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(www-ptex@ascii.co.jp) %%based on dvips(k) 5.86g Copyright 2001 Radical Eye Software (www.radicaleye.com) %%Title: paper.dvi %%Pages: 10 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: Times-Bold Times-Roman CMSY10 CMR8 Times-Italic CMMI10 %%+ CMR10 CMMI8 CMEX10 CMSY8 CMMI6 Helvetica %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips paper.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2002.05.16:1453 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /dir 0 def/dyy{/dir 0 def}B/dyt{/dir 1 def}B/dty{/dir 2 def}B/dtt{/dir 3 def}B/p{dir 2 eq{-90 rotate show 90 rotate}{dir 3 eq{-90 rotate show 90 rotate}{show}ifelse}ifelse}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)(LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse} forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{ BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat {BDot}imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B /M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M} B/g{0 M}B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{ 0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: 8r.enc % @@psencodingfile@{ % author = "S. 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All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 3 /asteriskmath put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 32 /parenleftBigg put dup 33 /parenrightBigg put dup 56 /bracelefttp put dup 58 /braceleftbt put dup 60 /braceleftmid put dup 62 /braceex put dup 80 /summationtext put dup 116 /radicalbt put dup 117 /radicalvertex put dup 118 /radicaltp put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 97 /a put dup 98 /b put dup 104 /h put dup 105 /i put dup 109 /m put dup 110 /n put dup 112 /p put dup 113 /q put dup 116 /t put dup 120 /x put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 2 /multiply put dup 17 /equivalence put dup 20 /lessequal put dup 21 /greaterequal put dup 32 /arrowleft put dup 102 /braceleft put dup 103 /braceright put dup 121 /dagger put dup 122 /daggerdbl put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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0C0B8B73E940F9C6142C7C9D5F8D45373DCE24664470570AD76085B99A3C48FF 35B88A76B620DDB938A0FC96290E8689B7661A2D6CBA2696FC733D4D5A52FD09 4806C078E9107EFB37AFA993A427C5BE3A4DD540381396AEFAA3B589FFA4AB80 50C6EF252ED9C1C45613DC7B4C0FB04EF81C210C94A0B943F421381A93AF6A4A B21C045F8CCC970F06E2D56605BE3001874AF8302EE9A7B8F8282E0B8A92BBD0 39C760CC42B1523542F9553901E2B5FE9C193B678CDCF0504327FF4E15602023 3DF8AAFE547560860104716444014B09CE83B52473300368A488F9ADF6F26E07 337EE7411B4D47A955EDDD6856D3893741332C2F48E8732AC96B58C5F4E43A27 A1B86A14EEF72F7863F50A864E 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 22 /macron put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 61 /equal put dup 94 /circumflex put dup 103 /g put dup 108 /l put dup 111 /o put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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p Fq 1369 590 a(y) p Fr 1410 626 a(,) h(Hiro) o(yuki) f(Ohsaki) p Fq 2127 590 a(y) p Fr 2193 626 a(and) g(Masayuki) g(Murata) p Fq 3067 590 a(z) 399 769 y(y) p Fr 466 804 a(Graduate) h(School) g(of) g (Information) e(Science) j(and) f(T) -7 b(echnology) h(,) 23 b(Osaka) i(Uni) n(v) o(e) n(rsity) 1250 921 y(T) -8 b(o) o(yonaka,) 24 b(Osaka) h(560-8531,) f(Japan) 1056 1037 y(E-mail:) p Fp 30 w(f) p Fr(t-e) o(guti) n(,) h(oosaki) p Fp(g) p Fr(@is) n(t.osaka-u.ac.jp) p Fq 1146 1179 a(z) p Fr 1212 1215 a(Cybermedia) g(Center) l(,) h(Osaka) f(Uni) n(v) m(ersity) 1250 1331 y(T) -8 b(o) o(yonaka,) 24 b(Osaka) h(560-0043,) f(Japan) 1229 1448 y(E-mail:) 29 b(murata@cmc.osaka-u.ac.jp) p Fo 1667 1701 a(ABST) r(RA) -5 b(CT) p Fn -72 1861 a(A) g(QM) 31 b(\(Acti) n(v) o(e) i(Queue) g(Manage) r(ment\)) g(mechani) r(sm,) h (which) f(perfo) r(rms) f(cong) r(estion) i(contro) r(l) e(at) h(a) f (route) r(r) g(for) h(assist) r(ing) -72 1974 y(the) i(end-) r(to-end) h (conge) r(stion) g(contro) r(l) e(mechan) r(ism) g(of) h(TCP) -12 b(,) 34 b(has) h(been) h(acti) n(v) o(ely) g(studie) r(d) e(by) h(man) o (y) g(resear) r(chers.) 63 b(F) o(or) -72 2087 y(insta) r(nce,) 29 b(RED) e(\(Rando) r(m) g(Early) h(Detect) r(ion\)) h(is) f(a) g(repre) r (senta) r(ti) n(v) o(e) g(A) -5 b(QM) 27 b(mechani) r(sm,) h(which) h (drop) r(s) f(arri) n(vin) r(g) g(pack) q(ets) -72 2200 y(with) 23 b(a) g(pro) r(babili) r(ty) g(bein) r(g) g(propo) r(rtiona) r (l) g(to) g(its) h(a) n(v) o(erag) r(e) f(queu) r(e) g(length) r(.) 28 b(The) 23 b(RED) e(rout) r(er) i(has) h(four) g(cont) r(rol) f(para) r (meters,) -72 2313 y(and) i(its) f(ef) n(fec) r(ti) n(v) o(enes) r(s) f (heavily) i(depen) r(ds) f(on) h(a) f(choic) r(e) g(of) g(these) h (cont) r(rol) f(para) r(meters.) 32 b(This) 24 b(is) g(why) g(man) o(y) g(resear) r(ches) h(on) -72 2426 y(the) k(para) r(meter) g(tuni) r(ng) g (of) g(RED) e(contr) r(ol) i(paramete) r(rs) g(ha) n(v) o(e) g(been) h (perf) r(ormed.) 45 b(Ho) n(we) n(v) o(er) l(,) 30 b(most) f(of) g(tho) r(se) g(studie) r(s) f(ha) n(v) q(e) -72 2538 y(in) l(v) q(estigated) 21 b(the) f(ef) n(fect) h(of) e(RED) f(con) r(trol) i(paramet) r(ers) g (on) g(its) g(perfor) r(mance) g(from) g(a) f(small) h(numbe) r(r) f (of) h(simulati) r(on) g(result) r(s.) -72 2651 y(In) 35 b(this) h(pap) r(er) l(,) i(we) c(the) r(refore) i(stati) r(stical) r (ly) f(analy) r(ze) g(a) g(grea) r(t) f(numb) r(er) h(of) g(simula) r (tion) h(result) r(s) f(using) h(the) g(multi) n(v) n(ari) r(ate) -72 2764 y(analy) r(sis.) 29 b(W) -7 b(e) 22 b(qua) r(ntitat) r(i) n(v) o (ely) i(sho) n(w) f(the) h(relati) r(on) f(betwee) r(n) g(RED) e(con) r (trol) j(paramete) r(rs) f(and) h(its) g(perfo) r(rmance.) p Fm -72 2937 a(K) n(eyw) o(ords:) p Fn 31 w(A) -5 b(QM) 23 b(\(Acti) n(v) o(e) h(Queue) h(Manage) r(ment\)) g(Mechani) r(sm,) e (RED) g(\(Random) i(Early) f(Detecti) r(on\),) g(P) o(arameter) h(T) l (un-) -72 3050 y(ing,) f(Multi) n(v) n(ari) r(ate) f(Analys) r(is) p Fo 1487 3328 a(1.) 29 b(INTR) m(ODUCTION) p Fn -72 3488 a(In) 20 b(the) g(last) h(fe) n(w) e(years) r(,) g(A) -5 b(QM) 19 b(\(Acti) n(v) o(e) h(Queue) g(Manag) r(ement\)) g(mecha) r (nism,) g(which) g(sup) r(ports) h(the) f(end-t) r(o-end) h(cong) r (estion) -72 3601 y(cont) r(rol) e(mechan) r(ism) f(of) i(TCP) -12 b(,) 18 b(has) i(been) g(acti) n(v) o(el) r(y) e(stud) r(ied) h(by) h (man) o(y) f(resear) r(chers) r(.) 26 b(A) -5 b(QM) 17 b(mecha) r(nism) i(contr) r(ols) g(the) h(queue) -72 3714 y(leng) r(th) 26 b(of) g(a) f(rou) r(ter) h(\(i.e.,) g(the) g (numb) r(er) g(of) g(pack) o(e) r(ts) g(in) g(the) g(b) n(uf) n(f) r (er\)) g(by) g(acti) n(v) q(ely) g(dropp) r(ing) g(arri) n(v) r(ing) g (pack) q(ets.) 37 b(It) 26 b(has) g(been) -72 3827 y(repo) r(rted) e (that) g(the) g(A) -5 b(QM) 21 b(mecha) r(nism) i(can) h(solv) q(e) e (se) n(v) o(er) r(al) h(prob) r(lems) g(of) g(con) n(v) o(enti) r(onal) h(Drop-T) -7 b(ail) 24 b(route) r(rs.) p Fl 3453 3794 a(1) p Fn 69 3979 a(RED) 31 b(\(Random) i(Early) g(Detectio) r(n\)) f (is) h(the) f(most) h(popu) r(lar) g(A) -5 b(QM) 30 b(mecha) r(nism.) p Fl 2726 3946 a(2) p Fn 2853 3979 a(A) h(rou) r(ter) h(emplo) q(ying) h (the) g(RED) -72 4092 y(mechan) r(ism) 23 b(is) h(called) h(a) p Fk 23 w(RED) d(r) l(outer) p Fn 2 w(.) 28 b(The) c(RED) d(rou) r(ter) i (ran) r(domly) h(drops) h(arri) n(vin) r(g) e(pack) q(ets) h(with) f(a) h(proba) r(bility) l(,) f(which) -72 4205 y(is) h(calcu) r(lated) h (from) f(four) g(RED) e(con) r(trol) i(parame) r(ters) g(and) h(its) f (a) n(v) o(erag) r(e) f(que) r(ue) h(length) r(.) 29 b(The) 24 b(RED) e(route) r(r) h(does) i(not) f(dist) r(in-) -72 4318 y(guis) r(h) j(TCP) f(conne) r(ctions) r(;) j(i.e.,) f(it) f(use) r (s) g(the) h(same) g(pack) o(e) r(t) f(drop) r(ping) h(disc) r(ipline) h (for) f(all) f(TCP) f(conn) r(ection) r(s.) 41 b(Hence,) 29 b(the) -72 4430 y(implemen) r(tation) d(of) e(the) h(RED) e(route) r(r) h(is) g(simple) r(.) 31 b(Ho) n(we) n(v) o(er) l(,) 25 b(the) g(RED) d(rou) r(ter) i(has) i(se) n(v) o(eral) f(dra) o(wbac) r (ks.) 32 b(In) 25 b(partic) r(ular) l(,) g(it) -72 4543 y(is) d(kno) n(wn) g(that) h(ef) n(fectiv) o(eness) g(of) e(the) i(RED) d(route) r(r) h(is) h(hea) n(v) r(ily) g(depen) r(dent) h(on) f(a) f (choi) r(ce) h(of) g(contro) r(l) f(para) r(meters.) p Fl 3586 4510 a(2,) 12 b(3) p Fn 3742 4543 a(Since) -72 4656 y(it) 25 b(is) g(compl) r(icated) h(to) g(analy) r(ze) f(both) h (TCP) d(and) j(the) g(RED) d(rou) r(ter) i(simulta) r(neou) r(sly) -6 b(,) 26 b(most) f(resea) r(rches) h(on) g(the) f(RED) f(router) -72 4769 y(ha) n(v) o(e) 29 b(been) f(perf) r(ormed) g(based) h(on) f (simulat) r(ion) g(e) o(xper) r(iments.) 42 b(F) o(or) 27 b(insta) r(nce,) i(simulati) r(on) f(e) o(xperi) r(ments) g(are) g (repea) r(ted) g(by) -72 4882 y(chan) r(ging) c(RED) d(contr) r(ol) i (paramete) r(rs,) g(and) g(ef) n(fec) r(ts) f(of) i(RED) d(contro) r(l) i(paramete) r(rs) g(on) g(its) g(resp) r(onse) h(time) f(are) g(in) l (v) o(es) r(tigated) -72 4995 y(in) 28 b(the) g(past) g(stud) r(y.) p Fl 557 4962 a(4) p Fn 665 4995 a(In) f(ano) r(ther) h(stud) r(y,) p Fl 1287 4962 a(5) p Fn 1381 4995 a(the) h(ef) n(fect) f(of) g(each) h (RED) c(con) r(trol) j(parame) r(ter) f(on) h(its) g(thro) r(ughp) r (ut) f(is) h(in) l(v) q(esti-) -72 5108 y(gated) g(from) e(se) n(v) o (era) r(l) g(simula) r(tion) h(resu) r(lts.) 38 b(Ho) n(we) n(v) o(er) l (,) 28 b(these) f(simula) r(tion) g(stud) r(ies) g(are) g(simply) h (based) g(on) f(a) f(small) h(number) p dyy eop end %%Page: 2 2 TeXDict begin 2 1 bop Fn -72 153 a(of) 23 b(simulati) r(on) g(result) r (s,) f(and) h(ef) n(fect) r(s) f(of) h(RED) d(con) r(trol) j(paramet) r (ers) g(on) g(its) f(perf) r(ormance) i(ha) n(v) o(e) f(not) g(been) h (in) l(v) o(es) r(tigated) g(in) e(a) -72 266 y(syste) r(matic) i(w) o (ay) -6 b(.) 69 418 y(In) 21 b(this) g(paper) n(,) f(we) g(theref) r (ore) g(sys) r(tematica) r(lly) g(ana) r(lyze) h(the) g(perfor) r (mance) g(of) f(the) h(RED) d(rou) r(ter) i(by) h(apply) r(ing) g(the) f (multi-) -72 531 y(v) n(ariat) r(e) g(anal) r(ysis) h(for) g(a) g(lar) n (g) r(e) f(number) i(of) f(simulati) r(on) g(result) r(s.) 27 b(Namely) -6 b(,) 21 b(we) f(\002rst) h(perfo) r(rm) f(a) g(grea) r(t) g (numbe) r(r) g(of) h(simulat) r(ion) -72 644 y(e) o(xper) r(iments) 31 b(by) h(chang) r(ing) f(the) h(combin) r(ation) g(of) f(RED) e(con) r (trol) i(para) r(meters.) 52 b(W) -7 b(e) 30 b(the) r(n) g(ana) r(lyze) h(tho) r(usand) r(s) g(of) g(simu-) -72 756 y(latio) r(n) d(result) r (s) f(stat) r(istica) r(lly) -6 b(.) 43 b(In) 28 b(this) h(paper) n(,) f (we) g(in) l(v) o(es) r(tigate) h(ef) n(fects) g(of) f(RED) e(con) r (trol) i(par) r(ameters) h(on) f(its) g(perf) r(ormance) -72 869 y(by) f(app) r(lying) h(the) f(multi) n(v) n(a) r(riate) g(ana) r (lysis;) j(i.e.,) d(one) h(of) f(se) n(v) o(eral) h(perfo) r(rmance) g (metrics) g(\(i.e.,) f(the) g(a) n(v) o(er) r(age) g(que) r(ue) g (lengt) r(h,) -72 982 y(the) f(thro) r(ughp) r(ut,) g(and) g(the) g (pac) r(k) o(et) g(loss) g(pro) r(babili) r(ty\)) g(is) g(chose) r(n) f (as) h(a) g(respo) r(nse) g(v) n(ariab) r(le,) g(and) g(RED) e(con) r (trol) i(paramet) r(ers) -72 1095 y(are) h(chose) r(n) f(as) g(pred) r (ictor) h(v) n(aria) r(bles.) 38 b(Of) 25 b(se) n(v) o(er) r(al) h (multi) n(v) n(ari) r(ate) g(ana) r(lysis) h(method) r(s,) f(we) g (utili) r(ze) g(the) h(multiple) g(re) o(gre) r(ssion) -72 1208 y(analy) r(sis.) 69 1360 y(The) 33 b(rest) i(of) e(this) i(paper) f (is) g(or) n(gan) r(ized) g(as) g(follo) n(ws.) 60 b(In) 33 b(Sectio) r(n) g(2,) j(we) c(brie) r(\003y) h(e) o(xplai) r(n) g(the) h (RED) e(router) j(and) f(its) -72 1473 y(cont) r(rol) h(para) r (meters.) 65 b(In) 36 b(Section) g(3,) i(o) o(v) o(ervi) r(e) n(w) c (of) i(the) f(multip) r(le) g(re) o(gre) r(ssion) h(anal) r(ysis) g(is) f(pres) r(ented) r(.) 64 b(In) 35 b(Section) i(4,) -72 1586 y(we) d(e) o(xplain) h(the) g(simula) r(tion) g(model,) i(which) e (will) f(be) g(used) h(thro) r(ugho) r(ut) f(this) h(paper) m(.) 60 b(In) 34 b(Sectio) r(n) g(5,) i(the) f(multi) n(v) n(ari) r(ate) -72 1699 y(analy) r(sis) 28 b(is) f(per) r(formed) h(for) g(thou) r(sands) g (of) g(simula) r(tion) g(resul) r(ts) f(obta) r(ined,) i(and) f(ef) n (fec) r(ts) f(of) h(RED) e(contro) r(l) h(para) r(meters) h(on) -72 1812 y(its) k(perfo) r(rmance) g(is) g(thoro) r(ughly) h(in) l(v) o (est) r(igated.) 54 b(Finally) l(,) 32 b(in) g(Section) h(6,) g(we) e (concl) r(ude) h(this) g(pape) r(r) f(and) h(disc) r(uss) g(future) -72 1925 y(w) o(orks.) p Fo 676 2182 a(2.) e(RED) 25 b(\(RANDOM) f(EARL) -9 b(Y) 26 b(DETECTION\)) g(ALGORITHM) p Fn -72 2343 a(In) i(this) g(sect) r(ion,) h(we) e(brie\003y) h(e) o(xpl) r(ain) g(the) g(oper) r(ation) h (algori) r(thm) e(of) h(the) g(RED) e(rout) r(er) -5 b(.) 41 b(Refer) 28 b(to) g(ano) r(ther) g(pape) r(r) p Fl 3633 2310 a(2) p Fn 3700 2343 a(for) g(the) -72 2455 y(detai) r(ls.) g(The) 21 b(RED) f(route) r(r) h(rando) r(mly) g(drop) r (s) g(arri) n(vi) r(ng) g(pac) r(k) o(ets) h(with) g(a) f(prob) r (ability) l(,) g(which) h(is) g(determin) r(ed) g(by) f(its) h(a) n(v) o (er) r(age) -72 2568 y(queu) r(e) 31 b(lengt) r(h) g(\(i.e.,) h(the) g (a) n(v) o(era) r(ge) f(numbe) r(r) f(of) i(pack) o(e) r(ts) f(in) h (the) f(rout) r(er') -5 b(s) 32 b(b) n(uf) n(fer) r(\).) 52 b(Let) p Fj 30 w(q) p Fn 34 w(be) 31 b(the) h(curre) r(nt) f(queu) r(e) g(lengt) r(h.) -72 2681 y(When) 24 b(a) f(pack) q(et) g(arri) n(v) o (es) h(at) g(the) g(RED) d(rout) r(er) l(,) i(the) h(estimat) r(ed) f (v) n(alue) h(of) g(the) g(a) n(v) o(erag) r(e) f(queu) r(e) g(lengt) r (h,) p 3211 2632 44 4 v Fj 22 w(q) p Fn 3 w(,) g(is) g(upda) r(ted) h (as) p Fi 1451 2886 a(\026) p Fj -52 w(q) p Fh 28 w( ) p Fi 25 w(\(1) p Fh 21 w(\000) p Fj 20 w(w) p Fg 1886 2900 a(q) p Fi 1924 2886 a(\)) 7 b(\026) p Fj -52 w(q) p Fi 24 w(+) p Fj 20 w(w) p Fg 2180 2900 a(q) p Fj 2218 2886 a(q) p Fn 1579 w(\(1\)) -72 3090 y(where) p Fj 22 w(w) p Fg 236 3104 a(q) p Fn 295 3090 a(is) 22 b(a) f(contr) r(ol) g(para) r (meter) l(,) h(which) g(is) g(the) g(weight) g(of) g(a) f(lo) n(w) g (pass) i(\002lter) -5 b(.) 28 b(The) 21 b(RED) f(router) j(determin) r (es) e(the) h(pac) r(k) o(et) -72 3203 y(loss) i(prob) r(abilit) r(y) p Fj 23 w(p) p Fg 560 3218 a(b) p Fn 617 3203 a(based) g(on) g(the) g(a) n (v) o(era) r(ge) f(queu) r(e) g(lengt) r(h) p 1886 3154 V Fj 23 w(q) p Fn 25 w(as) p Fj 821 3521 a(p) p Fg 867 3536 a(b) p Fi 926 3521 a(=) p Ff 1022 3324 a(8) 1022 3399 y(>) 1022 3424 y(<) 1022 3573 y(>) 1022 3598 y(:) p Fi 1138 3401 a(0) p Fn 800 w(if) p Fi 30 w(\026) p Fj -52 w(q) 28 b(<) d(min) p Fg 2392 3416 a(th) p Fi 1138 3514 a(1) p Fn 800 w(if) p Fi 30 w(\026) p Fj -52 w(q) p Fh 28 w(\025) p Fj 25 w(max) p Fg 2406 3529 a(th) p Fj 1138 3632 a(max) p Fg 1318 3646 a(p) p Fi 1357 3632 a(\() p Fl 1492 3592 a(\026) p Fg -40 w(q) p Fe 2 w(\000) p Fg(min) p Fd 1705 3604 a(th) p 1402 3611 452 4 v Fg 1402 3664 a(max) p Fd 1541 3676 a(th) p Fe 1606 3664 a(\000) p Fg(min) p Fd 1790 3676 a(th) p Fi 1864 3632 a(\)) p Fn 84 w(if) p Fj 23 w(min) p Fg 2227 3647 a(th) p Fh 2322 3632 a(\024) p Fi 32 w(\026) p Fj -52 w(q) j(<) d(max) p Fg 2763 3647 a(th) p Fn 3838 3521 a(\(2\)) -72 3837 y(where) p Fj 25 w(min) p Fg 340 3852 a(th) p Fn 434 3837 a(is) f(the) h(minimum) g (thresh) r(old,) p Fj 25 w(max) p Fg 1596 3852 a(th) p Fn 1690 3837 a(is) f(the) h(maximum) g(thresh) r(old,) p Fj 25 w(max) p Fg 2867 3851 a(p) p Fn 2930 3837 a(is) g(the) g(maximum) f(pack) q(et) g(loss) -72 3950 y(prob) r(abilit) r(y) -6 b(.) 34 b(These) 26 b(are) g(contr) r(ol) f(para) r(meters) h(of) f (the) h(RED) e(route) r(r) -5 b(.) 34 b(Finally) l(,) 25 b(the) h(RED) d(rout) r(er) i(rand) r(omly) g(dro) r(ps) g(arri) n(v) r (ing) -72 4063 y(pack) q(ets) e(with) h(the) g(proba) r(bility) p Fj 24 w(p) p Fg 1008 4077 a(a) p Fn 1072 4063 a(de\002ne) r(d) f(by) p Fj 1453 4283 a(p) p Fg 1499 4297 a(a) p Fi 1566 4283 a(=) p Fj 1917 4221 a(p) p Fg 1963 4236 a(b) p 1672 4262 571 4 v Fi 1672 4345 a(1) p Fh 21 w(\000) p Fj 19 w(count) p Fh 20 w(\002) p Fj 20 w(p) p Fg 2208 4360 a(b) p Fn 3838 4283 a(\(3\)) -72 4524 y(where) p Fj 26 w(count) p Fn 25 w(is) j(the) g(number) h(of) f(pack) o(e) r(ts) f(tha) r(t) g(ha) n (v) o(e) h(arriv) o(ed) f(at) h(the) g(RED) e(rout) r(er) h(sinc) r(e) g (the) h(last) h(pack) o(e) r(t) e(drop) r(ping.) 36 b(The) -72 4637 y(RED) 23 b(rou) r(ter) i(does) h(not) g(dist) r(inguis) r(h) f (TCP) e(conn) r(ectio) r(ns,) i(and) h(drop) r(s) f(all) g(pack) q(ets) h(identi) r(cally) g(with) f(the) h(same) f(pac) r(k) o(et) g(loss) -72 4750 y(prob) r(abilit) r(y) p Fj 35 w(p) p Fg 408 4764 a(a) p Fn 449 4750 a(.) 64 b(Since) 36 b(the) g(pack) q(et) f(loss) i (proba) r(bility) p Fj 36 w(p) p Fg 1846 4764 a(a) p Fn 1923 4750 a(is) e(deter) r(mined) h(from) f(RED) f(cont) r(rol) h (para) r(meters) h(\(i.e.,) p Fj 38 w(w) p Fg 3883 4764 a(q) p Fn 3921 4750 a(,) p Fj -72 4863 a(min) p Fg 94 4878 a(th) p Fn 164 4863 a(,) p Fj 26 w(max) p Fg 393 4878 a(th) p Fn 463 4863 a(,) p Fj 25 w(max) p Fg 691 4877 a(p) p Fn 731 4863 a(\),) 26 b(chan) r(ging) h(RED) d(contro) r(l) h(par) r(ameters) i(direct) r(ly) f(af) n(fects) h(its) f(perfo) r (rmance) h(metrics) g(such) g(as) f(the) -72 4976 y(a) n(v) o(era) r (ge) d(queu) r(e) g(leng) r(th.) p dyy eop end %%Page: 3 3 TeXDict begin 3 2 bop Fo 1025 153 a(3.) 29 b(MUL) -9 b(TIPLE) 26 b(REGRESSION) g(AN) n(AL) -9 b(YSIS) p Fn -72 313 a(In) 28 b(this) h(paper) n(,) f(we) g(analy) r(ze) g(the) g (perf) r(ormance) h(of) f(the) h(RED) d(route) r(r) h(usin) r(g) h(the) g(multi) n(v) n(ar) r(iate) g(ana) r(lysis) h(for) f(thou) r(sands) h (of) -72 426 y(simulat) r(ion) j(resul) r(ts.) 54 b(Of) 31 b(se) n(v) o(eral) i(multi) n(v) n(aria) r(te) e(ana) r(lysis) i (methods) r(,) g(we) e(utiliz) r(e) g(a) p Fk 32 w(multiple) i(r) m(e) l (gr) m(es) r(sion) f(ana) r(lysis) p Fn(.) p Fl 3743 393 a(6) p Fn 3868 426 a(In) -72 539 y(what) 26 b(follo) n(ws,) g(we) f (brie\003y) h(e) o(xpla) r(in) f(the) h(multipl) r(e) f(re) o(gres) r (sion) h(analy) r(sis.) 35 b(Refer) 26 b(to) f(the) h(refer) r(ence) p Fl 3138 506 a(6) p Fn 3203 539 a(for) g(the) g(detai) r(ls) f(of) h (the) -72 652 y(multipl) r(e) d(re) o(gres) r(sion) h(analy) r(sis.) 69 804 y(The) 29 b(multipl) r(e) g(re) o(gress) r(ion) g(ana) r(lysis) h (is) f(a) g(method) h(of) f(stat) r(istical) r(ly) g(analy) r(zing) h (ef) n(fect) r(s) e(of) p Fk 30 w(pr) m(edic) r(tor) h(vari) r(ables) p Fn 30 w(on) g(a) p Fk -72 917 a(r) m(espo) r(nse) 19 b(variab) r(le) p Fn(.) p Fl 591 884 a(6) p Fn 675 917 a(Predicto) r(r) f(v) n(ariab) r(les) g(are) h(para) r(meters) g(that) g (shou) r(ld) f(af) n(fect) h(the) g(resp) r(onse) g(v) n(ariab) r(le,) g (and) g(the) g(respo) r(nse) -72 1030 y(v) n(ariab) r(le) 36 b(is) g(a) f(para) r(meter) h(that) h(shoul) r(d) e(be) h(cha) r(nged) h (when) f(predic) r(tor) g(v) n(aria) r(bles) g(are) h(chang) r(ed.) 66 b(When) 36 b(app) r(lying) h(the) -72 1142 y(multipl) r(e) 26 b(re) o(gre) r(ssion) i(analy) r(sis,) f(bot) r(h) f(pred) r(ictor) i (v) n(ariab) r(les) f(and) g(the) h(respon) r(se) f(v) n(ariab) r(le) g (must) g(be) g(chose) r(n) f(appr) r(opria) r(tely) -6 b(.) -72 1255 y(If) 19 b(these) h(v) n(aria) r(bles) f(are) h(chos) r (en) f(inapp) r(ropria) r(tely) -6 b(,) 20 b(the) g(resul) r(t) e(of) h (the) h(multipl) r(e) e(re) o(gre) r(ssion) i(analy) r(sis) f(w) o (ould) h(be) f(meanin) r(gless) -72 1368 y(altho) r(ugh) 26 b(it) g(seems) g(to) g(be) g(plau) r(sible.) 36 b(F) o(or) 25 b(inst) r(ance,) i(the) f(multipl) r(e) f(re) o(gres) r(sion) h(ana) r (lysis) h(might) f(indic) r(ate) g(the) g(corre) r(lation) -72 1481 y(between) 35 b(predi) r(ctor) f(v) n(ariab) r(les) g(and) g(the) g (resp) r(onse) g(v) n(aria) r(ble,) i(e) n(v) o(en) e(thou) r(gh) f (the) i(respon) r(se) f(v) n(ariab) r(le) f(is) h(indep) r(enden) r(t) f (of) -72 1594 y(pred) r(ictor) k(v) n(ariabl) r(es.) 66 b(Thus,) 40 b(before) d(perfo) r(rming) g(the) f(multipl) r(e) g(re) o (gress) r(ion) g(anal) r(ysis,) j(it) d(is) g(nec) r(essary) h(to) f (chec) r(k) g(the) -72 1707 y(corre) r(lation) 29 b(bet) r(ween) f (these) i(v) n(ariabl) r(es) e(for) h(choos) r(ing) g(predic) r(tor) f (v) n(ari) r(ables) h(and) g(the) g(respo) r(nse) f(v) n(ari) r(able) h (appro) r(priate) r(ly) f(.) -72 1820 y(In) 23 b(this) g(pape) r(r) l (,) f(we) g(ther) r(efore) h(use) g(a) p Fk 23 w(pairwis) r(e) f(scatt) r(er) g(plo) r(t) p Fn(,) p Fl 1875 1787 a(7) p Fn 1958 1820 a(which) h(is) g(a) f(set) h(of) g(scatt) r(er) f(plot) r(s) g (for) h(each) h(v) n(ariab) r(le) e(pair) n(,) g(for) -72 1933 y(chec) r(king) i(the) g(correl) r(ation) g(betwee) r(n) f(v) n (ariab) r(les.) 69 2085 y(In) 33 b(the) h(multipl) r(e) f(re) o(gress) r (ion) g(ana) r(lysis,) j(a) p Fk 33 w(r) m(e) l(gr) m(es) r(sion) e (equa) r(tion) p Fn 34 w(repres) r(enting) g(the) g(a) n(v) o(era) r (ge) f(relat) r(ionsh) r(ip) g(between) -72 2198 y(the) f(resp) r(onse) g(v) n(ari) r(able) g(and) h(predic) r(tor) f(v) n(ariab) r(les) g(is) g (obtai) r(ned) g(from) g(a) f(set) h(of) g(measu) r(red) g(predi) r (ctor) g(v) n(aria) r(bles) g(and) h(the) -72 2311 y(respo) r(nse) 22 b(v) n(ariabl) r(e.) 27 b(Pro) o(vide) r(d) 21 b(that) g(the) h(respo) r (nse) f(v) n(aria) r(ble) p Fj 21 w(y) p Fn 24 w(has) g(line) r(arity) h (re) o(gardin) r(g) f(predic) r(tor) g(v) n(aria) r(bles,) h(a) e(re) o (gre) r(ssion) -72 2424 y(equa) r(tion) k(for) g(the) f(resp) r(onse) h (v) n(aria) r(ble) f(is) h(gi) n(v) o(en) g(by) g(linear) g(combi) r (nation) h(of) p Fj 23 w(n) p Fn 22 w(pred) r(ictor) f(v) n(aria) r (bles) p Fj 24 w(x) p Fg 3233 2438 a(i) p Fn 3261 2424 a(.) p Fj 1250 2628 a(y) p Fi 85 w(=) p Fj 83 w(\014) p Fl 1585 2642 a(0) p Fi 1645 2628 a(+) p Fj 20 w(\014) p Fl 1787 2642 a(1) p Fj 1842 2628 a(x) p Fl 1894 2642 a(1) p Fi 1954 2628 a(+) p Fj 20 w(:) 15 b(:) g(:) p Fi 21 w(+) p Fj 20 w(\014) p Fg 2313 2642 a(n) p Fj 2375 2628 a(x) p Fg 2427 2642 a(n) p Fi 2494 2628 a(+) p Fj 20 w(\017) p Fn 1216 w(\(4\)) -72 2832 y(where) 21 b(the) g(coef) n (\002ci) r(ent) g(of) g(a) f(predi) r(ctor) h(v) n(aria) r(ble,) p Fj 21 w(\014) p Fg 1592 2846 a(i) p Fn 1621 2832 a(,) f(is) h(called) h (a) p Fk 20 w(r) m(e) l(gr) o(ession) g(coef) n(\002) r(cient) p Fn 2 w(,) e(which) h(indi) r(cates) g(ho) n(w) g(much) g(the) -72 2945 y(pred) r(ictor) j(v) n(ariab) r(le) p Fj 23 w(x) p Fg 644 2959 a(i) p Fn 694 2945 a(af) n(fect) r(s) f(the) g(resp) r (onse) h(v) n(ariabl) r(e) p Fj 23 w(y) p Fn 3 w(.) j(In) c(the) h(abo) o(v) o(e) g(equat) r(ion,) p Fj 23 w(\017) p Fn 22 w(is) f(call) r(ed) g (a) p Fk 23 w(r) m(esidu) r(al) p Fn(.) 28 b(W) -7 b(e) 22 b(intr) r(oduce) p Fi -66 3058 a(^) p Fj -51 w(y) p Fn 22 w(as) f(the) f(esti) r(mated) g(v) n(alu) r(e) g(of) g(the) g(resp) r (onse) h(v) n(aria) r(ble) f(from) h(measured) g(pre) r(dictor) g(v) n (aria) r(bles) g(and) f(the) h(re) o(gres) r(sion) g(equa) r(tion,) -72 3171 y(i.e.,) p Fi 30 w(^) p Fj -51 w(y) p Fh 30 w(\021) p Fj 27 w(y) p Fh 24 w(\000) p Fj 21 w(\017) p Fn(.) 31 b(In) 24 b(the) h(multip) r(le) f(re) o(gre) r(ssion) h(ana) r(lysis,) g (by) g(assumin) r(g) f(that) h(the) g(mean) g(of) g(residu) r(als) g (is) f(zero) h(and) g(tha) r(t) f(the) -72 3284 y(distr) r(ib) n(uti) r (on) 29 b(of) h(resid) r(uals) g(follows) f(the) h(normal) g(dist) r (rib) n(uti) r(on,) p Fj 31 w(\014) p Fg 2079 3298 a(i) p Fn 2136 3284 a(is) g(deter) r(mined) g(from) p Fj 30 w(m) p Fn 28 w(sets) h(of) e(measu) r(red) h(respo) r(nse) -72 3397 y(v) n(ariab) r(le) g(and) i(predic) r(tor) f(v) n(ariabl) r(es.) 50 b(Once) 30 b(the) h(re) o(gre) r(ssion) h(equati) r(on) e(is) h (obta) r(ined) g(appro) r(priat) r(ely) -6 b(,) 32 b(ef) n(fect) r(s) e (of) h(predic) r(tor) -72 3510 y(v) n(ariab) r(les) 24 b(on) f(the) h(resp) r(onse) g(v) n(ariab) r(le) f(can) h(be) g(in) l (v) o(es) r(tigated) g(from) g(re) o(gress) r(ion) g(coef) n(\002cien) r (ts) p Fj 23 w(\014) p Fg 2977 3524 a(i) p Fn 3006 3510 a(.) 69 3662 y(In) 33 b(the) h(multip) r(le) f(re) o(gress) r(ion) h (analys) r(is,) h(the) f(smaller) g(the) g(residu) r(al) f(is,) i(the) f (bette) r(r) f(the) g(accu) r(rac) o(y) h(of) f(the) g(re) o(gre) r (ssion) -72 3775 y(equa) r(tion) e(is.) 51 b(As) 30 b(an) h(inde) o(x) g (for) h(measurin) r(g) e(the) i(accura) r(c) o(y) e(of) h(the) g(re) o (gre) r(ssion) h(equat) r(ion,) p Fj 32 w(R) p Fl 3007 3742 a(2) p Fn 3077 3775 a(\(multipl) r(e) p Fj 30 w(R) p Fn 1 w(-squa) r(red\)) f(is) -72 3887 y(widely) e(used) g(in) f(the) g (multip) r(le) g(re) o(gress) r(ion) g(anal) r(ysis.) p Fj 43 w(R) p Fl 1791 3854 a(2) p Fn 1857 3887 a(is) g(de\002ned) h (from) f(the) h(ratio) g(of) f(residu) r(al) g(v) n(arian) r(ce) g(to) g (respo) r(nse) -72 4000 y(v) n(ariab) r(le') -5 b(s) 24 b(v) n(arian) r(ce.) k(More) c(spec) r(i\002cally) -6 b(,) p Fj 24 w(R) p Fl 1402 3967 a(2) p Fn 1464 4000 a(is) 23 b(de\002ned) h(as) p Fj 1056 4257 a(R) p Fl 1126 4219 a(2) p Fi 1248 4257 a(=) 83 b(1) p Fh 21 w(\000) p Ff 1694 4131 a(P) p Fg 1782 4157 a(m) 1782 4218 y(i) p Fl(=1) p Fj 1915 4195 a(\017) p Fl 1952 4162 a(2) p Fg 1952 4220 a(i) p 1569 4236 548 4 v Ff 1569 4255 a(P) p Fg 1656 4281 a(m) 1656 4342 y(i) p Fl(=1) p Fi 1775 4319 a(\() 6 b(^) p Fj -51 w(y) p Fg 1855 4333 a(i) p Fh 1903 4319 a(\000) p Fi 26 w(\026) p Fj -51 w(y) p Fi 3 w(\)) p Fl 2077 4293 a(2) p Fi 2152 4257 a(=) p Ff 2258 4131 a(P) p Fg 2345 4157 a(m) 2345 4218 y(i) p Fl(=1) p Fi 2464 4195 a(\() p Fj(y) p Fg 2544 4209 a(i) p Fh 2592 4195 a(\000) p Fi 26 w(\026) p Fj -51 w(y) p Fi 3 w(\)) p Fl 2766 4162 a(2) p 2258 4236 V Ff 2258 4255 a(P) p Fg 2345 4281 a(m) 2345 4342 y(i) p Fl(=1) p Fi 2464 4319 a(\() g(^) p Fj -51 w(y) p Fg 2544 4333 a(i) p Fh 2592 4319 a(\000) p Fi 26 w(\026) p Fj -51 w(y) p Fi 3 w(\)) p Fl 2766 4293 a(2) p Fn 3838 4257 a(\(5\)) -72 4505 y(where) p Fi 26 w(\026) p Fj -51 w(y) p Fn 21 w(is) 19 b(the) h(mean) f(of) p Fj 19 w(m) p Fn 19 w(respo) r(nse) g(v) n(aria) r(bles.) 28 b(In) 19 b(the) g(abo) q(v) o(e) f(equ) r(ation,) p Fj 21 w(y) p Fg 2421 4519 a(i) p Fn 2448 4505 a(,) p Fi 26 w(^) p Fj -52 w(y) p Fg 2535 4519 a(i) p Fn 2563 4505 a(,) h(and) p Fj 20 w(\017) p Fg 2792 4519 a(i) p Fn 2839 4505 a(repres) r(ent) p Fj 19 w(y) p Fn 3 w(,) p Fi 25 w(^) p Fj -51 w(y) p Fn 3 w(,) g(and) p Fj 20 w(\017) p Fn 18 w(calc) r(ulated) -72 4618 y(from) p Fj 30 w(i) p Fn(th) 31 b(set) f(of) g(measu) r(red) g(resp) r(onse) h(v) n(ariab) r (les) f(and) h(predi) r(ctor) f(v) n(aria) r(bles.) p Fj 49 w(R) p Fl 2567 4585 a(2) p Fn 2636 4618 a(tak) o(es) h(a) f(v) n (alue) h(betwee) r(n) f(0) f(and) i(1,) g(and) -72 4731 y(it) d(indica) r(tes) g(ho) n(w) f(well) h(the) g(resp) r(onse) g(v) n (aria) r(ble) g(is) g(e) o(xplain) r(ed) g(by) g(predi) r(ctor) g(v) n (aria) r(bles.) 42 b(If) p Fj 28 w(R) p Fl 3010 4698 a(2) p Fn 3076 4731 a(is) 28 b(lar) n(ge) r(,) g(it) f(sugg) r(ests) h (that) -72 4844 y(the) g(resp) r(onse) h(v) n(ariab) r(le) f(is) g (well) g(e) o(xplain) r(ed) g(by) g(pred) r(ictor) h(v) n(ariab) r (les.) 43 b(Con) l(v) o(ers) r(ely) -6 b(,) 29 b(if) p Fj 28 w(R) p Fl 2853 4811 a(2) p Fn 2919 4844 a(is) f(small,) i(it) e (sugge) r(sts) g(that) h(the) -72 4957 y(respo) r(nse) 24 b(v) n(ariab) r(les) f(can) r(not) h(be) f(e) o(xpla) r(ined) h(by) g (predic) r(tor) f(v) n(ari) r(ables.) p dyy eop end %%Page: 4 4 TeXDict begin 4 3 bop 932 1087 a @beginspecial 15 @llx 309 @lly 786 @urx 703 @ury 2409 @rwi @setspecial %%BeginDocument: figure/model2.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 15 309 786 703 %%Title: model2 %%CreationDate: Thu Mar 28 02:56:25 2002 %%Creator: Tgif-4.1.35 by William Chia-Wei Cheng (william@cs.UCLA.edu) %%ProducedBy: (unknown) %%Pages: 1 %%DocumentFonts: (atend) %%EndComments %%BeginProlog /tgifdict 51 dict def tgifdict begin /TGMAX { exch dup 3 1 roll exch dup 3 1 roll gt { pop } { exch pop } ifelse } def /TGMIN { exch dup 3 1 roll exch dup 3 1 roll lt { pop } { exch pop } ifelse } def /TGSW { stringwidth pop } def /bd { bind def } bind def /GS { gsave } bd /GR { grestore } bd /NP { newpath } bd /CP { closepath } bd /CHP { charpath } bd /CT { curveto } bd /L { lineto } bd /RL { rlineto } bd /M { moveto } bd /RM { rmoveto } bd /S { stroke } bd /F { fill } bd /TR { translate } bd /RO { rotate } bd /SC { scale } bd /MU { mul } bd /DI { div } bd /DU { dup } bd /NE { neg } bd /AD { add } bd /SU { sub } bd /PO { pop } bd /EX { exch } bd /CO { concat } bd /CL { clip } bd /EC { eoclip } bd /EF { eofill } bd /IM { image } bd /IMM { imagemask } bd /ARY { array } bd /SG { setgray } bd /RG { setrgbcolor } bd /SD { setdash } bd /W { setlinewidth } bd /SM { setmiterlimit } bd /SLC { setlinecap } bd /SLJ { setlinejoin } bd /SH { show } bd /FF { findfont } bd /MS { makefont setfont } bd /AR { arcto 4 {pop} repeat } bd /CURP { currentpoint } bd /FLAT { flattenpath strokepath clip newpath } bd /TGSM { tgiforigctm setmatrix } def /TGRM { savematrix setmatrix } def end %%EndProlog %%Page: 1 1 %%PageBoundingBox: 15 309 786 703 tgifdict begin /tgifsavedpage save def 1 SM 1 W 0 SG 72 0 MU 72 11 MU TR 72 128 DI 100.000 MU 100 DI DU NE SC GS /tgiforigctm matrix currentmatrix def % POLY/OPEN-SPLINE 0 SG GS NP 196 208 M 428 432 L TGSM 7 W S 1 W GR % POLY/OPEN-SPLINE 0 SG GS NP 196 348 M 424 436 L TGSM 7 W S 1 W GR % POLY/OPEN-SPLINE 0 SG GS NP 196 472 M 424 452 L TGSM 7 W S 1 W GR % POLY/OPEN-SPLINE 0 SG GS NP 200 600 M 424 468 L TGSM 7 W S 1 W GR % POLY/OPEN-SPLINE 0 SG GS NP 196 728 M 424 492 L TGSM 7 W S 1 W GR % POLY/OPEN-SPLINE 0 SG NP 1228 204 M 956 444 L 948 448 L CP 1 SG EF 0 SG GS NP 1228 204 M 956 444 L 948 448 L TGSM 7 W S 1 W GR % POLY/OPEN-SPLINE 0 SG GS NP 952 464 M 1224 340 L TGSM 7 W S 1 W GR % POLY/OPEN-SPLINE 0 SG GS NP 1224 468 M 944 468 L TGSM 7 W S 1 W GR % POLY/OPEN-SPLINE 0 SG GS NP 1220 592 M 940 480 L TGSM 7 W S 1 W GR % POLY/OPEN-SPLINE 0 SG GS NP 1224 724 M 940 492 L TGSM 7 W S 1 W GR % BOX 0 SG NP 46 176 M 206 176 L 206 272 L 46 272 L CP F GS 10 SM GS NP 46 176 M 206 176 L 206 272 L 46 272 L CP S GR GR % BOX 0 SG NP 32 160 M 192 160 L 192 256 L 32 256 L CP 1 SG F 0 SG GS 10 SM GS NP 32 160 M 192 160 L 192 256 L 32 256 L CP S GR GR % BOX 0 SG NP 46 304 M 206 304 L 206 400 L 46 400 L CP F GS 10 SM GS NP 46 304 M 206 304 L 206 400 L 46 400 L CP S GR GR % BOX 0 SG NP 32 288 M 192 288 L 192 384 L 32 384 L CP 1 SG F 0 SG GS 10 SM GS NP 32 288 M 192 288 L 192 384 L 32 384 L CP S GR GR % BOX 0 SG NP 46 432 M 206 432 L 206 528 L 46 528 L CP F GS 10 SM GS NP 46 432 M 206 432 L 206 528 L 46 528 L CP S GR GR % BOX 0 SG NP 32 416 M 192 416 L 192 512 L 32 512 L CP 1 SG F 0 SG GS 10 SM GS NP 32 416 M 192 416 L 192 512 L 32 512 L CP S GR GR % BOX 0 SG NP 46 560 M 206 560 L 206 656 L 46 656 L CP F GS 10 SM GS NP 46 560 M 206 560 L 206 656 L 46 656 L CP S GR GR % BOX 0 SG NP 32 544 M 192 544 L 192 640 L 32 640 L CP 1 SG F 0 SG GS 10 SM GS NP 32 544 M 192 544 L 192 640 L 32 640 L CP S GR GR % BOX 0 SG NP 46 688 M 206 688 L 206 784 L 46 784 L CP F GS 10 SM GS NP 46 688 M 206 688 L 206 784 L 46 784 L CP S GR GR % BOX 0 SG NP 32 672 M 192 672 L 192 768 L 32 768 L CP 1 SG F 0 SG GS 10 SM GS NP 32 672 M 192 672 L 192 768 L 32 768 L CP S GR GR % BOX 0 SG NP 1230 176 M 1390 176 L 1390 272 L 1230 272 L CP F GS 10 SM GS NP 1230 176 M 1390 176 L 1390 272 L 1230 272 L CP S GR GR % BOX 0 SG NP 1216 160 M 1376 160 L 1376 256 L 1216 256 L CP 1 SG F 0 SG GS 10 SM GS NP 1216 160 M 1376 160 L 1376 256 L 1216 256 L CP S GR GR % BOX 0 SG NP 1230 304 M 1390 304 L 1390 400 L 1230 400 L CP F GS 10 SM GS NP 1230 304 M 1390 304 L 1390 400 L 1230 400 L CP S GR GR % BOX 0 SG NP 1216 288 M 1376 288 L 1376 384 L 1216 384 L CP 1 SG F 0 SG GS 10 SM GS NP 1216 288 M 1376 288 L 1376 384 L 1216 384 L CP S GR GR % BOX 0 SG NP 1230 432 M 1390 432 L 1390 528 L 1230 528 L CP F GS 10 SM GS NP 1230 432 M 1390 432 L 1390 528 L 1230 528 L CP S GR GR % BOX 0 SG NP 1216 416 M 1376 416 L 1376 512 L 1216 512 L CP 1 SG F 0 SG GS 10 SM GS NP 1216 416 M 1376 416 L 1376 512 L 1216 512 L CP S GR GR % BOX 0 SG NP 1230 560 M 1390 560 L 1390 656 L 1230 656 L CP F GS 10 SM GS NP 1230 560 M 1390 560 L 1390 656 L 1230 656 L CP S GR GR % BOX 0 SG NP 1216 544 M 1376 544 L 1376 640 L 1216 640 L CP 1 SG F 0 SG GS 10 SM GS NP 1216 544 M 1376 544 L 1376 640 L 1216 640 L CP S GR GR % BOX 0 SG NP 1230 688 M 1390 688 L 1390 784 L 1230 784 L CP F GS 10 SM GS NP 1230 688 M 1390 688 L 1390 784 L 1230 784 L CP S GR GR % BOX 0 SG NP 1216 672 M 1376 672 L 1376 768 L 1216 768 L CP 1 SG F 0 SG GS 10 SM GS NP 1216 672 M 1376 672 L 1376 768 L 1216 768 L CP S GR GR % BOX 0 SG NP 430 432 M 590 432 L 590 528 L 430 528 L CP F GS 10 SM GS NP 430 432 M 590 432 L 590 528 L 430 528 L CP S GR GR % BOX 0 SG NP 416 416 M 576 416 L 576 512 L 416 512 L CP 1 SG F 0 SG GS 10 SM GS NP 416 416 M 576 416 L 576 512 L 416 512 L CP S GR GR % BOX 0 SG NP 814 432 M 974 432 L 974 528 L 814 528 L CP F GS 10 SM GS NP 814 432 M 974 432 L 974 528 L 814 528 L CP S GR GR % BOX 0 SG NP 800 416 M 960 416 L 960 512 L 800 512 L CP 1 SG F 0 SG GS 10 SM GS NP 800 416 M 960 416 L 960 512 L 800 512 L CP S GR GR % POLY/OPEN-SPLINE 0 SG GS NP 576 470 M 800 470 L TGSM 7 W S 1 W GR % TEXT NP 0 SG NP 29 804 M 209 804 L 209 843 L 29 843 L CP 1 SG F 0 SG GS 1 W 30 836 M GS 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (Source Host) SH GR GR % TEXT NP 0 SG NP 1157 816 M 1396 816 L 1396 855 L 1157 855 L CP 1 SG F 0 SG GS 1 W 1158 848 M GS 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (Destination Host) SH GR GR % TEXT NP 0 SG NP 415 550 M 593 550 L 593 589 L 415 589 L CP 1 SG F 0 SG GS 1 W 416 582 M GS 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (RED Router) SH GR GR % TEXT NP 0 SG NP 801 548 M 979 548 L 979 587 L 801 587 L CP 1 SG F 0 SG GS 1 W 802 580 M GS 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (RED Router) SH GR GR % TEXT NP 0 SG NP 653 412 M 742 412 L 742 451 L 653 451 L CP 1 SG F 0 SG GS 1 W 654 444 M GS 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (50 ms) SH GR GR % TEXT NP 0 SG NP 639 498 M 773 498 L 773 537 L 639 537 L CP 1 SG F 0 SG GS 1 W 640 530 M GS 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (1.5 Mbps) SH GR GR % TEXT NP 0 SG NP 333 246 M 404 246 L 404 285 L 333 285 L CP 1 SG F 0 SG GS 1 W 334 278 M GS 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (2 ms) SH GR GR % TEXT NP 0 SG NP 991 250 M 1062 250 L 1062 289 L 991 289 L CP 1 SG F 0 SG GS 1 W 992 282 M GS 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (2 ms) SH GR GR % TEXT NP 0 SG NP 287 696 M 412 696 L 412 735 L 287 735 L CP 1 SG F 0 SG GS 1 W 288 728 M GS 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (10 Mbps) SH GR GR % TEXT NP 0 SG NP 973 694 M 1098 694 L 1098 733 L 973 733 L CP 1 SG F 0 SG GS 1 W 974 726 M GS 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (10 Mbps) SH GR GR GR tgifsavedpage restore end showpage %%Trailer %MatchingCreationDate: Thu Mar 28 02:56:25 2002 %%DocumentFonts: Helvetica %%EOF %%EndDocument @endspecial Fc 1471 1283 a(Figur) o(e) 19 b(1.) p Fb 20 w(Simulation) g(model) p Fo 1562 1645 a(4.) 29 b(SIMULA) -9 b(TION) p Fn -72 1805 a(Figure) 25 b(1) f(illustr) r(ates) g(the) h (netw) o(or) r(k) e(model) i(used) g(in) f(our) h(simulati) r(on.) 30 b(There) 25 b(e) o(xists) g(tw) o(o) f(RED) e(route) r(rs) i(and) g (\002) n(v) o(e) g(homoge-) -72 1918 y(neou) r(s) h(TCP) e(con) r (nectio) r(ns.) 35 b(In) 25 b(this) h(netw) o(or) r(k) f(model,) h(the) g(link) g(betwee) r(n) f(tw) o(o) g(RED) f(router) r(s) h(is) g(the) h (bottl) r(eneck) r(.) 34 b(W) -7 b(e) 24 b(ha) n(v) q(e) -72 2031 y(run) e(thous) r(ands) g(of) f(simula) r(tion) h(e) o(xperi) r (ments) g(using) g(this) g(netw) o(or) r(k) f(model.) 28 b(T) -7 b(able) 22 b(1) f(summarize) r(s) g(paramete) r(rs) g(used) h (in) g(our) -72 2144 y(simulat) r(ion.) 69 2295 y(Each) 30 b(simula) r(tion) h(has) f(been) h(run) g(for) f(30) g([s],) i(and) f (the) f(simula) r(tion) g(resu) r(lt) g(of) g(the) g(last) h(5) f([s]) g (is) g(used) h(for) g(e) n(v) n(aluat) r(ing) -72 2408 y(the) 26 b(RED) e(perfor) r(mance.) 35 b(Namely) -6 b(,) 26 b(three) h(perfor) r(mance) f(measure) r(s) f(of) g(the) h(RED) e(route) r(r) l(,) h(the) h(a) n(v) o(era) r(ge) f(que) r(ue) g(leng) r (th,) h(the) -72 2521 y(throu) r(ghpu) r(t,) c(and) i(the) g(pack) q (et) f(loss) i(proba) r(bility) l(,) d(are) i(calcu) r(lated) g(from) g (the) f(simula) r(tion) h(resul) r(t) f(of) g(25\226) r(30) g([s].) 29 b(Under) 24 b(these) -72 2634 y(cond) r(itions) r(,) e(we) h(ha) n(v) o (e) h(obta) r(ined) g(thou) r(sands) g(of) g(simulat) r(ion) f(resu) r (lts) h(while) f(chan) r(ging) h(RED) e(contr) r(ol) h(para) r(meters.) p Fo 937 2891 a(5.) 30 b(AN) n(AL) -9 b(YSIS) 26 b(RESUL) -9 b(TS) 26 b(AND) f(DISCUSSIONS) -72 3054 y(5.1.) k(P) o(ack) o(et) d (Loss) f(Pr) n(obability) p Fn -72 3209 a(The) e(pairwis) r(e) g (scatte) r(r) g(plot) h(when) f(the) h(pack) q(et) f(loss) h(pro) r (babili) r(ty) f(of) h(the) f(RED) f(route) r(r) h(is) g(chos) r(en) g (as) h(the) f(resp) r(onse) h(v) n(aria) r(ble) -72 3322 y(is) c(sho) n(wn) g(in) f(Fig.) h(2.) 27 b(This) 19 b(\002gure) h(shows,) f(for) h(e) o(xample) r(,) f(that) h(ther) r(e) f (is) h(almost) g(line) r(ar) f(relat) r(ion) h(between) p Fj 21 w(w) p Fg 3370 3336 a(q) p Fn 3427 3322 a(and) g(the) g(pac) r(k) o(et) -72 3435 y(loss) g(proba) r(bility) l(,) f(and) g(that) g(the) h (relati) r(on) f(between) p Fj 20 w(max) p Fg 1753 3450 a(th) p Fn 1841 3435 a(and) g(the) h(pack) o(e) r(t) e(loss) i(proba) r (bility) g(is) f(nonli) r(near) -5 b(.) 28 b(In) 18 b(the) i(multiple) -72 3548 y(re) o(gres) r(sion) f(analy) r(sis,) g(it) g(is) f(assu) r (med) g(that) h(the) g(relati) r(on) f(betwee) r(n) g(pred) r(ictor) h (v) n(ariab) r(les) g(and) g(the) f(resp) r(onse) h(v) n(aria) r(ble) g (is) f(linea) r(r) -5 b(.) -72 3661 y(If) 26 b(it) g(is) g(nonli) r (near) l(,) h(the) g(multiple) g(re) o(gres) r(sion) g(analy) r(sis) f (cann) r(ot) g(be) g(appli) r(ed.) 36 b(In) 26 b(suc) r(h) f(a) h(case) r(,) f(it) h(is) g(nece) r(ssary) h(to) f(perfo) r(rm) -72 3774 y(some) f(v) n(ari) r(able) h(transf) r(ormation) r(.) 33 b(In) 25 b(what) h(follo) n(ws,) g(for) f(demon) r(strati) r(ng) g(ef) n (fec) r(ti) n(v) o(eness) h(of) g(v) n(ariab) r(le) f(transf) r (ormatio) r(n,) g(we) -72 3887 y(\002rst) e(sho) n(w) h(the) f(resu) r (lt) g(when) h(v) n(ariab) r(le) f(trans) r(formatio) r(n) g(is) g(not) h(used) r(.) 69 4038 y(T) -7 b(able) 30 b(2) f(sho) n(ws) h(the) g (resul) r(t) f(of) g(the) h(multip) r(le) f(re) o(gre) r(ssion) h(ana) r (lysis) g(when) g(RED) e(contr) r(ol) h(para) r(meters) h(are) g(chose) r(n) f(as) -72 4151 y(pred) r(ictor) g(v) n(aria) r(bles) g(and) g(the) g(pack) q(et) f(loss) i(proba) r(bility) g(is) e(chos) r(en) h(as) f (the) h(resp) r(onse) g(v) n(aria) r(ble.) 44 b(In) 29 b(this) g(table) r(,) g(a) f(colu) r(mn) p Fc 1127 4465 a(T) -8 b(able) 21 b(1.) p Fb 20 w(P) o(arameter) f(v) n(alu) n(es) h (used) f(in) h(the) f(simulation) p 876 4478 2119 4 v Fn 926 4557 a(band) r(width) k(of) f(bott) r(leneck) i(link) 433 b(1.) 28 b(5) 101 b([Mbit/s]) 926 4670 y(band) r(width) 24 b(of) f(acce) r(ss) g(link) 631 b(10) 101 b([Mbit/s]) 926 4783 y(prop) r(agatio) r(n) 23 b(delay) h(of) g(bottl) r(eneck) g(link) 215 b(50) 101 b([ms]) 926 4896 y(prop) r(agatio) r(n) 23 b(delay) h(of) g(acces) r(s) f(link) 406 b(2) 101 b([ms]) 926 5009 y(TCP) 22 b(pack) o(e) r(t) h(size) 828 b(1,000) 102 b([byte]) 926 5121 y(b) n(uf) n(f) r(er) 23 b(size) h(of) f(RED) f (route) r(r) 561 b(100) 101 b([pack) o(e) r(t]) p 876 5159 V dyy eop end %%Page: 5 5 TeXDict begin 5 4 bop Fc 602 202 a(T) -8 b(able) 21 b(2.) p Fb 20 w(Result) g(of) f(the) g(multiple) g(re) o(gr) n(ession) h(analy) n(sis) h(on) e(the) g(pack) o(et) f(loss) i(prob) n(ability) p 74 231 3701 4 v Fn 124 310 a(pred) r(ictor) j(v) n(aria) r(ble) 100 b(re) o(gre) r(ssion) 24 b(coef) n(\002ci) r(ent) 100 b(stan) r(dardi) r(zed) 24 b(re) o(gress) r(ion) g(coef) n(\002cien) r (t) 100 b(t-v) n(alue) h(P-v) n(alue) p 74 347 V 124 427 a(\(inte) r(rcept) r(\)) 980 b(4.63) 1504 b(70.94) 331 b(0) p Fj 124 539 a(w) p Fg 189 553 a(q) p Fn 1407 539 a(-19.54) 1171 b(-0.08) 161 b(-7.11) 331 b(0) p Fj 124 652 a(min) p Fg 290 667 a(th) p Fn 1483 652 a(0.01) 1200 b(0.05) 192 b(4.73) 330 b(0) p Fj 124 765 a(max) p Fg 304 780 a(th) p Fn 1483 765 a(0.07) 1200 b(0.74) 116 b(-58.32) 331 b(0) p Fj 124 878 a(max) p Fg 304 892 a(p) p Fn 1407 878 a(-10.77) 1171 b(-0.10) 161 b(-8.71) 331 b(0) p 74 915 V Fj 124 994 a(R) p Fl 194 961 a(2) p Fn 1483 994 a(0.50) p 74 1032 V -72 1379 a(named) p Fk 24 w(r) m(e) l(gr) o(ession) 24 b(coef) n(\002) r(cien) r(t) p Fn 23 w(sho) n(ws) f(coe) r(f) n(\002cients) h(of) f(pred) r(ictor) h (v) n(ariab) r(les) g(of) f(the) h(re) o(gress) r(ion) g(equat) r(ion,) f(and) h(a) f(colu) r(mn) -72 1492 y(named) p Fk 28 w(stand) r(ar) m (dize) r(d) k(r) m(e) l(gr) m(es) r(sion) h(coef) n(\002) r(cien) r(t) p Fn 27 w(sho) n(ws) f(re) o(gres) r(sion) h(coef) n(\002cie) r(nts) f (nor) r(malized) h(by) f(stan) r(dard) h(de) n(via) r(tions) g(of) -72 1605 y(pred) r(ictor) 36 b(v) n(ariabl) r(es) f(and) g(the) h(respo) r (nse) f(v) n(aria) r(ble.) 64 b(Using) 35 b(thes) r(e) f(stan) r(dardi) r(zed) h(re) o(gre) r(ssion) h(coef) n(\002cie) r(nts,) i(it) d (becomes) -72 1718 y(poss) r(ible) e(to) g(compare) h(ef) n(fects) g (of) e(multip) r(le) h(predic) r(tor) g(v) n(ariab) r(les,) i(which) e (origi) r(nally) g(ha) n(v) q(e) f(dif) n(fere) r(nt) h(distributio) r (ns.) 56 b(A) -72 1831 y(colu) r(mn) 20 b(named) p Fk 22 w(t-va) r(lue) p Fn 21 w(is) h(the) h(resul) r(t) e(of) i(t-test) r (,) e(which) i(in) l(v) q(estigates) g(wheth) r(er) f(the) g(dist) r (rib) n(ut) r(ions) h(of) f(resid) r(uals) h(is) f(chang) r(ed) -72 1944 y(by) 34 b(remo) o(vin) r(g) f(one) h(of) g(pred) r(ictor) g(v) n (aria) r(bles) g(from) g(the) g(re) o(gres) r(sion) g(equ) r(ation.) 60 b(A) 33 b(column) i(named) p Fk 34 w(P-value) p Fn 35 w(sho) n(ws) f(the) -72 2057 y(prob) r(abilit) r(y) 28 b(that) h(the) g(distri) r(b) n(utio) r(n) f(of) h(residu) r(als) g(is) f(the) h(same) g(when) f(one) h(of) g(predi) r(ctor) g(v) n(ariab) r (les) g(is) f(remo) o(v) o(ed) h(from) g(the) -72 2169 y(re) o(gres) r(sion) d(equa) r(tion.) 35 b(A) 24 b(column) i(named) p Fj 26 w(R) p Fl 1419 2136 a(2) p Fn 1483 2169 a(sho) n(ws) f(ho) n(w) g (much) h(in\003uenc) r(e) f(a) g(predi) r(ctor) h(v) n(ariabl) r(e) f (has) g(on) h(the) g(respo) r(nse) -72 2282 y(v) n(ariab) r(le.) 69 2434 y(From) 32 b(T) -7 b(ab) l(.) 33 b(2,) h(one) g(can) f(\002nd) g (that) g(all) g(P-v) n(alue) r(s) f(of) h(pred) r(ictor) g(v) n(ari) r (ables) g(are) h(zero.) 57 b(This) 33 b(sugg) r(ests) g(that) h(from) f (the) -72 2547 y(multipl) r(e) e(re) o(gres) r(sion) h(analy) r(sis,) h (all) f(predi) r(ctor) g(v) n(ariab) r(les) f(af) n(fec) r(t) g(the) g (resp) r(onse) h(v) n(aria) r(ble.) 53 b(Ho) n(we) n(v) o(er) l(,) p Fj 33 w(R) p Fl 3391 2514 a(2) p Fn 3461 2547 a(is) 31 b(small) h(\(i.e.,) -72 2660 y(0.50\),) 25 b(which) h(implies) f(tha) r (t) f(the) h(re) o(gres) r(sion) g(equ) r(ation) h(canno) r(t) e(predi) r(ct) g(the) i(respon) r(se) f(v) n(ariab) r(le) f(so) h(accu) r (rately) l(.) 32 b(Hence,) 25 b(in) -72 2773 y(what) i(follo) n(ws,) g (we) f(impro) q(v) o(es) g(the) h(accur) r(ac) o(y) f(of) h(the) g(re) o (gres) r(sion) g(equa) 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0.9115824 0.1314261 0.9115824 0.1314261 c 0.9115824 0.1314261 0.9098123 0.1314261 0.9098123 0.1314261 c 0.9098123 0.1444235 m 0.9098123 0.1457224 0.9095164 0.1468062 0.9089272 0.1476709 c 0.9084554 0.1483634 0.9078342 0.1487116 0.9070665 0.1487116 c 0.9064773 0.1487116 0.9059441 0.1483634 0.9054723 0.1476709 c 0.9048831 0.1468062 0.9045872 0.1454212 0.9045872 0.1435119 c 0.9045872 0.1415204 0.9049125 0.1400493 0.9055603 0.1390946 c 0.9059735 0.1384882 0.9064773 0.1381830 0.9070665 0.1381830 c 0.9077169 0.1381830 0.9082767 0.1385312 0.9087486 0.1392238 c 0.9094577 0.1402645 0.9098123 0.1414343 0.9098123 0.1427333 c 0.9098123 0.1427333 0.9098123 0.1444235 0.9098123 0.1444235 c currentflat dup { gsave { clip } stopped { grestore 2 mul dup setflat dup 200 ge { pop exit } if }{ grestore setflat exit } ifelse } loop clip setflat newpath 12 dict begin /ImageType 1 def /Width cols def /Height rows def /ImageMatrix [cols 0 0 rows neg 0 rows] def /BitsPerComponent 8 def /Decode [0 1] def 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0.1323808 c 0.8991356 0.1337658 0.8986638 0.1356282 0.8986638 0.1379678 c 0.8986638 0.1403075 0.8991649 0.1422129 0.9001700 0.1436879 c 0.9009964 0.1449008 0.9020574 0.1455072 0.9033583 0.1455072 c 0.9045979 0.1455072 0.9056589 0.1448578 0.9065440 0.1435549 c 0.9073704 0.1423420 0.9077862 0.1404797 0.9077862 0.1379678 c 0.9077862 0.1379678 0.9006125 0.1379678 0.9006125 0.1379678 c 0.9006125 0.1361485 0.9009084 0.1348065 0.9014975 0.1339380 c 0.9057469 0.1400493 m 0.9057469 0.1409140 0.9055123 0.1416925 0.9050404 0.1423851 c 0.9046272 0.1429915 0.9040354 0.1432967 0.9032677 0.1432967 c 0.9025612 0.1432967 0.9019694 0.1429485 0.9014975 0.1422559 c 0.9010843 0.1416495 0.9008178 0.1409140 0.9007005 0.1400493 c 0.9007005 0.1400493 0.9057469 0.1400493 0.9057469 0.1400493 c currentflat dup { gsave { clip } stopped { grestore 2 mul dup setflat dup 200 ge { pop exit } if }{ grestore setflat exit } ifelse } loop clip setflat newpath 12 dict begin /ImageType 1 def /Width cols def /Height rows def 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1D35AE731E3F33DB93F47FD1DD5AE8EC7635B8F650FBFD2DC5E0B9966C78873B % E8BDA77355AD3C9556FA7E97F85FE6ECE7E9448DD3FF0009FE892521662E1B6D % 6D9F6DB89619DA720969D776D73376D7225F7D4EC8AB63C3B4D431E01D6DA1BF % E92AFF00CCFE87E93F99B48EF4F7E9EA4FA8DFA3C4EDFF00CF5B7F9C53A3D3F4 % BF3B6EF77F39CCEF747D2FCDDDFCCFF23624A7FFD9003842494D04211A566572 % 73696F6E20636F6D7061746962696C69747920696E666F000000005500000001 % 010000000F00410064006F00620065002000500068006F0074006F0073006800 % 6F00700000001300410064006F00620065002000500068006F0074006F007300 % 68006F007000200036002E003000000001003842494D03FD0845505320496E66 % 6F00000000070000000000000000 %EndPhotoshop gsave % EPS gsave 40 dict begin /_image systemdict /image get def /_setgray systemdict /setgray get def /_currentgray systemdict /currentgray get def /_settransfer systemdict /settransfer get def /_currenttransfer systemdict /currenttransfer get def /blank 0 _currenttransfer exec 1 _currenttransfer exec eq def /negative blank {0 _currenttransfer exec 0.5 lt} {0 _currenttransfer exec 1 _currenttransfer exec gt} ifelse def /inverted? negative def /level2 systemdict /languagelevel known {languagelevel 2 ge} {false} ifelse def /level3 systemdict /languagelevel known {languagelevel 3 ge} {false} ifelse def gsave % Image Header gsave /rows 541 def /cols 794 def 794 541 scale level2 { /DeviceGray setcolorspace currentdict /PhotoshopDuotoneColorSpace undef currentdict /PhotoshopDuotoneAltColorSpace undef } if /beginimage level2 {/image load def} {{pop .9 setgray 0 0 moveto 0 1 lineto 1 1 lineto 1 0 lineto fill 0 setgray 0 1 translate 1 cols div 1 rows div scale /ratio {cols 400 div mul} def /Helvetica findfont 15 ratio scalefont setfont 5 ratio -20 ratio moveto (JPEG \211\346\221\234\202\311\202\315\203|\203X\203g\203X\203N\203\212\203v\203g \203\214\203x\203\213 2 \202\252\225K\227v) show /x 128 string def {currentfile x readline {} {pop exit} ifelse (~>) search {pop pop pop exit} {pop} ifelse } loop } def} ifelse /m {moveto} bind def /c 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