistical self-similarity in a general N- We provide relationship withtheHurst exponent H andthe dimensional setting inourearlier work[1]. Itwasshown fractional parameter r fortheseclasses ofself-similar thatby usinga matrix-scaling operator fordefiningprocesses. We foundthatthepowerspectrum ofthenstatistical self-similarity, awideclass ofcontinuous-space dimensional stationary random field under bilinear warping N-dimensional processes canbecharacterized asself-similar transform isthesameaspowerspectrum ofthenwithrespect tospecific matrix classes. Inthis workwe dimensional fBmfor0<H <1[12]. Merging isabasic discuss thevarious classes ofself-similar processes that can operation carried outinthepresent dayhigh-speed networks begenerated bymatrix scaling operation andtheconditions duetosharing ofthecontents androuting decisions. underwhichtheyexist. We provide relationship withthe Majority ofthemultimedia traffic ontheInternet hasbeen Hurst exponent H andthefractional parameter rfortheseshowntohaveself-similar properties [13, 14]. Basedonthe classes ofself-similar processes. Intheend,we provideformulation ofscaling, weprovide someinsights intothe someinsights intothemerging ofself-similar trafficmerging ofself-similar traffic streams andshowthatthe streams. merging process isself-similar ifeachoftheconstituent traffic streams isself-similar withdegree H.