.. \8 rurc,,,h defined in Sedion 1,1, h~ical ",,,k di.<taw:".' a,,' thE' diff~r('!1CC" LX',w""n lfJll,ecllli"e ,\.ait. add"",,,,", pithE'r 1m ,JIIC<!;ical volurn~" t,«etber or lor .1'II<t O<le I":"kal ,,,,Iume ill a ~iYen or.ora~" oyotelll 'Iwklmd, l\ot." thai v,,' ,,,w]pxod ""n. ""dn""", in tbio way solely h· H •• ldling 1''''1.'''''. That i, 10 ('orn~ up with model, in the forIll of probability di,tributi<m nm'ticn, thai can loe uood VJ ~enel'ate ,Ian add[("""
lor , .. ntbetic v,"Jl'klnad" Comrary VJ 'Ill'" Son •• I~"pl" Illight "xI~d., .m,J)"/.in~ <tarl
".<Id"",;.-.,. ill t.hi' vmy i, nol "'" n",lul in wld<>rotruldin,,, tbe I'Jcality di'll'ibuIYJll of the o!!.ta ,torc<l in a 'tora~e .y,[ellL Thl> is du.e VJ the f2t('l that a .;ill~lE' 1<>;Iiml ",Ium,' m"y be svread o"el' "'\pml phy;;ic,,1 ,,,Inllx,,. Th~rC'l'or~ I'M) cOll"Ceutiw ,tml ado"""" in
!!. t.m .. " 1m the 'am~ Ioo;icru ,"olume may loe l'el'nin~ "J lwo diUerem phY'~'al ""IUH'"
'~ld h.'~J colloecuth-e " "''' addr",."'" for diff .. rPnI 10!"ie,,1 volnllX" may k referrin~ to thE' "Ul.' phy"ic,,1 ",Inn[(' In ,hol't, v,'C ('all not Idl how tile d"ta ;s di,triblHed !UlJOn~
til<' phy,iuJ volum'" ming the ic>:>:kal ,,,,",,k disl<1.llces,
BeleW! are [he <1.ll~IY'i.; lesulb 01 OLTP logic,,1 ",,,k rli,,,,",,,,,< lor logkal volume numl.,! ~II :uld W .. b l<:»:iuJ ",ocic di,l:ln'>::l' for logi"al w~unX' nunlloel' 0,
(l,;;.1
Table (i.l~ gi
w,
th' h,y >t·!!.!';"i", 01 II., OLTP I<:»:i .. al scd rlis,",uw", m~""urcd in bh>eks fm I<:»:i .. al volume lllllllloer 20. The diMribul> HI of lh,.' dat,!!. ,.-.1 is In<ili ,,,I)' ,h'm,," with the C(x,jjic-iellt of ,h,w ",JnE' 01 0.02 The hhtCl':l am of Ih~ oata set wilhmll (~illicroi, ,llOvm ;11 f'i~ure ~.12 Ta~1c 6.19 oh'"",'8 a frequency t!!.ble of the abwlnte vail", of ,be data oe\, 'lYe have Vr~."'llted ,he al::..ol,,", valLm' t.o minimm' 'h, nnrnl.,r of in"''''ab/bi", m," whidl tlw •• 'g·i('al ,." k di-t')Il("'" arc split.
Table !i,~11 ~i,," the fu')' .<t!!.tj,t.ir., of ,.1", W .. b loo;i('al ",,,k di,twlC~" measurC'<:! in blc",ks 10< logie,,1 vol UnLE' llumber 0 'Ll.e "oefficient ,,f ,k"w ;, ""l'O lneallin~ Iha, 'he dis[r ibu-ti", 01 Ihi' dam "Ct is ,ymmetric. The disttiLUl"~l 'Jf I'J~ieal sed di.""'l""" for all th'
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('HArTER (; RRsur:TSHallp;c Count
,iJ
Thhh, G. I~; n""II~"lCY I,able of ahsolute (lLTI' \ogleRI ,eek di"ane", fur lugical ,'c.lUlne
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\\'I'U 1<'1':;"01 VOIUlIl(" i, "h, 'Y'lllnet.ri", TI,,· r"b-, of tIM' wnnl><" of'l'o,il.iw k>gil al ",,·k dblallees [.U Ihe llUlllUI'r of lJI'P;R live "'1':;"01 ,,,,,k ~ i>,-"""" "OW'
w"
,*"",,.w~ t h",- for each j)(",ili,,, kJg:ical ,eek U"'1\ll(OC ,h<'1'<';'; a (OOl""ron~illg ll('gi\l'V" II'I':ical """,k eli,·'an", of t he "'~ Ile ""'gHit,tlle, S"dL ,'allies do nol. lloces",.-ily o(em ill ckJ,e 3uccesoioll anM "" have HO explanaliuH fot LlLi' ""y inl.e!'e,;lil.l.!> pheu<ml<'llcu. All explaualiUlJ lllay well Ue fOUllU uy dC''''lllining ho\\' the ",,,~d, "Ignrithlll(.,::, elllplo)",,1 by LlLe awlh.al.ion ,,,!tk(,;<, T alJlc G.21 '" 0 frf'qucnI-y ""hie Ii the "t-",.nl"te Weh Iugi( al
".·k
Ili,L:Ul('e, f(~logi",1 ,,,11111>" llI11nile! 0 The hiSlOf!:mm of th<' data "" wi,hout outii"r, i, ,hno,,-n in Figure Ii, n ,
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,
--i
I
I I
! L
, • •• • • " "
... . ... ... .
F;~1J'~ 6. 12' )I\!I(I~rnm of OL'll' ~ktll """k di.;l"",.,,; rm logi,'& ,'olum .. ILll1"I~'r :.'0 wilh""t
,mil,.."
_ ....
l'i~\llC G 1:1 Hi,l,~r~",.oj
w,· )'
jog""J ",,·k ,Ii"",,,",, 10'- logic,,1 ,,-oium(' !!lWl.l~·! 0with'~lt ,,,,tlll'T!
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fabic (,,2D: Statistic~ of Web l~ical """k di"~n,,,, lor lUgi",,: WJ:lIttLf II
G.5.::l !l.lodellillg Logical &'"k Di~ta"ce
Sin(,c 'he lc.gienl ;;('Ck d"t"n", p"rmnetcr " di""H~". it. is nrrlloptiate Iu me ~ rrob.<l.bilit: ml'"" fWH'l"m t.o model i" Sl~\i",ico fm l~)lh tlH' OLl'P aml \Ye), :u!',i,',d ""k rli,l;l"""
'how ,h"l ,1)(, r"n~e of ,"Zllu~" d,Zl' the l()~kZll SCf·k di,I,,"ec eml t"k., 0<1 i, vcry lm'ge, As ~ rf,ull., Jefinin~ ~ mnJom vmi~bJe '" 'he iogical seek disi.allCf of an I/O lkjllbl
"nd formulating" prob"bility In;,,,-,< funl'tion with ,,11 th~ I~)"ibl~ "dues" nd, fp,,,ibk Tlwreforc we ,ul'J!:e,\ two "Pfl)'(>a<'h,,, t.h"t ""n oc us<cxl \0 mrxid \hc lc.gknl seck di,(mlC'8
III the fi"bl. ~l'l'rc«ch we ,U!0Wil Ilw\ a random vruiable, X. slJOuld be defineJ as
tl,~ ';l"!'," 11IJn'","!' in whi,l! Lhe logi,""l ,,,,,,1 di,t."n('e of an I/O reqlH',l will fall "lld
!lH'll ,h4iw' ~ I'm),,,),ili,,: rna.,> fUllct.!O<l ill ("1m, of X, n,,' ~x"rnl'le, we C~ll Jdille ~
prol",")ili'y funeli", of X ,,'in~ "DlN" fUI. to m()(ld ,Iw' ".h",~ut,· Weh logi,',J ",,·k
,hSlIiliOO> as,
1'("') 11,41\'0.';
i"
.~ -,
p{rJ 1I,1~lfi
J"
.~ _. ~.PI",)
1I,(jj.!f;Jm
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(; :,_ U1GI(;AL SEEK DISTANrE
.'lumber
Table 6_21- Fr""1uency table of alHolutc Web logical SO<'k distances for logical Yol11me n11mher 0
p(x) 1l,1l1ll1 for .J; = 18,
Similarly a I'rohaLilit)- ['ili{;lion 01 X call be <ietlu"d lor the emire mnp;e of Web k'l':i<'al """k distm1<'cs and not jrnt the abwl\ltc val\le"_ 'T() )',cncrate " i<¥;i,:al "",k di.>lauoos lor a symhetic "OlkJo.-.d wp'BsenUltive of tho Weh wOlklo .. d. one ('an 11"", Ihis l'rolialiility l,motion 10 !\euemte " ran~e llumhers. Then tor oa"h 1 all~C Illll\lhcl
~"lH'rat.ed, "'Y k. pmduce a """l()m value w\thin (he l'Uli(, ollrulge k, I'o.- instflllce, if mIL)',e IL11mhe .. I h"., "ran~~ (.2.IKKUKII • III in a h'eq"ency ~alile such"" Talile fi.2L then for efl('h ""Ille of I p;enerated '" " range Il11mher " logi""j ""eK <ii,tallce yal\le between -2,(j(j(J,(j(j(J and Il should he pl'oduced,
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CHilpi'}:H 6 HJ;'Sl·'LTS, l 1 •
~
B. S"e"Ilti Approach
The 'if{lTl~ "l'pro;1,Ch ilLy"i""" filL(\iTl!,;" prol»,hihty (lr'mity flllH,tMlTl lH"t.('hiTl~ " gi'''lL dala 'IN of logical =k Ji,'anCC'b as an aw,'O~';malc mod". 1'hi, mcans that we have to prcsOllll(, that til(' l.we>,i ""k di,I.",,·,· l'''m11H'\('' i, a contilL'""" ",ri"hl<·. "I,,·, "II it Ci<J1 lak on ,,,lues Jl'OllJ a "t'rV large rang"_ Tlm""",r. it 'ho11ld be ck"". from f'i~"""
n. 12 ,,,,d ii.l:ll.hal \lOlLe of I.he "'Hlall',-obabilil;- dele,ily f"''''I,ioll' would iii· I,he lo!;lcal
=k di,tancc, for both OJ:TP "wi W .. b.