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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: 2 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: Times-Bold Times-Roman CMR7 CMR6 CMMI10 CMMI7 CMR10 %%+ Helvetica Helvetica-Oblique Symbol CMSY10 CMEX10 CMSY7 Times-Italic %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips paper.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2002.07.04:0556 %%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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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 1 /periodcentered put dup 39 /similarequal put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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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 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 49 /one put dup 50 /two put dup 51 /three put dup 61 /equal put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F D1F017CE45884D76EF2CB9BC5821FD25365DDEA6E45F332B5F68A44AD8A530F0 92A36FAC8D27F9087AFEEA2096F839A2BC4B937F24E080EF7C0F9374A18D565C 295A05210DB96A23175AC59A9BD0147A310EF49C551A417E0A22703F94FF7B75 409A5D417DA6730A69E310FA6A4229FC7E4F620B0FC4C63C50E99E179EB51E4C 4BC45217722F1E8E40F1E1428E792EAFE05C5A50D38C52114DFCD24D54027CBF 2512DD116F0463DE4052A7AD53B641A27E81E481947884CE35661B49153FA19E 0A2A860C7B61558671303DE6AE06A80E4E450E17067676E6BBB42A9A24ACBC3E B0CA7B7A3BFEA84FED39CCFB6D545BB2BCC49E5E16976407AB9D94556CD4F008 24EF579B6800B6DC3AAF840B3FC6822872368E3B4274DD06CA36AF8F6346C11B 43C772CC242F3B212C4BD7018D71A1A74C9A94ED0093A5FB6557F4E0751047AF D72098ECA301B8AE68110F983796E581F106144951DF5B750432A230FDA3B575 5A38B5E7972AABC12306A01A99FCF8189D71B8DBF49550BAEA9CF1B97CBFC7CC 96498ECC938B1A1710B670657DE923A659DB8757147B140A48067328E7E3F9C3 7D1888B284904301450CE0BC15EEEA00E48CCD6388F3FC390C98D93BE299A9CB 689CDA9BE6BEA47570D9D15DC614719507F27069622E7DB1A97F7B6FF5A5A0C5 78162E7A9CF76FF72A34097236DF64DA4B61645C7326058030E2B5AABFCC44D0 49E9CD83D81D8ECA953BDB8CA81CD3D122FAB35612C9C3F6C7F22B666462A78C AC5473F8755B70B582C0D4C3C9D8C70EE755D41A42C8C17F066414DC21B33111 A188A5FDDC2D6B02C0965CDC0D91DF1A487ABBBBE2E2896CE0B4BFBE38C79866 BCD14C2C92449525BD879F6BC320C05FEF8BF68D616695ACD14B3594882B4914 5B7569629AF50EBCF7152E3715510FBF60F1675D5259715B293A3D7E844764F8 4B88D997BA5C7B7AB6B104E77F7769C22788334A91C91F02CE675DC14E1FDE5A F8A03756C12F189494DBC735E3C86A6D4BC4D005E323AC4D7CEF6E1820F9F184 4DD2EC4C5C58AEE4B5344077AFCCCD82CFC289D46552563B36DA5DAF3C179C90 BBB4163F2E88909E040769367672B37254345F892D42DF5D5261EAB4CFD4745D 7D72D01D779DEA580D7AA0897250CB8CC10EF282B3A1899F63F375E39C44176C BC5F159F6A66A32FC8E6E9B29598B5CC1AAEE157F181E0CD1F6A6905A2EFB24C 2D535A2A468368B888AC9F80D9D5559754494C63ADD6A4D14DEDEF6C3F7B56F8 FAC6CCF50FDFA1EFE7143155FF13598AEA14B87E9969A298C31E368A3389F086 AA15FD0DDFB389B220F8348A59EC91F0EA1D5B1F44F560DF42BB81A7E4757ECA 4B0546612A3303F3A270364D626900347194C40B044541344B190EEB0CD3544D 40CD48B0C180AEA1328305A9FFE35FA56CF0E4A74931B46BEB3845A1954CB230 2D77B2095CF9730947BCE40E976D17852FF49E41169E30A8D044D691C8124541 47197DF842F1FE44F5BE1580C83C9A47649094377DA499D118ECA8000E8B005A FFBB132FA364BFACD87167E50ADB7DE4E437AA742D94B7023E5156925FF9A15E 15FA85076928F8B4B92ACEAF1DA66D484EE2474F1CEE2588F6323421DA00655C 7D2650F0297054BC0322E39D1DE01197BDA008C134EEED24CAED95522EA39741 7C6CC4CE485DBD86E16FDA4B76C42D671039C175AD0BE096760D7D4DB6B31F3D B5CFCD55B1924AAFCF374AA4983FDB7CECBFCF1B60294A1C50FF46B71BAF8E4D 075BBBDBBD98502EEFA781650E97711279DCF88F80DF645E7024C90D2013EF01 BA8B4D5D3899F4C6EF675E3852BE951A2B6A285CCAECD89B63CB49E86C06DA12 9D72672800930BC38730DAED3FF374BB6DEB417BEC1C5618EDBA005A81C900E7 68E603104612AFE10D3877B205F77F4632FB75137F1B13A7FC57EEB6968351BC 0731ECED739F1E0CDCCC86A89F2E3B841563E80B2AE2621C293D1D30B60F76EE 9FB6F6171A73BD43C85C0F6E1179DF98098225BDFA21200ECD96B271D4E9DB01 A192358974FCEE950CA5C1CF1B839C25F21EF233E30E0B6388552C2356F9193E 87EC144ABFB5B1CE7069F5CE83E1A3F9F3E365A004848CB5EC41EB81B4C12997 62EC0466A58F9C0FE6598A4DF3F27F5C071E92FFF3E6728FC7C3D8689510BFC0 8247C4450DCB5F83B2FF52DD7038238D3A4CE61C6A76EA0301922D61AE057353 346F66BA6964E09C74222B048C763287431B4413DD9E481BFCC5987478B9FB38 4588205CCF083CB83A9B47573971B4AEAE6985297629BE2EF286E68261136D1E 9F4EB5481D1FFE78DF337A0DDBD4A0D3171DAAE601264ED3E3EC245EF2EC4454 8A621E45DDE73A9DBD58C75EFE585FC10C34B7C4E6F63A2495AC5F79562E160E B3182E02318D586011EB2E9BB918C5FC674C141B3FEB00AE98D49237B642C400 7C9F05B997BAF223F808D7FC9BC3C48FDF1EBB0E75CAFBE623A1BFE6ABDC944B 5A86CD19D9DD141BF803FD764C1C7F74ACA67C823EB6F5A75486D5CDCD00545E 53C3A848E0FA60E6432B60C81C80C5BB305320D8C3CD0F630C188679378BE68C 50C5AFBED6411A0BB32D7A9303677A2F74FB8F7AC6FC31044710EDAC12A4F3F3 D06BB8D9B0C67E1E03029AD788EED3B205621ADB84641F4FCB13D94A692C35DD 02788E0773A958EA1B21DF73820BE8ABBA2A 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % 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 (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 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 21 /lambda put dup 22 /mu put dup 78 /N put dup 98 /b put dup 107 /k put dup 109 /m put dup 110 /n put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueID 5087382 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D77639DF1232A4D6233A9CAF69B151DFD33F 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h(similar) f(mode) n (ling) g(approa) n(ch) h(pro) n(posed) -166 2738 y(in) 24 b([1],) h(we) f(analyze) f(the) h(netw) o(ork) f(with) i(multiple) e (TCP) i(conne) n(c-) -166 2834 y(tions,) 30 b(where) d(each) h(TCP) h (conn) n(ection) f(is) h(allo) n(wed) e(to) i(ha) n(v) o(e) e(dif-) -166 2930 y(feren) n(t) h(prop) n(agation) e(delay) -5 b(.) 45 b(W) -7 b(e) 28 b(\002rst) g(presen) n(t) g(the) f(steady) g(state) -166 3027 y(analysis) h(for) f(a) h(netw) o(or) n(k) g(with) g(a) g(single) f (TCP) i(conn) n(ection,) g(and) -166 3123 y(deri) n(v) m(e) h(the) g (TCP) g(throug) n(hput,) h(the) f(TCP) g(roun) n(d-trip) f(time,) j (and) -166 3220 y(the) 23 b(pack) o(et) g(loss) h(proba) n(bility) g (in) f(the) h(netw) o(ork) n(.) 35 b(W) -7 b(e) 25 b(then) e(e) o(xten) n(d) -166 3316 y(it) e(to) f(a) h(netw) o(ork) e(with) h(heterog) n (eneou) n(s) h(TCP) g(connectio) n(ns.) p Fi -166 3553 a(2) 99 b(Analytic) 25 b(Model) p Fm -166 3675 a(Figure) g(1) i (illustrates) f(our) g(analy) n(tic) h(model.) 42 b(The) 26 b(numb) n(er) p Fh 26 w(N) p Fm 36 w(of) -166 3772 y(TCP) c(conne) n (ctions) g(share) f(the) g(single) h(bottlen) n(eck) g(link,) f(and) g (each) -166 3868 y(TCP) 27 b(conne) n(ction) f(has) h(a) g(dif) n(fer) n (ent) g(pro) n(pagatio) n(n) g(delay) p Fh 26 w(\034) p Fg 1583 3880 a(n) p Fm 1628 3868 a(.) 44 b(W) -7 b(e) -166 3965 y(mode) n(l) 24 b(the) e(entire) h(netw) o(or) n(k,) h(includ) n (ing) e(TCP) i(mechan) n(isms) g(run) n(-) -166 4061 y(ning) k(on) h(source) f(hosts,) j(as) f(a) g(single) f(feedb) n(ack) g (system,) i(where) -166 4157 y(the) 22 b(cong) n(estion) g(contro) n(l) h(mech) n(anism) f(of) g(TCP) g(and) g(the) g(netw) o(or) n(k) -166 4254 y(seen) 28 b(by) f(TCP) i(interact) e(each) h(other) -7 b(.) 49 b(T) -7 b(able) 28 b(1) g(summa) n(rizes) g(the) -166 4350 y(de\002nition) 20 b(of) h(symbo) n(ls) h(used) f(throug) n(hout) f (this) i(paper) -7 b(.) 29 b(Note) 21 b(that) -166 4447 y(the) 28 b(TCP) i(thro) n(ughp) n(ut) p Fh 29 w(\025) p Fg 587 4459 a(n) p Fm 662 4447 a(is) f(de\002ned) e(as) j(the) e(pack) o (et) g(transmis-) -166 4543 y(sion) 17 b(rate) g(fro) n(m) g(the) g (source) f(host,) i(and) e(is) i(dif) n(fe) n(rent) f(from) f(the) h (TCP) -166 4639 y(goo) n(dput.) p Fi -166 4876 a(3) 99 b(Steady) 26 b(State) g(Analysis) p Ff -166 4999 a(3.1) 82 b(Case) 20 b(of) g(a) g(single) h(TCP) g(connectio) n(n) p Fm -166 5103 a(W) -7 b(e) 33 b(\002rst) f(presen) n(t) g(the) g(steady) f(state) h(analysis) g(for) e(the) i(netw) o(or) n(k) -166 5200 y(with) 17 b(a) g(single) g(TCP) g(connectio) n(n.) 24 b(The) 17 b(TCP) g(source) f(host) h(is) h(mod) n(-) -166 5296 y(eled) 29 b(by) g(a) h(SISO) g(\(Single) f(Inpu) n(t) i(and) e (Single) g(Outpu) n(t\)) h(system;) -166 5392 y(i.e.,) 20 b(the) g(pack) o(et) g(loss) h(pro) n(bability) p Fh 20 w(p) p Fm 20 w(in) g(the) f(netw) o(ork) f(is) i(the) f(input) -166 5489 y(to) d(the) h(system,) g(and) e(the) i(TCP) g(throu) n(ghpu) n(t) p Fh 18 w(\025) p Fm 18 w(is) h(the) e(outp) n(ut.) 25 b(Let) p Fh 17 w(p) p Fm -166 5585 a(and) p Fh 23 w(r) p Fm 26 w(be) e(the) g(pack) o(et) g(loss) h(pro) n(bability) f(in) g (the) g(netw) o(ork) f(and) g(the) -166 5682 y(roun) n(d-trip) 28 b(time) i(of) f(the) g(TCP) h(conn) n(ection,) h(respecti) n(v) o(e) n (ly) -5 b(.) 52 b(The) -166 5778 y(TCP) 25 b(throu) n(ghpu) n(t) p Fh 25 w(\025) p Fe(\() p Fh(p;) 14 b(r) p Fe 2 w(\)) p Fm 27 w(is) 25 b(appro) n(ximately) f(gi) n(v) o(e) n(n) h(by) f(the) g (fol-) 2028 2406 y @beginspecial 34 @llx 190 @lly 766 @urx 786 @ury 2214 @rwi @setspecial %%BeginDocument: figure/model2.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 34 190 766 786 %%Title: model2 %%CreationDate: Thu Jul 4 05:12:32 2002 %%Creator: Tgif-4.1.42-QPL written by William Chia-Wei Cheng (bill.cheng@acm.org) %%ProducedBy: (unknown) %%Pages: 1 %%DocumentFonts: (atend) %%EndComments %%BeginProlog /tgifdict 88 dict def tgifdict begin /tgifellipsedict 6 dict def tgifellipsedict /mtrx matrix put /TGEL % tgifellipse { tgifellipsedict begin /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y translate xrad yrad scale 0 0 1 0 360 arc savematrix setmatrix end } def /tgifarrowtipdict 8 dict def tgifarrowtipdict /mtrx matrix put /TGAT % tgifarrowtip { tgifarrowtipdict begin /dy exch def /dx exch def /h exch def /w exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y translate dy dx atan rotate 0 0 moveto w neg h lineto w neg h neg lineto savematrix setmatrix end } def /tgifpatdict 10 dict def /tgifpatbyte { currentdict /retstr get exch pat i cellsz mod get put } def /tgifpatproc { 0 1 widthlim {tgifpatbyte} for retstr /i i 1 add def } def /TGPF % tgifpatfill { tgifpatdict begin /h exch def /w exch def /lty exch def /ltx exch def /cellsz exch def /pat exch def /widthlim w cellsz div cvi 1 sub def /retstr widthlim 1 add string def /i 0 def tgiforigctm setmatrix ltx lty translate w h true [1 0 0 1 0 0] {tgifpatproc} imagemask ltx neg lty neg translate end } def /pat3 <8000000008000000> def /pat4 <8800000022000000> def /pat5 <8800220088002200> def /pat6 <8822882288228822> def /pat7 def /pat8 <77dd77dd77dd77dd> def /pat9 <77ffddff77ffddff> def /pat10 <77ffffff77ffffff> def /pat11 <7fffffff7fffffff> def /pat12 <8040200002040800> def /pat13 <40a00000040a0000> def /pat14 def /pat15 def /pat16 def /pat17 <038448300c020101> def /pat18 <081c22c180010204> def /pat19 <8080413e080814e3> def /pat20 <8040201008040201> def /pat21 <8844221188442211> def /pat22 <77bbddee77bbddee> def /pat23 def /pat24 <7fbfdfeff7fbfdfe> def /pat25 <3e1f8fc7e3f1f87c> def /pat26 <0102040810204080> def /pat27 <1122448811224488> def /pat28 def /pat29 <83070e1c3870e0c1> def /pat30 def /pat31 <7cf8f1e3c78f1f3e> def /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: 34 190 766 786 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 % BOX 0 SG NP 80 176 M 592 176 L 592 944 L 80 944 L CP F GS 10 SM GS NP 80 176 M 592 176 L 592 944 L 80 944 L CP S GR GR % BOX 0 SG NP 64 160 M 576 160 L 576 928 L 64 928 L CP 1 SG F 0 SG GS 10 SM GS NP 64 160 M 576 160 L 576 928 L 64 928 L CP S GR GR % BOX 0 SG NP 848 176 M 1360 176 L 1360 944 L 848 944 L CP F GS 10 SM GS NP 848 176 M 1360 176 L 1360 944 L 848 944 L CP S GR GR % BOX 0 SG NP 832 160 M 1344 160 L 1344 928 L 832 928 L CP 1 SG F 0 SG GS 10 SM GS NP 832 160 M 1344 160 L 1344 928 L 832 928 L CP S GR GR % TEXT NP 0 SG GS 1 W 493 784 M GS 0 SG /Symbol FF [34 0 0 -34 0 0] MS (l) SH 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (N) SH GR GR % BOX 0 SG NP 208 768 M 448 768 L 448 864 L 208 864 L CP F GS 10 SM GS NP 208 768 M 448 768 L 448 864 L 208 864 L CP S GR GR % BOX 0 SG NP 192 752 M 432 752 L 432 848 L 192 848 L CP 1 SG F 0 SG GS 10 SM GS NP 192 752 M 432 752 L 432 848 L 192 848 L CP S GR GR % TEXT NP 0 SG GS 1 W 308 797 M GS GS 0 /Helvetica FF [25 0 0 -25 0 0] MS (TCP Source Host) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [25 0 0 -25 0 0] MS (TCP Source Host) SH GR 0 29 RM GS GS 0 /Helvetica FF [25 0 0 -25 0 0] MS (N) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [25 0 0 -25 0 0] MS (N) SH GR GR % POLY/OPEN-SPLINE 0 SG GS NP 436 801 M 0 127 atan DU cos 22.000 MU 563 exch SU exch sin 22.000 MU 801 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 563 801 22.000 9.000 127 0 TGAT 1 SG CP F 0 SG NP 563 801 22.000 9.000 127 0 TGAT CP F GR % TEXT NP 0 SG GS 1 W 493 640 M GS 0 SG /Symbol FF [34 0 0 -34 0 0] MS (l) SH 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (N-1) SH GR GR % BOX 0 SG NP 208 624 M 448 624 L 448 720 L 208 720 L CP F GS 10 SM GS NP 208 624 M 448 624 L 448 720 L 208 720 L CP S GR GR % BOX 0 SG NP 192 608 M 432 608 L 432 704 L 192 704 L CP 1 SG F 0 SG GS 10 SM GS NP 192 608 M 432 608 L 432 704 L 192 704 L CP S GR GR % TEXT NP 0 SG GS 1 W 308 653 M GS GS 0 /Helvetica FF [25 0 0 -25 0 0] MS (TCP Source Host) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [25 0 0 -25 0 0] MS (TCP Source Host) SH GR 0 29 RM GS GS 0 /Helvetica FF [25 0 0 -25 0 0] MS (N-1) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [25 0 0 -25 0 0] MS (N-1) SH GR GR % POLY/OPEN-SPLINE 0 SG GS NP 436 657 M 0 127 atan DU cos 22.000 MU 563 exch SU exch sin 22.000 MU 657 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 563 657 22.000 9.000 127 0 TGAT 1 SG CP F 0 SG NP 563 657 22.000 9.000 127 0 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 84 657 M 0 111 atan DU cos 22.000 MU 195 exch SU exch sin 22.000 MU 657 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 195 657 22.000 9.000 111 0 TGAT 1 SG CP F 0 SG NP 195 657 22.000 9.000 111 0 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 84 801 M 0 111 atan DU cos 22.000 MU 195 exch SU exch sin 22.000 MU 801 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 195 801 22.000 9.000 111 0 TGAT 1 SG CP F 0 SG NP 195 801 22.000 9.000 111 0 TGAT CP F GR % TEXT NP 0 SG GS 1 W 128 640 M GS GS 0 /Helvetica-Oblique FF [34 0 0 -34 0 0] MS (p) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica-Oblique FF [34 0 0 -34 0 0] MS (p) SH GR GR % TEXT NP 0 SG GS 1 W 128 784 M GS GS 0 /Helvetica-Oblique FF [34 0 0 -34 0 0] MS (p) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica-Oblique FF [34 0 0 -34 0 0] MS (p) SH GR GR % POLY/OPEN-SPLINE 0 SG GS NP 596 353 M 0 223 atan DU cos 22.000 MU 819 exch SU exch sin 22.000 MU 353 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 819 353 22.000 9.000 223 0 TGAT 1 SG CP F 0 SG NP 819 353 22.000 9.000 223 0 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 596 737 M 0 223 atan DU cos 22.000 MU exch sin 22.000 MU RM 819 737 L TGSM 7 W S 1 W GR GS TGSM NP 596 737 22.000 9.000 -223 0 TGAT 1 SG CP F 0 SG NP 596 737 22.000 9.000 -223 0 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 850 519 M 0 127 atan DU cos 22.000 MU 977 exch SU exch sin 22.000 MU 519 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 977 519 22.000 9.000 127 0 TGAT 1 SG CP F 0 SG NP 977 519 22.000 9.000 127 0 TGAT CP F GR % TEXT NP 0 SG GS 1 W 1200 752 M GS GS 0 /Helvetica-Oblique FF [34 0 0 -34 0 0] MS (p) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica-Oblique FF [34 0 0 -34 0 0] MS (p) SH GR GR % TEXT NP 0 SG GS 1 W 909 496 M GS 0 SG /Symbol FF [34 0 0 -34 0 0] MS (l) SH GR GR % TEXT NP 0 SG GS 1 W 685 336 M GS 0 SG /Symbol FF [34 0 0 -34 0 0] MS (S) SH 0 SG /Symbol FF [34 0 0 -34 0 0] MS (l) SH 0 SG /Helvetica-Oblique FF [34 0 0 -34 0 0] MS (n) SH GR GR % POLY/OPEN-SPLINE 0 SG GS NP 1200 592 M 112 0 atan DU cos 22.000 MU 1200 exch SU exch sin 22.000 MU 704 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 1200 704 22.000 9.000 0 112 TGAT 1 SG CP F 0 SG NP 1200 704 22.000 9.000 0 112 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 1232 624 M 0 96 atan DU cos 12.000 MU 1328 exch SU exch sin 12.000 MU 624 exch SU L TGSM 3 W S 1 W GR GS TGSM NP 1328 624 12.000 5.000 96 0 TGAT 1 SG CP F 0 SG NP 1328 624 12.000 5.000 96 0 TGAT CP F GR % TEXT NP 0 SG GS 1 W 1280 608 M GS GS 0 /Symbol FF [34 0 0 -34 0 0] MS (m) TGSW AD GR 2 DI NE 0 RM 0 SG /Symbol FF [34 0 0 -34 0 0] MS (m) SH GR GR % TEXT NP 0 SG GS 1 W 714 706 M GS GS 0 /Helvetica-Oblique FF [34 0 0 -34 0 0] MS (p) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica-Oblique FF [34 0 0 -34 0 0] MS (p) SH GR GR % POLY/OPEN-SPLINE 0 SG GS NP 992 640 M 0 160 atan DU cos 12.000 MU exch sin 12.000 MU RM 0 160 atan DU cos 12.000 MU 1152 exch SU exch sin 12.000 MU 640 exch SU L TGSM 3 W S 1 W GR GS TGSM NP 992 640 12.000 5.000 -160 0 TGAT 1 SG CP F 0 SG NP 992 640 12.000 5.000 -160 0 TGAT CP F GR GS TGSM NP 1152 640 12.000 5.000 160 0 TGAT 1 SG CP F 0 SG NP 1152 640 12.000 5.000 160 0 TGAT CP F GR % TEXT NP 0 SG GS 1 W 1074 620 M GS GS 0 /Helvetica FF [34 0 0 -34 0 0] MS (m) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (m) SH GR GR % TEXT NP 0 SG GS 1 W 310 212 M GS GS 0 /Helvetica FF [34 0 0 -34 0 0] MS (TCP model) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (TCP model) SH GR GR % TEXT NP 0 SG GS 1 W 1082 214 M GS GS 0 /Helvetica FF [34 0 0 -34 0 0] MS (network model) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (network model) SH GR GR % TEXT NP 0 SG GS 1 W 698 114 M GS GS 0 /Symbol FF [34 0 0 -34 0 0] MS (t) TGSW AD /Helvetica FF [34 0 0 -34 0 0] MS (N) TGSW AD GR 2 DI NE 0 RM 0 SG /Symbol FF [34 0 0 -34 0 0] MS (t) SH 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (N) SH GR GR % TEXT NP 0 SG GS 1 W 493 304 M GS 0 SG /Symbol FF [34 0 0 -34 0 0] MS (l) SH 0 SG /Helvetica-Oblique FF [25 0 0 -25 0 0] MS (1) SH GR GR % BOX 0 SG NP 208 288 M 448 288 L 448 384 L 208 384 L CP F GS 10 SM GS NP 208 288 M 448 288 L 448 384 L 208 384 L CP S GR GR % BOX 0 SG NP 192 272 M 432 272 L 432 368 L 192 368 L CP 1 SG F 0 SG GS 10 SM GS NP 192 272 M 432 272 L 432 368 L 192 368 L CP S GR GR % TEXT NP 0 SG GS 1 W 308 317 M GS GS 0 /Helvetica FF [25 0 0 -25 0 0] MS (TCP Source Host) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [25 0 0 -25 0 0] MS (TCP Source Host) SH GR 0 29 RM GS GS 0 /Helvetica FF [25 0 0 -25 0 0] MS (1) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [25 0 0 -25 0 0] MS (1) SH GR GR % POLY/OPEN-SPLINE 0 SG GS NP 436 321 M 0 127 atan DU cos 22.000 MU 563 exch SU exch sin 22.000 MU 321 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 563 321 22.000 9.000 127 0 TGAT 1 SG CP F 0 SG NP 563 321 22.000 9.000 127 0 TGAT CP F GR % TEXT NP 0 SG GS 1 W 493 448 M GS 0 SG /Symbol FF [34 0 0 -34 0 0] MS (l) SH 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (2) SH GR GR % BOX 0 SG NP 208 432 M 448 432 L 448 528 L 208 528 L CP F GS 10 SM GS NP 208 432 M 448 432 L 448 528 L 208 528 L CP S GR GR % BOX 0 SG NP 192 416 M 432 416 L 432 512 L 192 512 L CP 1 SG F 0 SG GS 10 SM GS NP 192 416 M 432 416 L 432 512 L 192 512 L CP S GR GR % TEXT NP 0 SG GS 1 W 308 461 M GS GS 0 /Helvetica FF [25 0 0 -25 0 0] MS (TCP Source Host) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [25 0 0 -25 0 0] MS (TCP Source Host) SH GR 0 29 RM GS GS 0 /Helvetica FF [25 0 0 -25 0 0] MS (2) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [25 0 0 -25 0 0] MS (2) SH GR GR % POLY/OPEN-SPLINE 0 SG GS NP 436 465 M 0 127 atan DU cos 22.000 MU 563 exch SU exch sin 22.000 MU 465 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 563 465 22.000 9.000 127 0 TGAT 1 SG CP F 0 SG NP 563 465 22.000 9.000 127 0 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 84 321 M 0 111 atan DU cos 22.000 MU 195 exch SU exch sin 22.000 MU 321 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 195 321 22.000 9.000 111 0 TGAT 1 SG CP F 0 SG NP 195 321 22.000 9.000 111 0 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 84 465 M 0 111 atan DU cos 22.000 MU 195 exch SU exch sin 22.000 MU 465 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 195 465 22.000 9.000 111 0 TGAT 1 SG CP F 0 SG NP 195 465 22.000 9.000 111 0 TGAT CP F GR % TEXT NP 0 SG GS 1 W 128 304 M GS GS 0 /Helvetica-Oblique FF [34 0 0 -34 0 0] MS (p) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica-Oblique FF [34 0 0 -34 0 0] MS (p) SH GR GR % TEXT NP 0 SG GS 1 W 128 448 M GS GS 0 /Helvetica-Oblique FF [34 0 0 -34 0 0] MS (p) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica-Oblique FF [34 0 0 -34 0 0] MS (p) SH GR GR % POLY/OPEN-SPLINE 0 SG NP 320 960 M 1184 960 L 1184 1024 L 320 1024 L CP 1 SG EF 0 SG GS [16 16] 0 SD NP 320 960 M 1184 960 L 1184 1024 L 0 -864 atan DU cos 12.000 MU 320 exch SU exch sin 12.000 MU 1024 exch SU L TGSM 3 W S [] 0 SD 1 W GR GS TGSM NP 320 1024 12.000 5.000 -864 0 TGAT 1 SG CP F 0 SG NP 320 1024 12.000 5.000 -864 0 TGAT CP F GR % TEXT NP 0 SG GS 1 W 704 936 M GS GS 0 /Symbol FF [34 0 0 -34 0 0] MS (t) TGSW AD /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (N) TGSW AD GR 2 DI NE 0 RM 0 SG /Symbol FF [34 0 0 -34 0 0] MS (t) SH 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (N) SH GR GR % POLY/OPEN-SPLINE 0 SG NP 320 64 M 1184 64 L 1184 128 L 320 128 L CP 1 SG EF 0 SG GS [16 16] 0 SD NP 320 64 M 1184 64 L 1184 128 L 0 -864 atan DU cos 12.000 MU 320 exch SU exch sin 12.000 MU 128 exch SU L TGSM 3 W S [] 0 SD 1 W GR GS TGSM NP 320 128 12.000 5.000 -864 0 TGAT 1 SG CP F 0 SG NP 320 128 12.000 5.000 -864 0 TGAT CP F GR % TEXT NP 0 SG GS 1 W 704 40 M GS GS 0 /Symbol FF [34 0 0 -34 0 0] MS (t) TGSW AD /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (1) TGSW AD GR 2 DI NE 0 RM 0 SG /Symbol FF [34 0 0 -34 0 0] MS (t) SH 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (1) SH GR GR % TEXT NP 0 SG GS 1 W 1090 426 M GS GS 0 /Helvetica FF [24 0 0 -24 0 0] MS (bottleneck router) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [24 0 0 -24 0 0] MS (bottleneck router) SH GR GR % BOX 0 SG NP 1144 474 M 1160 474 L 1160 586 L 1144 586 L CP F GS 10 SM GS NP 1144 474 M 1160 474 L 1160 586 L 1144 586 L CP S GR GR % BOX 0 SG NP 1128 474 M 1144 474 L 1144 586 L 1128 586 L CP F GS 10 SM GS NP 1128 474 M 1144 474 L 1144 586 L 1128 586 L CP S GR GR % BOX 0 SG NP 1112 474 M 1128 474 L 1128 586 L 1112 586 L CP F GS 10 SM GS NP 1112 474 M 1128 474 L 1128 586 L 1112 586 L CP S GR GR % BOX 0 SG NP 1096 474 M 1112 474 L 1112 586 L 1096 586 L CP F GS 10 SM GS NP 1096 474 M 1112 474 L 1112 586 L 1096 586 L CP S GR GR % BOX 0 SG NP 1080 474 M 1096 474 L 1096 586 L 1080 586 L CP F GS 10 SM GS NP 1080 474 M 1096 474 L 1096 586 L 1080 586 L CP S GR GR % BOX 0 SG NP 1064 474 M 1080 474 L 1080 586 L 1064 586 L CP F GS 10 SM GS NP 1064 474 M 1080 474 L 1080 586 L 1064 586 L CP S GR GR % BOX 0 SG NP 1048 474 M 1064 474 L 1064 586 L 1048 586 L CP F GS 10 SM GS NP 1048 474 M 1064 474 L 1064 586 L 1048 586 L CP S GR GR % BOX 0 SG NP 1032 474 M 1048 474 L 1048 586 L 1032 586 L CP F GS 10 SM GS NP 1032 474 M 1048 474 L 1048 586 L 1032 586 L CP S GR GR % BOX 0 SG NP 1016 474 M 1032 474 L 1032 586 L 1016 586 L CP F GS 10 SM GS NP 1016 474 M 1032 474 L 1032 586 L 1016 586 L CP S GR GR % BOX 0 SG NP 1000 474 M 1016 474 L 1016 586 L 1000 586 L CP F GS 10 SM GS NP 1000 474 M 1016 474 L 1016 586 L 1000 586 L CP S GR GR % OVAL 0 SG NP 1208 529 64 64 TGEL F GS GS NP 1208 529 64 64 TGEL S GR GR % BOX 0 SG GS NP 1136 464 M 1152 464 L 1152 576 L 1136 576 L CP 1 SG F 0 SG NP 1136 464 M 1152 464 L 1152 576 L 1136 576 L CP EC NP pat6 8 1128 456 32 128 TGPF GR GS 10 SM GS NP 1136 464 M 1152 464 L 1152 576 L 1136 576 L CP S GR GR % BOX 0 SG GS NP 1120 464 M 1136 464 L 1136 576 L 1120 576 L CP 1 SG F 0 SG NP 1120 464 M 1136 464 L 1136 576 L 1120 576 L CP EC NP pat6 8 1112 456 32 128 TGPF GR GS 10 SM GS NP 1120 464 M 1136 464 L 1136 576 L 1120 576 L CP S GR GR % BOX 0 SG GS NP 1104 464 M 1120 464 L 1120 576 L 1104 576 L CP 1 SG F 0 SG NP 1104 464 M 1120 464 L 1120 576 L 1104 576 L CP EC NP pat6 8 1096 456 32 128 TGPF GR GS 10 SM GS NP 1104 464 M 1120 464 L 1120 576 L 1104 576 L CP S GR GR % BOX 0 SG GS NP 1088 464 M 1104 464 L 1104 576 L 1088 576 L CP 1 SG F 0 SG NP 1088 464 M 1104 464 L 1104 576 L 1088 576 L CP EC NP pat6 8 1080 456 32 128 TGPF GR GS 10 SM GS NP 1088 464 M 1104 464 L 1104 576 L 1088 576 L CP S GR GR % BOX 0 SG GS NP 1072 464 M 1088 464 L 1088 576 L 1072 576 L CP 1 SG F 0 SG NP 1072 464 M 1088 464 L 1088 576 L 1072 576 L CP EC NP pat6 8 1064 456 32 128 TGPF GR GS 10 SM GS NP 1072 464 M 1088 464 L 1088 576 L 1072 576 L CP S GR 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MS (TCP) SH GR 0 38 RM GS GS 0 /Helvetica FF [34 0 0 -34 0 0] MS (throughput) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (throughput) SH GR GR % TEXT NP 0 SG NP 629 752 M 791 752 L 791 829 L 629 829 L CP 1 SG F 0 SG GS 1 W 710 784 M GS GS 0 /Helvetica FF [34 0 0 -34 0 0] MS (packet loss) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (packet loss) SH GR 0 38 RM GS GS 0 /Helvetica FF [34 0 0 -34 0 0] MS (probability) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (probability) SH GR GR % TEXT NP 0 SG NP 501 1028 M 886 1028 L 886 1067 L 501 1067 L CP 1 SG F 0 SG GS 1 W 694 1060 M GS GS 0 /Helvetica FF [34 0 0 -34 0 0] MS (two-way propagation delay) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (two-way propagation delay) SH GR GR GR tgifsavedpage restore end showpage %%Trailer %MatchingCreationDate: Thu Jul 4 05:12:32 2002 %%DocumentFonts: Helvetica %%+ Helvetica-Oblique %%+ Symbol %%EOF %%EndDocument @endspecial 2520 2585 a(Figure) 19 b(1:) 26 b(Analytic) 19 b(model.) 2417 2692 y(T) -7 b(able) 20 b(1) 79 b(De\002nition) 20 b(of) f(symbols.) p 1967 2735 1883 4 v Fh 1992 2803 a(N) p Fm 77 w(the) h(num) n(ber) g(of) g(TCP) h(conne) n(ctions) p Fh 1992 2899 a(\026) p Fm 94 w(pack) m(et) g(processing) e(speed) h(of) g(bottlen) n(eck) g(router) p Fh 1992 2996 a(m) p Fm 71 w(b) n(uf) n(f) n(er) g(size) h(of) f(bottleneck) f(route) n(r) p Fh 1992 3092 a(\034) p Fg 2028 3104 a(n) p Fm 2136 3092 a(tw) o(o-w) o(ay) g(prop) n(agation) g(delay) h(of) p Fh 20 w(n) p Fm(th) g(TCP) h(conn) n(ection) p Fh 1992 3188 a(r) p Fg 2029 3200 a(n) p Fm 2136 3188 a(rou) n(nd-trip) e(time) h (of) p Fh 20 w(n) p Fm(th) g(TCP) h(connectio) n(n) p Fh 1992 3285 a(\025) p Fg 2040 3297 a(n) p Fm 2136 3285 a(thro) n(ughp) n(ut) g(of) p Fh 20 w(n) p Fm(th) f(TCP) h(conn) n (ection) p Fh 1992 3381 a(p) p Fm 102 w(pack) m(et) g(loss) g(prob) n (ability) f(in) h(the) f(netw) o(ork) p 1967 3413 V 1967 3547 a(lo) n(wing) g(equ) n(ation) g([2].) p Fh 2558 3768 a(\025) p Fe(\() p Fh(p;) 14 b(r) p Fe 2 w(\)) p Fd 84 w(') p Fe 3030 3712 a(1) p 3030 3749 42 4 v Fh 3031 3825 a(r) p Fc 3095 3646 a(r) p 3178 3646 167 4 v Fe 3241 3712 a(3) p 3188 3749 147 4 v 3188 3825 a(2) p Fh 14 w(b) g(p) p Fm 3838 3768 a(\(1\)) 1967 3973 y(In) 29 b(the) g(abo) o(v) m(e) g(equation) n(,) p Fh 32 w(b) p Fm 29 w(\(usually) p Fh 28 w(b) p Fe 39 w(=) 39 b(1) p Fm 29 w(or) p Fh 28 w(b) p Fe 39 w(=) g(2) p Fm(\)) 29 b(is) h(the) 1967 4070 y(numb) n(er) 22 b(of) g(pack) o(ets) g(requ) n (ired) g(for) f(the) h(TCP) h(destination) e(host) h(to) 1967 4166 y(send) e(an) g(A) m(CK) h(pack) o(et.) 2047 4262 y(W) -7 b(e) 32 b(then) d(model) h(the) g(netw) o(ork) f(seen) h(from) f (the) i(TCP) g(sourc) n(e) 1967 4359 y(host) 24 b(by) f(a) h(single) g (FIFO) g(\(First-In) e(First-Out\)) i(queu) n(e.) 36 b(Pro) o(v) n(ided) 1967 4455 y(that) 19 b(queu) n(eing) f(delay) g (occu) n(rs) h(only) f(at) h(the) f(bottlenec) n(k) h(rou) n(ter) m(,) g (the) 1967 4551 y(bottleneck) 24 b(router) h(is) h(mode) n(led) g(by) f (a) h(M/M/1) f(queuin) n(g) h(system.) 1967 4648 y(In) d(other) g(w) o (ords,) g(the) h(netw) o(ork) e(is) i(modeled) e(by) h(a) h(SISO) g (system,) 1967 4744 y(where) h(the) g(inpu) n(t) h(is) g(the) f(TCP) h (throug) n(hput) p Fh 24 w(\025) p Fm 26 w(and) f(the) g(outpu) n(t) h (is) 1967 4841 y(the) c(pack) o(et) g(loss) h(pro) n(bability) p Fh 21 w(p) p Fm 23 w(at) f(the) g(bottleneck) f(route) n(r) -5 b(.) 32 b(Let) p Fh 22 w(\025) p Fm 1967 4937 a(and) p Fh 18 w(m) p Fm 19 w(be) 18 b(the) g(TCP) h(throu) n(ghpu) n(t) g(and) f (the) g(b) n(uf) n(f) n(er) h(size) f(of) g(the) g(bot-) 1967 5033 y(tleneck) h(rou) n(ter) -5 b(.) 26 b(The) 18 b(pack) o(et) h (loss) h(pro) n(bability) f(in) g(the) g(netw) o(ork) f(is) 1967 5130 y(appro) n(ximated) i(as) p Fh 2509 5437 a(p) p Fe(\() p Fh(\025) p Fe(\)) p Fd 84 w(') p Fe 83 w(1) p Fd 18 w(\000) p Fg 3069 5333 a(m) p Fc 3038 5358 a(X) p Fg 3038 5537 a(k) p Fl 1 w(=0) p Fh 3186 5437 a(P) p Fg 3239 5449 a(k) p Fe 3280 5437 a(\() p Fh(\025) p Fe(\)) p Fm 446 w(\(2\)) 1967 5682 y(where) p Fh 30 w(P) p Fg 2254 5694 a(k) p Fe 2295 5682 a(\() p Fh(\025) p Fe(\)) p Fm 32 w(is) 31 b(the) f(state) g(probab) n(ility) h(of) e(a) i(M/M/1) f (queu) n(ing) 1967 5778 y(system.) k(By) 24 b(letting) p Fh 22 w(\026) p Fm 24 w(be) f(the) g(pack) o(et) g(pro) n(cessing) g (speed) g(of) g(the) p dyy eop end %%Page: 2 2 TeXDict begin 2 1 bop Fm -166 173 a(bottlene) n(ck) 21 b(rou) n(ter) m(,) p Fh 20 w(P) p Fg 490 185 a(k) p Fe 531 173 a(\() p Fh(\025) p Fe(\)) p Fm 22 w(is) g(gi) n(v) o(en) e(by) p Fh 301 429 a(P) p Fg 354 441 a(k) p Fe 395 429 a(\() p Fh(\025) p Fe(\)) 84 b(=) p Fc 739 312 a(\022) p Fe 800 429 a(1) p Fd 18 w(\000) p Fh 954 373 a(\025) p 953 410 51 4 v 953 486 a(\026) p Fc 1013 312 a(\023) 28 b(\022) p Fh 1174 373 a(\025) p 1173 410 V 1173 486 a(\026) p Fc 1233 312 a(\023) p Fg 1294 329 a(k) p Fm 1705 429 a(\(3\)) -166 665 y(Thus,) p Fh 20 w(p) p Fe(\() p Fh(\025) p Fe(\)) p Fm 21 w(is) 21 b(obtained) e(from) g(Eqs.) h(\(2\)) g(and) f(\(3\)) h (as) p Fh 456 918 a(p) p Fe(\() p Fh(\025) p Fe(\)) p Fd 83 w(') p Fc 841 801 a(\022) p Fh 913 862 a(\025) p 912 899 V 912 975 a(\026) p Fc 972 801 a(\023) p Fl 1033 818 a(1+) p Fg(m) p Fm 1705 918 a(\(4\)) -166 1148 y(Since) 31 b(the) g(windo) l(w-based) f(\003o) n(w) h(contro) n(l) h(mech) n (anism) f(of) g(TCP) -166 1245 y(oper) n(ates) d(arou) n(nd) f(the) f (100\045) g(of) n(fered) f(traf) n(\002c) i(load,) p Fh 28 w(p) p Fe(\() p Fh(\025) p Fe(\)) p Fm 28 w(in) f(the) -166 1341 y(abo) o(v) m(e) 20 b(equation) f(can) h(be) g(appro) n(ximated) g (by) p Fh 354 1568 a(p) p Fe(\() p Fh(\025) p Fe(\)) p Fd 83 w(') p Fh 749 1511 a(\025) p Fe 19 w(+) p Fh 18 w(\025) 14 b(m) p Fd 19 w(\000) p Fh 18 w(m) g(\026) p 749 1549 524 4 v 986 1625 a(\026) p Fm 1705 1568 a(\(5\)) -166 1792 y(W) -7 b(e) 25 b(then) e(deri) n(v) o(e) g(the) g(roun) n(d-trip) g(time) h(of) g(the) f(TCP) i(conn) n(ection.) -166 1889 y(Let) p Fh 28 w(\034) p Fm 38 w(be) j(the) g(pro) n(pagatio) n(n) g (delay) f(of) h(a) g(TCP) h(conn) n(ection.) 47 b(W) -7 b(e) -166 1985 y(assume) 29 b(that) h(the) g(queu) n(eing) f(delay) g (occur) n(s) i(only) e(at) h(the) f(bottle-) -166 2081 y(neck) 19 b(rou) n(ter) -5 b(.) 25 b(F) o(or) 19 b(a) h(gi) n(v) o(en) e(TCP) i(throu) n(ghpu) n(t) p Fh 20 w(\025) p Fm(,) g(the) g(TCP) g (rou) n(nd-) -166 2178 y(trip) 29 b(time) p Fh 30 w(r) p Fe 2 w(\() p Fh(\025) p Fe(\)) p Fm 31 w(is) h(obtained) e(using) h (the) g(a) n(v) o(erage) f(queue) g(length) p Fh -166 2274 a(L) p Fe 31 w(=) p Fh 30 w(\025=) p Fe(\() p Fh(\026) p Fd 22 w(\000) p Fh 22 w(\025) p Fe(\)) p Fm 26 w(of) c(a) h(M/M/1) f (queuein) n(g) h(system) g(and) f(the) g(Lit-) -166 2370 y(tle') -5 b(s) 21 b(theorem) p Fh 19 w(N) p Fe 32 w(=) p Fh 22 w(\025) 14 b(T) p Fm 12 w(.) 25 b(Thus,) p Fh 276 2590 a(r) p Fe 2 w(\() p Fh(\025) p Fe(\)) 84 b(=) p Fh 669 2534 a(L) p 669 2571 57 4 v 673 2647 a(\025) p Fe 754 2590 a(+) p Fh 18 w(\034) p Fe 33 w(=) 1082 2534 y(1) p 1003 2571 200 4 v Fh 1003 2647 a(\026) p Fd 19 w(\000) p Fh 18 w(\025) p Fe 1232 2590 a(+) p Fh 18 w(\034) p Fm 354 w(\(6\)) -166 2815 y(Let) p Fh 29 w(\025) p Fb 22 2785 a(\003) p Fm 60 2815 a(,) p Fh 31 w(r) p Fb 151 2785 a(\003) p Fm 190 2815 a(,) 31 b(and) p Fh 28 w(p) p Fb 433 2785 a(\003) p Fm 500 2815 a(be) d(the) g(TCP) i(thro) n(ughp) n (ut,) h(the) d(roun) n(d-trip) -166 2912 y(time) 20 b(of) f(the) h(TCP) g(conne) n(ction,) f(and) h(the) f(pack) o(et) g(loss) i(pro) n (bability) -166 3008 y(in) i(the) g(netw) o(ork) f(in) i(steady) f (state,) h(respecti) n(v) o(e) n(ly) -5 b(.) 34 b(From) 22 b(Eqs.) h(\(1\),) -166 3105 y(\(5\),) 28 b(and) f(\(6\),) h(the) g (follo) l(wing) f(relations) g(are) g(satis\002ed) h(in) g(steady) -166 3201 y(state.) p Fh 482 3384 a(\025) p Fe(\() p Fh(p) p Fb 604 3350 a(\003) p Fh 643 3384 a(;) 14 b(r) p Fb 719 3350 a(\003) p Fe 758 3384 a(\)) 23 b(=) p Fh 23 w(\025) p Fb 949 3350 a(\003) p Fh 604 3505 a(p) p Fe(\() p Fh(\025) p Fb 726 3471 a(\003) p Fe 765 3505 a(\)) g(=) p Fh 23 w(p) p Fb 950 3471 a(\003) p Fh 608 3627 a(r) p Fe 2 w(\() p Fh(\025) p Fb 727 3592 a(\003) p Fe 767 3627 a(\)) g(=) p Fh 23 w(r) p Fb 949 3592 a(\003) p Fm -166 3809 a(By) 17 b(solving) f(these) h(equation) n(s,) h(we) g(can) e (obtain) g(the) h(TCP) h(throu) n(gh-) -166 3906 y(put) p Fh 25 w(\025) p Fb 14 3876 a(\003) p Fm 53 3906 a(,) 27 b(the) e(roun) n(d-trip) g(time) p Fh 26 w(r) p Fb 804 3876 a(\003) p Fm 869 3906 a(of) g(the) g(TCP) i(conn) n(ection,) f (and) -166 4002 y(the) c(pack) o(et) g(loss) g(proba) n(bility) p Fh 22 w(p) p Fb 777 3972 a(\003) p Fm 838 4002 a(in) g(steady) g (state.) 31 b(F) o(or) 22 b(e) o(xamp) n(le,) -166 4099 y(the) g(TCP) h(thro) n(ughp) n(ut) p Fh 23 w(\025) p Fb 568 4068 a(\003) p Fm 629 4099 a(in) f(steady) f(state) i(is) g(gi) n (v) o(e) n(n) f(by) g(the) g(solu-) -166 4195 y(tion) e(of) g(the) g (follo) n(win) n(g) h(equ) n(ation.) p Fe 208 4405 a(\() p Fh(\026) p Fd 19 w(\000) p Fh 18 w(\025) p Fe(\)) p Fc 500 4314 a(q) p 583 4314 520 4 v Fl 801 4368 a(3) p Fg 11 w(\026) p 593 4386 500 4 v Fl 593 4434 a(2) p Fg 12 w(b) p Fl 11 w(\() p Fg(\025) p Fl(+) p Fg(\025) 12 b(m) p Fb(\000) p Fg(m) f(\026) p Fl(\)) p 208 4474 895 4 v Fe 424 4550 a(1) p Fd 18 w(\000) p Fh 18 w(\025) j(\034) p Fe 29 w(+) p Fh 18 w(\026) g(\034) p Fe 1136 4493 a(=) p Fh 22 w(\025) p Fm 434 w(\(7\)) p Ff -166 4720 a(3.2) 82 b(Case) 20 b(of) g(multiple) h(TCP) g(connectio) n(ns) p Fm -166 4820 a(In) 26 b(what) g(follo) n(ws,) h(we) g(e) o(xten) n(d) g (the) f(pre) n(v) n(ious) h(analy) n(sis) h(to) e(a) h(net-) -166 4917 y(w) o(ork) f(with) h(hetero) n(geneo) n(us) g(TCP) h(conn) n (ections.) 44 b(Let) p Fh 27 w(N) p Fm 36 w(be) 26 b(the) -166 5013 y(numb) n(er) i(of) f(TCP) h(conne) n(ctions,) p Fh 29 w(\025) p Fg 888 5025 a(n) p Fm 962 5013 a(be) f(the) h(throu) n (ghpu) n(t) g(of) p Fh 27 w(n) p Fm(th) -166 5109 y(TCP) 23 b(conn) n(ection,) f(and) p Fh 22 w(r) p Fg 597 5121 a(n) p Fm 665 5109 a(be) h(the) f(rou) n(nd-trip) f(time) i(of) p Fh 21 w(n) p Fm(th) g(TCP) -166 5206 y(conn) n(ection.) 54 b(W) -7 b(e) 30 b(assume) g(rando) n(m) g(pack) o(et) f(losses) i(in) f (the) g(net-) -166 5302 y(w) o(ork.) 46 b(From) 27 b(Eq.) g(\(1\),) h (for) f(a) h(gi) n(v) o(e) n(n) g(pack) o(et) f(loss) h(pro) n (bability) p Fh 27 w(p) p Fm -166 5398 a(in) f(the) g(netw) o(ork,) h (the) f(throu) n(ghpu) n(t) h(of) f(each) g(TCP) h(con) n(nection) f (is) -166 5495 y(gi) n(v) o(en) 19 b(by) p Fh 360 5737 a(\025) p Fg 408 5749 a(n) p Fe 454 5737 a(\() p Fh(p;) 14 b(r) p Fg 602 5749 a(n) p Fe 647 5737 a(\)) p Fd 83 w(') p Fe 941 5681 a(1) p 920 5718 83 4 v Fh 920 5794 a(r) p Fg 957 5806 a(n) p Fc 1026 5614 a(r) p 1109 5614 167 4 v Fe 1172 5681 a(3) p 1119 5718 147 4 v 1119 5794 a(2) p Fh 14 w(b) g(p) p Fm 1705 5737 a(\(8\)) 2047 173 y(W) -7 b(e) 24 b(then) e(mod) n(el) i(the) e(netw) o(ork) f(seen) i(from) e (TCP) j(source) e(hosts) 1967 270 y(as) j(a) f(MISO) h(\(Multi) e (Input) g(and) h(Single) g(Outpu) n(t\)) g(system,) h(where) 1967 366 y(the) h(inpu) n(ts) g(are) g(thro) n(ughp) n(uts) p Fh 26 w(\025) p Fg 2921 378 a(n) p Fm 2993 366 a(of) f(TCP) h(conn) n (ections) f(and) g(the) 1967 462 y(outpu) n(t) c(is) g(the) f(pack) m (et) h(loss) g(pro) n(bability) p Fh 20 w(p) p Fm 20 w(in) f(the) g(netw) o(or) n(k.) 25 b(From) 1967 559 y(Eq.) 18 b(\(2\),) f(the) h(pack) o(et) f(loss) i(prob) n(ability) f (in) g(the) g(netw) o(or) n(k) g(with) g(mul-) 1967 655 y(tiple) j(TCP) g(conn) n(ections,) p Fh 20 w(p) p Fe(\() p Fh(\025) p Fl 2869 667 a(1) p Fh 2906 655 a(;) p Fd 14 w(\001) 14 b(\001) g(\001) p Fh 14 w(;) g(\025) p Fg 3139 667 a(N) p Fe 3202 655 a(\)) p Fm(,) 21 b(is) g(obtained) e(as) p Fh 2251 919 a(p) p Fe(\() p Fh(\025) p Fl 2373 931 a(1) p Fh 2410 919 a(;) p Fd 14 w(\001) 14 b(\001) g(\001) p Fh 14 w(;) g(\025) p Fg 2643 931 a(N) p Fe 2706 919 a(\)) p Fd 84 w(') p Fe 82 w(1) p Fd 18 w(\000) p Fg 3143 815 a(m) p Fc 3113 840 a(X) p Fg 3112 1019 a(k) p Fl 1 w(=0) p Fh 3261 919 a(P) p Fg 3314 931 a(k) p Fe 3355 919 a(\() p Fg 3420 815 a(N) p Fc 3390 840 a(X) p Fg 3387 1016 a(n) p Fl(=1) p Fh 3526 919 a(\025) p Fg 3574 931 a(n) p Fe 3620 919 a(\)) p Fm 186 w(\(9\)) 1967 1176 y(Similarly) -5 b(,) 33 b(for) e(a) g(gi) n(v) o(en) f(TCP) i(throug) n(hput) p Fh 30 w(\025) p Fg 3364 1188 a(n) p Fm 3410 1176 a(,) i(the) e(rou) n (nd-trip) 1967 1273 y(time) p Fh 43 w(r) p Fg 2195 1285 a(n) p Fe 2241 1273 a(\() p Fh(\025) p Fg 2321 1285 a(n) p Fe 2366 1273 a(\)) p Fm 44 w(of) p Fh 42 w(n) p Fm(th) 43 b(TCP) g(conn) n(ections) f(is) i(obtain) n(ed) f(from) 1967 1369 y(Eq.) 20 b(\(6\).) p Fh 2376 1588 a(r) p Fg 2413 1600 a(n) p Fe 2459 1588 a(\() p Fh(\025) p Fg 2539 1600 a(n) p Fe 2585 1588 a(\)) 83 b(=) 3075 1532 y(1) p 2858 1569 476 4 v Fh 2858 1660 a(\026) p Fd 18 w(\000) p Fc 3009 1598 a(P) p Fg 3097 1618 a(N) 3097 1685 y(n) p Fl(=1) p Fh 3240 1660 a(\025) p Fg 3288 1672 a(n) p Fe 3362 1588 a(+) p Fh 18 w(\034) p Fg 3481 1600 a(n) p Fm 3797 1588 a(\(10\)) 1967 1833 y(where) p Fh 20 w(\034) p Fg 2227 1845 a(n) p Fm 2293 1833 a(is) 21 b(the) f(propa) n(gation) f(delay) h (of) p Fh 20 w(n) p Fm(th) g(TCP) h(conn) n(ection.) 2047 1929 y(Finally) -5 b(,) 34 b(we) e(deri) n(v) m(e) g(the) f(equilibriu) n(m) h(in) g(steady) f(state.) 60 b(Let) p Fh 1967 2026 a(\025) p Fb 2015 1996 a(\003) p Fg 2015 2046 a(n) p Fm 2061 2026 a(,) p Fh 30 w(r) p Fb 2151 1996 a(\003) p Fg 2149 2046 a(n) p Fm 2194 2026 a(,) 30 b(and) p Fh 27 w(p) p Fb 2435 1996 a(\003) p Fm 2501 2026 a(be) e(the) f(throug) n (hput) g(of) p Fh 27 w(n) p Fm(th) h(TCP) g(conne) n(ction,) 1967 2122 y(the) d(rou) n(nd-trip) e(time) h(of) p Fh 24 w(n) p Fm(th) h(TCP) g(con) n(nection,) f(and) g(the) g(pack) o(et) 1967 2219 y(loss) 29 b(pro) n(bability) e(in) h(steady) f(state,) k (respecti) n(v) m(ely) -5 b(.) 47 b(W) -7 b(e) 29 b(ha) n(v) o(e) e (the) 1967 2315 y(follo) n(wing) 19 b(equatio) n(ns) i(from) e(Eqs.) h (\(8\),) f(\(9\),) h(and) f(\(10\).) p Fh 2680 2494 a(\025) p Fl 2728 2506 a(1) p Fe 2765 2494 a(\() p Fh(p) p Fb 2839 2460 a(\003) p Fh 2878 2494 a(;) 14 b(r) p Fb 2954 2460 a(\003) p Fl 2952 2515 a(1) p Fe 2992 2494 a(\)) 84 b(=) p Fh 82 w(\025) p Fb 3303 2460 a(\003) p Fl 3303 2515 a(1) p Fm 3130 2607 a(.) 3130 2640 y(.) 3130 2673 y(.) p Fh 2631 2794 a(\025) p Fg 2679 2806 a(N) p Fe 2743 2794 a(\() p Fh(p) p Fb 2817 2760 a(\003) p Fh 2855 2794 a(;) 14 b(r) p Fb 2931 2760 a(\003) p Fg 2929 2815 a(N) p Fe 2992 2794 a(\)) 84 b(=) p Fh 82 w(\025) p Fb 3303 2760 a(\003) p Fg 3303 2815 a(N) p Fh 2536 2916 a(p) p Fe(\() p Fh(\025) p Fb 2658 2881 a(\003) p Fl 2658 2936 a(1) p Fh 2696 2916 a(;) p Fd 14 w(\001) 14 b(\001) g(\001) p Fh 14 w(;) g(\025) p Fb 2929 2881 a(\003) p Fg 2929 2936 a(N) p Fe 2992 2916 a(\)) 84 b(=) p Fh 82 w(p) p Fb 3297 2881 a(\003) p Fh 2834 3037 a(r) p Fe 2 w(\() p Fh(\025) p Fb 2953 3003 a(\003) p Fl 2953 3057 a(1) p Fe 2992 3037 a(\)) g(=) p Fh 82 w(r) p Fb 3294 3003 a(\003) p Fl 3292 3057 a(1) p Fm 3130 3149 a(.) 3130 3182 y(.) 3130 3215 y(.) p Fh 2809 3337 a(r) p Fe 2 w(\() p Fh(\025) p Fb 2928 3302 a(\003) p Fg 2928 3357 a(N) p Fe 2992 3337 a(\)) g(=) p Fh 82 w(r) p Fb 3294 3302 a(\003) p Fg 3292 3357 a(N) p Fm 1967 3516 a(By) 23 b(nume) n(rically) f(solving) g (these) g(equatio) n(ns) h(for) p Fh 22 w(\025) p Fb 3476 3486 a(\003) p Fg 3476 3537 a(n) p Fm 3521 3516 a(,) p Fh 23 w(r) p Fb 3604 3486 a(\003) p Fg 3602 3537 a(n) p Fm 3648 3516 a(,) g(and) p Fh 22 w(p) p Fb 3877 3486 a(\003) p Fm 3914 3516 a(,) 1967 3613 y(the) f(thro) n(ughpu) n(t) g(and) f(the) g(round) n(-trip) g(time) h(of) p Fh 21 w(n) p Fm(th) f(TCP) h(connec-) 1967 3709 y(tion,) k(and) e(the) h (pack) o(et) g(loss) g(proba) n(bility) g(in) g(the) g(netw) o(ork) f (can) h(be) 1967 3805 y(obtained) n(.) p Fi 1967 4026 a(4) 100 b(Conclusion) p Fm 1967 4141 a(In) 30 b(this) g(paper) m(,) h (we) f(ha) n(v) o(e) g(analyz) n(ed) g(the) g(steady) g(state) g(beha) n (vior) 1967 4237 y(of) 22 b(TCP) g(in) g(a) g(netw) o(or) n(k) g(with) g (hetero) n(geneou) n(s) g(TCP) h(conn) n(ections,) 1967 4334 y(where) c(each) h(TCP) h(con) n(nection) e(has) h(a) h(dif) n(f) n (erent) f(pro) n(pagatio) n(n) g(de-) 1967 4430 y(lay) -5 b(.) 38 b(As) 25 b(a) g(future) f(w) o(ork,) h(it) g(w) o(ould) f(be) g (interesting) g(to) h(apply) f(our) 1967 4526 y(analytic) 17 b(metho) n(d) g(to) h(mor) n(e) g(gener) n(al) g(netw) o(ork) e(mod) n (els,) j(for) d(e) o(xam-) 1967 4623 y(ple,) k(where) g(se) n(v) o (eral) f(bottleneck) g(router) n(s) i(e) o(xist) g(in) f(the) g(netw) o (ork) n(.) p Fi 1967 4843 a(Refer) o(nces) p Fm 1967 4958 a([1]) 41 b(H.) k(Hisamatu,) 50 b(H.) 45 b(Ohsaki,) 50 b(and) 45 b(M.) f(Murata,) 50 b(\223Steady) 2106 5055 y(state) d(and) g(transient) f(beha) n(vio) n(r) h(analyses) g(of) g (TCP) h(con-) 2106 5151 y(nectio) n(ns) 41 b(consid) n(ering) e (interaction) n(s) i(between) e(TCP) i(con-) 2106 5247 y(nectio) n(ns) f(and) f(netw) o(or) n(k,) -6 b(\224) 44 b(submitted) 38 b(to) p Fa 40 w(IEEE) g(GLOBE-) 2106 5344 y(COM2002) 19 b(\(GLOBE20) n(02\)) p Fm(,) g(Mar) -5 b(.) 20 b(2002.) 1967 5440 y([2]) 41 b(J.) 21 b(P) o(adhy) n(e,) g(V) -11 b(.) 22 b(Firoiu,) e(D.) h(T) -7 b(o) n(wsle) o(y) i(,) 20 b(and) g(J.) i(K) o(uro) n(se,) g(\223Mod-) 2106 5537 y(eling) i(TCP) i(throu) n(ghput:) 34 b(a) 26 b(simple) f(mode) n(l) h (and) f(its) h(empiri-) 2106 5633 y(cal) 17 b(v) n(alidatio) n(n,) -6 b(\224) 18 b(in) p Fa 17 w(Pr) l(oceeding) n(s) g(of) f(A) n(CM) h (SIGCOMM) f('98) p Fm -2 w(,) 2106 5729 y(pp.) i(303\226) n(314,) g (1998) n(.) p dyy eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF