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All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 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 59 /comma put dup 97 /a put dup 105 /i put dup 106 /j put dup 109 /m put dup 120 /x put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 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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 68 /D put dup 78 /N put dup 98 /b put dup 102 /f put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % 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 (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 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 readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % 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 (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 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 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 61 /equal put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 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 18 /parenleftbigg put dup 19 /parenrightbigg put dup 26 /braceleftbigg put dup 88 /summationdisplay put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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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 59 /comma put dup 78 /N put dup 97 /a put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 114 /r put dup 120 /x put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueID 5087382 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 20 /lessequal put dup 39 /similarequal put dup 112 /radical 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 1 /Delta 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 54 /six put dup 61 /equal put dup 105 /i put dup 109 /m put dup 110 /n put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec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h(lar) o(ge) 2000 3537 y(num) n(ber) 42 b(of) g(virtual) g(or) o(g) n(aniza) n(tions.) g (Our) g(prop) n(osed) g(RING-VPN) 2000 3637 y(dyn) n(amically) 26 b(b) n(uilds) g(secure) f(and) h(reliable) f(VPNs) i(with) f(high) f (scala-) 2000 3736 y(bility) e(in) g(terms) h(of) f(the) g(num) n(ber) g (of) g(VPNs) h(by) f(logically) g(conn) n(ecting) 2000 3836 y(nod) n(es) 30 b(in) e(a) h(ring) f(topolo) n(gy) -5 b(.) 2083 3936 y(T) e(o) 20 b(assist) i(v) n(ariou) n(s) f(social) g (acti) n(vities) f(o) o(v) o(er) f(netw) o(orks,) h(VPN) g(mech-) 2000 4035 y(anism) h(is) h(requir) n(ed) g(to) f(b) n(uild) g(a) g(VPN) h (that) g(conn) n(ects) g(dozen) n(s) g(of) f(users) 2000 4135 y(o) o(v) o(e) n(r) 29 b(a) f(wide-are) n(a) h(netw) o(ork) n(.) g (On) f(the) g(other) f(hand,) g(due) h(to) g(the) g(ring) 2000 4234 y(topo) n(logy) c(of) g(the) g(RING-VPN,) h(it) g(is) g (anticipated) e(that) h(perfor) n(mance) 2000 4334 y(such) 32 b(as) i(transmission) e(delay) h(and) f(throu) n(ghpu) n(t) i(w) o (ould) e(drastically) 2000 4434 y(deterio) n(rate) h(as) g(the) g(num) n (ber) g(of) f(participa) n(ting) h(nod) n(es) h(in) e(the) h(VPN) 2000 4533 y(increases) 41 b([12) n(,) g(13].) f(It) i(is) f(also) h(e) o(xp) n(ected) f(that) g(other) f(impor) n(tant) 2000 4633 y(perf) n(ormanc) n(e) 25 b(metrics) f(such) f(as) i(the) f(requ) n (ired) g(time) g(to) g(b) n(uild) g(a) g(VPN) 2000 4733 y(\(VPN) d(construc) n(tion) g(time\)) g(and) g(the) g(requ) n(ired) g (time) g(to) g(reco) o(v) o(e) n(r) h(fro) n(m) 2000 4832 y(netw) o(or) n(k) e(f) o(ailures) f(\(VPN) h(reco) o(v) m(ery) f (time\)) h(w) o(ould) e(be) i(af) n(fected) e(by) h(the) 2000 4932 y(increase) h(in) g(nod) n(es.) h(Ho) n(we) n(v) o(e) n(r) m(,) f (the) h(poten) n(tial) g(of) f(RING-VPN) g(\227) h(for) 2000 5031 y(e) o(xam) n(ple,) h(the) f(size) i(of) e(the) h(netw) o(ork) e (o) o(v) o(er) h(which) g(a) h(RING-VPN) g(can) 2000 5131 y(be) 31 b(b) n(uilt) g(and) f(the) h(numb) n(er) g(of) g(nod) n (es) h(that) f(can) f(participate) g(in) h(that) 2000 5231 y(VPN) e(\227) g(ha) n(v) o(e) f(not) g(yet) h(been) e (clari\002ed.) 2083 5330 y(There) n(fore,) 49 b(in) h(this) g(pape) n (r) m(,) g(we) g(qua) n(ntitati) n(v) o(ely) f(e) n(v) n(alua) n(te) h (the) 2000 5430 y(ef) n(fecti) n(v) m(eness) 26 b(of) f(our) g(pro) n (posed) g(RING-VPN) h(using) f(mathem) n(atical) p dyy eop end %%Page: 2 2 TeXDict begin 2 1 bop Fm 4055 -99 a(2) p Fr -192 -50 a(analysis.) 34 b(Speci\002cally) -5 b(,) 33 b(we) h(e) n(v) n(alu) n (ate) h(the) f(impac) n(t) h(of) f(the) g(num) n(ber) -192 49 y(of) 41 b(participating) f(nodes) h(in) h(a) g(VPN) g(as) h(well) f (as) g(the) g(impact) f(of) -192 149 y(link) 30 b(ban) n(dwidth) g(and) f(prop) n(agation) f(delay) i(on) f(the) h(perfo) n(rmance) f(of) -192 249 y(a) 42 b(RING-VPN) f(\(e.g.) n(,) h(VPN) f(constructio) n(n) h (time,) f(VPN) g(reco) o(v) m(ery) -192 348 y(time,) h(and) g(minimu) n (m) h(TCP) g(throu) n(ghpu) n(t\).) g(W) -7 b(e) 43 b(demo) n(nstrate) g (the) -192 448 y(prop) n(osed) d(RING-VPN) f(sho) n(ws) h(good) f(perf) n(orman) n(ce) h(in) g(terms) g(of) -192 547 y(se) n(v) o(eral) 25 b(perfo) n(rmance) g(metrics) h(includin) n(g) g(VPN) h(constru) n (ction) f(time) -192 647 y(and) 41 b(minimu) n(m) h(TCP) g(thro) n (ughp) n(ut) g(when) f(the) g(numb) n(er) g(of) g(nodes) -192 747 y(participa) n(ting) 29 b(in) f(the) h(VPN) g(is) g(relati) n(v) o (ely) f(small.) -109 847 y(The) 34 b(structur) n(e) h(of) f(this) g (paper) f(is) i(as) g(follo) n(ws.) f(First,) g(Section) g(II) -192 947 y(e) o(xplain) n(s) 28 b(our) e(prop) n(osed) h(RING-VPN.) g(In) f (particular) -5 b(,) 27 b(commu) n(nica-) -192 1047 y(tion,) 19 b(conne) n(ction,) g(and) g(disconnec) n(tion) h(contr) n(ols) h(of) e (the) h(RING-VPN) -192 1146 y(are) 28 b(e) o(xplain) n(ed) g(in) g (detail.) g(In) g(Section) f(III,) h(we) g(deri) n(v) m(e) h(perf) n (orman) n(ce) -192 1246 y(metrics) i(of) g(RING-VPN) g(throu) n(gh) g (mathema) n(tical) h(analysis.) f(These) -192 1346 y(metrics) i (include) f(VPN) i(constru) n(ction) f(time,) g(VPN) h(reco) o(v) m (ery) f(time,) -192 1445 y(and) 44 b(minimu) n(m) h(throu) n(ghpu) n (t,) g(roun) n(d-trip) f(time) g(and) g(pack) o(et) g(loss) -192 1545 y(prob) n(ability) 51 b(of) f(TCP) i(\003o) n(ws.) f(Additiona) n (lly) -5 b(,) 51 b(se) n(v) o(eral) f(numer) n(ical) -192 1644 y(e) o(xamp) n(les) 36 b(are) e(presented) g(for) g(demon) n (strating) g(the) h(character) n(istics) -192 1744 y(of) 52 b(the) g(RING-VPN.) g(Simulation) g(results) g(are) g(also) h (presented) -192 1844 y(for) 37 b(v) n(alid) n(ating) g(our) g(appr) n (oximate) f(analysis.) h(Finally) -5 b(,) 37 b(Section) g(IV) -192 1943 y(conclu) n(des) 29 b(this) g(paper) f(and) f(discusses) j(futu) n (re) f(w) o(orks.) -13 2109 y(I) t(I) t(.) 45 b(R) t(I) t(N) t(G) t(-) t (V) t(P) t(N) 25 b(\() t(R) p Fo 4 w(I) t(N) t(G) p Fr 4 w(-) p Fo 4 w(B) r(A) t(S) t(E) t(D) p Fr 25 w(V) p Fo 4 w(I) t(RT) t(U) q(A) t(L) p Fr 26 w(P) p Fo 4 w(R) t(I) t(V) -5 b(A) m(T) t(E) p Fr 654 2209 a(N) p Fo 4 w(E) t(T) t(W) s(O) t(R) t(K) p Fr 4 w(\)) -109 2342 y(In) 32 b(this) h(section,) f(we) g(e) o(xplain) f (our) h(pro) n(posed) g(RING-VPN.) g(The) -192 2442 y(k) o(e) o(y) 42 b(of) h(our) f(RING-VPN) h(is) h(to) f(logically) f(con) n(nect) h (nodes) f(in) h(a) -192 2541 y(ring) 37 b(topo) n(logy) g(for) f (minimizing) g(the) h(require) n(d) h(num) n(ber) f(of) g(IPsec) -192 2641 y(tunne) n(ls.) 45 b(In) g(our) e(prop) n(osed) h(RING-VPN,) h (dif) n(f) n(erent) f(from) g(other) -192 2740 y(VPN) 28 b(techn) n(ologies) f(with) g(a) g(central) f(managem) n(ent) h(system) g(such) g(as) -192 2840 y(represen) n(ted) 35 b(by) g(MPLS,) g(each) g (node) f(autono) n(mously) g(\002nds) h(nodes) -192 2940 y(participa) n(ting) 53 b(in) f(a) h(VPN,) g(connects) f(to) h(the) f (VPN,) h(and) f(then) -192 3039 y(disconn) n(ects) 27 b(fro) n(m) f(the) g(VPN.) g(Because) g(of) f(this) h(autono) n(my) g (of) f(each) -192 3139 y(node) n(,) d(reliable) e(commu) n(nications) g (can) h(be) g(realized) f(e) n(v) o(en) g(in) h(cases) h(of) -192 3239 y(f) o(ailures) h(such) g(as) h(netw) o(or) n(k) f(de) n(vices) g (f) o(ailures) g(and) f(routing) g(error) n(s.) i(In) -192 3338 y(addition) n(,) f(IPsec) g(tunnels) f(are) h(established) f (between) g(adjacen) n(t) h(nodes) -192 3438 y(to) 29 b(realize) f(secure) g(commu) n(nications.) -109 3539 y(Let) d(us) g(de\002ne) f(that) h(the) g(forw) o(ar) n(d) g(direction) f(is) h(counter) n(clockwise) -192 3638 y(in) 37 b(Fig.) g(1.) g(Each) g (VPN) g(node) f(establishes) i(an) f(IPsec) g(tunne) n(l) h(to) f(a) -192 3738 y(do) n(wn) n(stream) 28 b(VPN) g(nod) n(e,) g(and) f(the) g (IPsec) h(tunn) n(el) g(is) h(used) e(only) f(for) -192 3838 y(unidir) n(ectional) 38 b(transmission) h(fro) n(m) g(an) g (upstream) f(VPN) h(nod) n(e) h(to) -192 3937 y(a) g(do) n(wnstream) f (one.) g(Commun) n(ication) h(between) f(VPN) h(nodes) g(is) -192 4037 y(done) 35 b(via) g(VPN) h(nodes) f(along) g(the) g(ring.) g(F) o (or) g(e) o(xamp) n(le,) h(a) g(pack) o(et) -192 4136 y(transferr) n(ed) j(fro) n(m) g(VPN) g(node) f(1) g(to) h(VPN) g(nod) n (e) g(4) g(passes) g(VPN) -192 4236 y(node) 25 b(2) i(and) f(3) g(in) h (ord) n(er) g(and) f(\002nally) g(arri) n(v) o(e) n(s) i(at) e(VPN) h (node) f(4.) g(It) h(is) -192 4336 y(anticipated) f(that) h(pack) o (ets) g(ha) n(v) o(e) f(to) h(pass) h(a) f(lar) o(ge) f(numbe) n(r) i (of) e(nodes) -192 4435 y(in) h(this) f(type) g(of) g(ring-b) n(ased) h (netw) o(or) n(k.) g(Ther) n(efore,) f(comm) n(unication) -192 4535 y(delay) c(tends) g(to) h(be) g(lar) o(g) n(e) g(and,) f(as) h(a) g (result,) g(TCP) g(throu) n(ghpu) n(t) g(w) o(ould) -192 4635 y(be) 28 b(de) o(grad) n(ed) h([12) n(,) g(13].) -109 4735 y(In) 46 b(what) h(follo) n(ws,) f(we) h(will) g(e) o(xplain) f (essential) h(fun) n(ctions) g(of) -192 4835 y(the) 29 b(RING-VPN,) g(i.e.) h(con) n(trol) f(of) g(commu) n(nication) g (between) f(VPN) -192 4935 y(node) n(s,) f(control) f(of) g(VPN) h(nod) n(e) g(conne) n(ction) f(to) h(VPNs,) g(and) f(contro) n(l) -192 5034 y(of) i(VPN) h(node) f(disconn) n(ection) g(from) f(VPNs.) p Fn -192 5200 a(A.) 41 b(Communica) n(tion) 28 b(Contr) l(ol) h(between) f(VPN) h(Nodes) p Fr -109 5330 a(In) 40 b(our) f(RING-VPN,) h(a) h(VPN) g(nod) n(e) g(transfers) f(a) g(pack) o(et) g(to) g(a) -192 5430 y(do) n(wn) n(stream) 28 b(VPN) g(nod) n(e) g(throug) n(h) g(an) f (IPsec) h(tunn) n(el.) g(The) f(destina-) 2003 1071 y @beginspecial 9 @llx 558 @lly 440 @urx 814 @ury 2467 @rwi @setspecial %%BeginDocument: figure/ring-p2p-overview.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 9 558 440 814 %%Title: ring-p2p-overview %%CreationDate: Fri Oct 6 17:44:35 2006 %%Creator: Tgif-4.1.43-QPL written by William Chia-Wei Cheng (bill.cheng@acm.org) %%ProducedBy: (unknown) %%Pages: 1 %%DocumentFonts: (atend) %%EndComments %%BeginProlog /tgifdict 86 dict def tgifdict begin /tgifarrowtipdict 8 dict def tgifarrowtipdict /mtrx matrix put /TGAT % tgifarrowtip { 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GS 0 /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (VPN node 4) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (VPN node 4) SH GR GR % BOX 0 SG GS 10 SM GS NP 610 190 M 750 190 L 750 240 L 610 240 L CP S GR GR % TEXT NP 0 SG GS 1 W 680 220 M GS GS 0 /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (VPN node 3) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (VPN node 3) SH GR GR % BOX 0 SG GS 10 SM GS NP 640 390 M 780 390 L 780 440 L 640 440 L CP S GR GR % TEXT NP 0 SG GS 1 W 710 420 M GS GS 0 /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (VPN node 2) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (VPN node 2) SH GR GR % POLY/OPEN-SPLINE 0 SG GS NP 350 70 M 50 -160 atan DU cos 22.000 MU 190 exch SU exch sin 22.000 MU 120 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 190 120 22.000 9.000 -160 50 TGAT 1 SG CP F 0 SG NP 190 120 22.000 9.000 -160 50 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 160 190 M 80 -60 atan DU cos 22.000 MU 100 exch SU exch sin 22.000 MU 270 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 100 270 22.000 9.000 -60 80 TGAT 1 SG CP F 0 SG NP 100 270 22.000 9.000 -60 80 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 110 340 M 90 90 atan DU cos 22.000 MU 200 exch SU exch sin 22.000 MU 430 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 200 430 22.000 9.000 90 90 TGAT 1 SG CP F 0 SG NP 200 430 22.000 9.000 90 90 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 290 460 M 0 110 atan DU cos 22.000 MU 400 exch SU exch sin 22.000 MU 460 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 400 460 22.000 9.000 110 0 TGAT 1 SG CP F 0 SG NP 400 460 22.000 9.000 110 0 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 540 470 M -20 160 atan DU cos 22.000 MU 700 exch SU exch sin 22.000 MU 450 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 700 450 22.000 9.000 160 -20 TGAT 1 SG CP F 0 SG NP 700 450 22.000 9.000 160 -20 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 700 380 M -130 -20 atan DU cos 22.000 MU 680 exch SU exch sin 22.000 MU 250 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 680 250 22.000 9.000 -20 -130 TGAT 1 SG CP F 0 SG NP 680 250 22.000 9.000 -20 -130 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 660 180 M -110 -170 atan DU cos 22.000 MU 490 exch SU exch sin 22.000 MU 70 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 490 70 22.000 9.000 -170 -110 TGAT 1 SG CP F 0 SG NP 490 70 22.000 9.000 -170 -110 TGAT CP F GR % TEXT NP 0 SG GS 1 W 710 70 M GS GS 0 /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (IPsec tunnel) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (IPsec tunnel) SH GR GR % POLY/OPEN-SPLINE 0 SG GS NP 670 80 M 580 120 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS [12 4] 0 SD NP 420 430 M -330 -30 atan DU cos 22.000 MU 390 exch SU exch sin 22.000 MU 100 exch SU L TGSM 7 W S [] 0 SD 1 W GR GS TGSM NP 390 100 22.000 9.000 -30 -330 TGAT 1 SG CP F 0 SG NP 390 100 22.000 9.000 -30 -330 TGAT CP F GR % TEXT NP 0 SG GS 1 W 290 330 M GS GS 0 /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (ad-hoc) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica-Oblique FF [24 0 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@endspecial 2415 1254 a(Fig.) h(1:) h(Ov) o(er) n(vie) n(w) g(of) f (our) g(RING-VPN.) 2000 1576 y(tion) f(IP) g(address) g(of) g(the) g (encapsulate) n(d) h(pack) o(et) e(is) j(al) o(w) o(ays) e(set) h(to) g (be) 2000 1676 y(the) 23 b(IP) h(addre) n(ss) h(of) e(the) h(do) n(w) n (nstream) f(VPN) h(node,) e(re) o(gar) n(dless) i(of) f(the) 2000 1775 y(destination) k(VPN) i(node) f(of) g(the) g(pack) o(et) g(before) f(encapsulation) n(.) 2083 1873 y(Upon) 34 b(the) h(arri) n(v) n(al) g (of) f(the) i(encap) n(sulated) f(pack) o(et) g(from) f(the) h(up-) 2000 1973 y(stream) 25 b(VPN) i(nod) n(e,) f(the) g(VPN) g(nod) n(e) h(com) n (pares) f(the) g(destinatio) n(n) g(IP) 2000 2073 y(addr) n(ess) 39 b(of) f(the) g(pack) o(et) g(befo) n(re) g(encapsulatio) n(n) g(with) h (its) g(o) n(wn) e(IP) 2000 2172 y(addr) n(ess.) d(If) f(one) f(IP) h (addre) n(ss) h(matches) f(the) g(other) -5 b(,) 33 b(the) g(VPN) h (nod) n(e) 2000 2272 y(decap) n(sulates) 25 b(the) g(pack) m(et) h(and) d(recei) n(v) o(es) h(it.) h(If) f(one) g(IP) h(addr) n(ess) h(does) 2000 2371 y(not) 34 b(match) h(the) g(other) -5 b(,) 35 b(the) g(VPN) h(nod) n(e) f(compar) n(es) h(the) f(source) f(IP) 2000 2471 y(addr) n(ess) 39 b(of) f(the) g(pack) o(et) g(befo) n(re) g (encapsulatio) n(n) g(with) h(its) g(o) n(wn) e(IP) 2000 2571 y(addr) n(ess,) i(and) d(if) i(one) f(IP) h(addr) n(ess) h (matches) e(the) g(other) m(,) f(the) i(VPN) 2000 2670 y(nod) n(e) 27 b(discards) g(the) g(encap) n(sulated) g(pack) m(et.) h (The) e(VPN) h(node) f(judges) 2000 2770 y(that) j(the) h(source) f(IP) h(addre) n(ss) h(of) e(the) h(pack) o(et) f(befor) n(e) h(encapsulatio) n(n) 2000 2870 y(matches) 39 b(its) h(o) n(wn) f(IP) g(address.) g(It) g (is) h(because) f(the) g(encapsula) n(ted) 2000 2969 y(pack) o(et) 29 b(has) i(com) n(e) g(back) e(after) h(circulating) f (the) h(ring) n(-netw) o(ork) n(,) h(i.e.,) 2000 3069 y(there) g(e) o(xisted) h(no) g(VPN) h(nod) n(e) g(which) e(w) o(as) i (designated) e(to) i(recei) n(v) m(e) 2000 3169 y(the) h(pack) o(et.) f (If) h(the) g(source) g(IP) g(address) g(does) g(not) g(match) g(o) n (wn) f(IP) 2000 3268 y(addr) n(esses,) 45 b(then,) e(the) g(VPN) i(nod) n(e) f(change) n(s) h(the) f(destinatio) n(n) g(IP) 2000 3368 y(addr) n(ess) c(of) e(the) h(encap) n(sulated) g(pack) o(et) f (to) h(the) f(IP) h(addre) n(ss) h(of) e(its) 2000 3467 y(do) n(wn) n(stream) c(VPN) h(nod) n(e,) g(and) e(then) h(transfers) f (this) i(encapsula) n(ted) 2000 3567 y(pack) o(et.) p Fn 2000 3714 a(B.) 41 b(VPN) 29 b(Node) f(Connectio) n(n) h(Contr) l (ol) p Fr 2083 3839 a(The) j(contro) n(l) h(mechanism) f(of) g(the) h (con) n(nection) f(of) g(a) h(VPN) h(nod) n(e) 2000 3938 y(to) 28 b(the) f(RING-VPN) h(is) h(describ) n(ed) f(belo) n(w) -5 b(.) 26 b(Hereafter) m(,) g(we) j(den) n(ote) f(a) 2000 4038 y(VPN) 35 b(nod) n(e) g(that) g(is) h(ne) n(wly) d(connectin) n(g) i(to) g(the) f(RING-VPN) h(as) g(a) p Fn 2000 4138 a(ne) o(w) 28 b(VPN) h(node) p Fr(.) 2083 4236 y(A) 40 b(ne) n(w) g(VPN) h(nod) n(e) g (recei) n(v) m(es) g(the) f(list) h(of) e(the) h(nodes) g(alread) n(y) 2000 4335 y(particip) n(ating) 46 b(in) h(the) f(VPN) h(and) f(the) h (info) n(rmation) f(of) g(the) g(ring) 2000 4435 y(con\002g) n(uration) 39 b(from) g(the) i(VPN) f(manage) n(r) -5 b(.) 41 b(The) f(ne) n(w) g (VPN) h(nod) n(e) 2000 4535 y(then) 31 b(measures) h(a) n(v) o(era) n (ge) g(roun) n(d-trip) f(time) h(to) g(each) g(VPN) g(node) f(in) 2000 4634 y(VPN) e(using) f(ICMP) h(Echo) f(messages) g([14]) n(.) 2083 4733 y(Based) e(on) f(the) g(measured) f(roun) n(d-trip) h(time,) g (the) g(ne) n(w) h(VPN) g(nod) n(e) 2000 4832 y(determ) n(ines) f(the) f (position) f(in) h(the) g(ring) f(to) h(which) f(it) i(should) e(conn) n (ect.) 2000 4932 y(In) 44 b(particu) n(lar) m(,) g(for) g(each) g (adjacent) g(nod) n(e) h(pair) f(in) h(the) f(ring,) f(the) 2000 5031 y(ne) n(w) 34 b(VPN) g(node) f(measures) h(the) g(roun) n(d-trip) f (time) i(to) f(each) g(of) f(the) 2000 5131 y(upstream) 40 b(and) i(do) n(wn) n(stream) g(VPN) g(nodes) f(of) h(the) f(pair) h (and,) f(by) 2000 5231 y(summin) n(g) 30 b(up) f(the) h(time,) g (calculates) g(the) f(total) h(roun) n(d-trip) f(time) h(for) 2000 5330 y(the) h(pair) -5 b(.) 31 b(The) g(VPN) h(node) e(pair) h(with) h (the) f(minimum) f(total) i(rou) n(nd-) 2000 5430 y(trip) 26 b(time) g(is) g(determine) n(d) g(as) h(the) f(position) f(to) h(which) f(the) h(ne) n(w) g(VPN) p dyy eop end %%Page: 3 3 TeXDict begin 3 2 bop Fm 4055 -99 a(3) p Fr -192 -50 a(node) 23 b(conn) n(ects.) i(The) e(ne) n(w) h(VPN) h(nod) n(e) f (then) g(establishes) g(tw) o(o) g(IPsec) -192 49 y(tunne) n(ls:) 31 b(one) f(to) g(the) g(upstrea) n(m) h(VPN) f(node) f(and) g(the) h (other) f(one) h(to) -192 149 y(the) h(do) n(wn) n(stream) g(VPN) g (node.) f(Lastly) -5 b(,) 30 b(the) h(IPsec) g(tunn) n(el) h(between) -192 249 y(the) 25 b(upstrea) n(m) g(VPN) g(node) f(and) g(the) h(do) n (wn) n(stream) g(one,) e(which) i(is) g(no) -192 348 y(longe) n(r) k(requir) n(ed,) g(is) g(torn) f(do) n(wn) n(.) p Fn -192 555 a(C.) 42 b(VPN) 29 b(Node) f(Disconne) n(ction) h(Contr) l (ol) p Fr -109 703 a(In) j(our) g(RING-VPN,) h(VPN) g(nod) n(es) h (auton) n(omou) n(sly) f(re-establish) -192 802 y(the) 27 b(ring) f(when) g(the) h(commu) n(nication) f(between) h(VPN) g(node) n (s) h(termi-) -192 902 y(nated) c(for) f(some) h(reason.) f(Belo) n(w) i (is) g(the) f(contro) n(l) h(mechan) n(ism) g(of) f(the) -192 1001 y(VPN) 35 b(node) e(disconnec) n(tion,) h(during) f(the) i (re-estab) n(lishment) g(of) f(the) -192 1101 y(ring.) -109 1207 y(A) c(VPN) f(manag) n(ement) g(pack) o(et) f(circulates) h(throu) n(gh) g(VPN) g(nodes) -192 1306 y(along) 41 b(the) i(ring) n(.) g(In) f (this) h(mana) n(gement) f(pack) m(et,) h(the) f(list) i(of) e(the) -192 1406 y(VPN) 47 b(nod) n(es) g(and) e(the) h(infor) n(mation) g(of) f (the) h(ring) f(con\002gu) n(ration) -192 1506 y(are) 27 b(record) n(ed.) h(Each) f(VPN) h(nod) n(e) g(return) n(s) h(the) e (ackno) n(w) n(ledgmen) n(t) i(to) -192 1605 y(its) 40 b(upstream) e(VPN) h(node) f(e) n(v) o(ery) g(time) h(the) g(VPN) h (nod) n(e) f(recei) n(v) o(es) -192 1705 y(this) 50 b(manag) n(ement) f (pack) m(et.) h(Each) f(VPN) h(nod) n(e) g(judg) n(es) g(that) g(its) -192 1805 y(do) n(wn) n(stream) 23 b(VPN) h(nod) n(e) g(is) f(not) g (oper) n(ational) g(if) g(it) h(doe) n(s) g(not) f(recei) n(v) o(e) -192 1904 y(an) o(y) 28 b(ackn) n(o) n(wledgem) n(ent) h(after) f(a) h (certain) f(perio) n(d) h(of) f(time.) -109 2010 y(An) o(y) i(VPN) h (node) f(that) h(detects) f(a) h(non-o) n(peration) n(al) g(do) n (wnstream) -192 2109 y(VPN) g(nod) n(e) g(noti\002es) f(this) h(to) f (the) h(furth) n(er) f(do) n(wnstream) f(VPN) i(nod) n(e) -192 2209 y(conn) n(ecting) h(to) h(the) f(non-) n(operatio) n(nal) h(nod) n (e.) g(It) g(then) f(establishes) g(a) -192 2309 y(ne) n(w) 37 b(IPsec) g(tunne) n(l) h(to) f(this) g(further) f(do) n(wn) n(stream) h (VPN) g(node.) f(In) -192 2408 y(addition) n(,) j(the) f(IPsec) h (tunnels) f(between) g(the) g(VPN) h(node) f(and) g(the) -192 2508 y(non-) n(operatio) n(nal) 19 b(one) g(as) h(well) f(as) h (between) f(the) g(furth) n(er) g(do) n(wnstream) -192 2608 y(VPN) 25 b(nod) n(e) g(and) e(the) i(non) n(-oper) n(ational) f (one) g(are) g(termin) n(ated.) g(Lastly) -5 b(,) -192 2707 y(the) 50 b(VPN) h(nod) n(e,) f(which) g(detected) f(the) h(non) n (-oper) n(ational) g(node) n(,) -192 2807 y(upda) n(tes) 30 b(the) e(list) i(of) f(the) f(VPN) h(nodes) f(and) g(the) h(inform) n (ation) f(of) h(the) -192 2907 y(ring) f(con\002gu) n(ration) h(recor) n (ded) g(in) g(the) g(manag) n(ement) g(pack) m(et.) h(Then) n(,) -192 3006 y(it) f(transmits) g(this) g(pack) m(et) h(to) e(do) n(wnstrea) n (m) h(VPN) g(nodes.) 593 3213 y(I) t(I) t(I) t(.) 45 b(A) p Fo 4 w(N) r(A) t(L) m(Y) t(S) t(I) t(S) p Fr -109 3376 a(In) 22 b(this) h(section,) f(we) h(\002rst) g(model) f(the) g (RING-VPN) h(and) f(deri) n(v) m(e) h(its) -192 3475 y(VPN) g(constru) n(ction) f(time,) g(VPN) g(reco) o(v) m(ery) 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/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: 3 448 426 825 tgifdict begin /tgifsavedpage save def 1 SM 1 W 0 SG 72 0 MU 72 11.602 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 270 550 M 0 220 atan DU cos 22.000 MU 490 exch SU exch sin 22.000 MU 550 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 490 550 22.000 9.000 220 0 TGAT 1 SG CP F 0 SG NP 490 550 22.000 9.000 220 0 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 80 420 M 90 90 atan DU cos 22.000 MU 170 exch SU exch sin 22.000 MU 510 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 170 510 22.000 9.000 90 90 TGAT 1 SG CP F 0 SG NP 170 510 22.000 9.000 90 90 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 580 510 M -90 90 atan DU cos 22.000 MU 670 exch SU exch sin 22.000 MU 420 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 670 420 22.000 9.000 90 -90 TGAT 1 SG CP F 0 SG NP 670 420 22.000 9.000 90 -90 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 480 110 M 0 -220 atan DU cos 22.000 MU 260 exch SU exch sin 22.000 MU 110 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 260 110 22.000 9.000 -220 0 TGAT 1 SG CP F 0 SG NP 260 110 22.000 9.000 -220 0 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 660 240 M -90 -90 atan DU cos 22.000 MU 570 exch SU exch sin 22.000 MU 150 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 570 150 22.000 9.000 -90 -90 TGAT 1 SG CP F 0 SG NP 570 150 22.000 9.000 -90 -90 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 170 150 M 90 -90 atan DU cos 22.000 MU 80 exch SU exch sin 22.000 MU 240 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 80 240 22.000 9.000 -90 90 TGAT 1 SG CP F 0 SG NP 80 240 22.000 9.000 -90 90 TGAT CP F GR % BOX 0 SG GS 10 SM GS NP 120 520 M 260 520 L 260 570 L 120 570 L CP S GR GR % TEXT NP 0 SG GS 1 W 190 550 M GS GS 0 /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (VPN node i) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (VPN node i) SH GR GR % BOX 0 SG GS 10 SM GS NP 510 520 M 650 520 L 650 570 L 510 570 L CP S GR GR % TEXT NP 0 SG GS 1 W 580 550 M GS GS 0 /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (VPN node j) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (VPN node j) SH GR GR % BOX 0 SG GS 10 SM GS NP 110 90 M 250 90 L 250 140 L 110 140 L CP S GR GR % TEXT NP 0 SG GS 1 W 180 130 M GS GS 0 /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (VPN node 1) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (VPN node 1) SH GR GR % BOX 0 SG GS 10 SM GS NP 490 90 M 630 90 L 630 140 L 490 140 L CP S GR GR % TEXT NP 0 SG GS 1 W 560 130 M GS GS 0 /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (VPN node N) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (VPN node N) SH GR GR % POLY/OPEN-SPLINE 0 SG GS [4 4] 0 SD NP 80 250 M 80 400 L TGSM 4 W S [] 0 SD 1 W GR % POLY/OPEN-SPLINE 0 SG GS [4 4] 0 SD NP 670 260 M 670 410 L TGSM 4 W S [] 0 SD 1 W GR % POLY/OPEN-SPLINE 0 SG GS NP 380 540 M 430 450 L TGSM 1 W S GR % TEXT NP 0 SG GS 1 W 380 439 M GS 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (link bandwidth ) SH 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (b ) SH 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (i,j) SH GR GR % POLY/OPEN-SPLINE 0 SG GS NP 330 540 M 270 390 L TGSM 1 W S GR % TEXT NP 0 SG GS 1 W 170 380 M GS 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (link propagation delay ) SH 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (d) SH 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS ( ) SH 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (i,j) SH GR GR % TEXT NP 0 SG GS 1 W 10 70 M GS 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (f) SH 0 SG /Times-Italic FF [24 0 0 -24 0 0] MS ( ) SH 0 SG /Times-Italic FF [24 0 0 -24 0 0] MS (N,i=1) SH GR GR % TEXT NP 0 SG GS 1 W 530 260 M GS GS 0 /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (IPsec tunnel) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (IPsec tunnel) SH GR GR % POLY/OPEN-SPLINE 0 SG GS NP 620 200 M 530 240 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 130 160 M 50 -50 atan DU cos 10.000 MU 80 exch SU exch sin 10.000 MU 210 exch SU L TGSM 2 W S 1 W GR GS TGSM NP 80 210 10.000 4.000 -50 50 TGAT 1 SG CP F 0 SG NP 80 210 10.000 4.000 -50 50 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 610 510 M -50 50 atan DU cos 10.000 MU 660 exch SU exch sin 10.000 MU 460 exch SU L TGSM 2 W S 1 W GR GS TGSM NP 660 460 10.000 4.000 50 -50 TGAT 1 SG CP F 0 SG NP 660 460 10.000 4.000 50 -50 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS GS NP 310 60 M 0 -10 atan DU cos 12.000 MU exch sin 12.000 MU RM 300 60 L TGSM 3 W 1 SG S 1 W GR NP 310 60 M 0 -10 atan DU cos 12.000 MU exch sin 12.000 MU RM 300 60 L TGSM 3 W FLAT pat12 8 296 48 16 24 TGPF 1 W GR GS TGSM NP 310 60 12.000 5.000 10 0 TGAT 1 SG CP F 0 SG NP 310 60 12.000 5.000 10 0 TGAT CP EC NP pat12 8 296 48 16 24 TGPF GR % POLY/OPEN-SPLINE 0 SG GS NP 580 20 M 520 70 L 210 70 L -50 -70 atan DU cos 12.000 MU 140 exch SU exch sin 12.000 MU 20 exch SU L TGSM 3 W S 1 W GR GS TGSM NP 140 20 12.000 5.000 -70 -50 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 130 650 M 200 580 L 560 580 L 70 70 atan DU cos 12.000 MU 630 exch SU exch sin 12.000 MU 650 exch SU L TGSM 3 W S 1 W GR GS TGSM NP 630 650 12.000 5.000 70 70 TGAT 1 SG CP F 0 SG NP 630 650 12.000 5.000 70 70 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 150 650 M 210 590 L 550 590 L 540 590 L 550 590 L 540 590 L 550 590 L 60 60 atan DU cos 12.000 MU 610 exch SU exch sin 12.000 MU 650 exch SU L TGSM 3 W S 1 W GR GS TGSM NP 610 650 12.000 5.000 60 60 TGAT 1 SG CP F 0 SG NP 610 650 12.000 5.000 60 60 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 170 650 M 220 600 L 630 600 L 700 550 L 700 420 L TGSM 3 W S 1 W GR % POLY/OPEN-SPLINE 0 SG GS NP 700 110 M 630 70 L 550 70 L -50 -70 atan DU cos 12.000 MU 480 exch SU exch sin 12.000 MU 20 exch SU L TGSM 3 W S 1 W GR GS TGSM NP 480 20 12.000 5.000 -70 -50 TGAT 1 SG CP F 0 SG NP 480 20 12.000 5.000 -70 -50 TGAT CP F GR % TEXT NP 0 SG GS 1 W 610 680 M GS 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (f) SH 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS ( i,j=2) SH GR GR % TEXT NP 0 SG GS 1 W 680 90 M GS 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (f) SH 0 SG /Times-Italic FF [24 0 0 -24 0 0] MS ( ) SH 0 SG /Times-Italic FF [24 0 0 -24 0 0] MS (i,N=1) SH GR GR % TEXT NP 0 SG GS 1 W 320 50 M GS 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (f) SH 0 SG /Times-Italic FF [24 0 0 -24 0 0] MS ( ) SH 0 SG /Times-Italic FF [24 0 0 -24 0 0] MS (N,1=1) SH GR GR % TEXT NP 0 SG GS 1 W 300 680 M GS 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (number of TCP flows ) SH 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (f) SH 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS ( i,j) SH GR GR % POLY/OPEN-SPLINE 0 SG GS NP 390 650 M 380 610 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS [4 4] 0 SD NP 700 260 M 700 410 L TGSM 4 W S [] 0 SD 1 W GR % POLY/OPEN-SPLINE 0 SG GS NP 700 250 M 700 110 L TGSM 3 W S 1 W GR % POLY/OPEN-SPLINE 0 SG GS NP 580 30 M 520 80 L 100 80 L 60 130 L 60 240 L TGSM 3 W S 1 W GR % POLY/OPEN-SPLINE 0 SG GS [4 4] 0 SD NP 60 250 M 60 400 L TGSM 4 W S [] 0 SD 1 W GR % POLY/OPEN-SPLINE 0 SG GS NP 60 420 M 60 550 L 120 600 L 190 600 L 50 40 atan DU cos 12.000 MU 230 exch SU exch sin 12.000 MU 650 exch SU L TGSM 3 W S 1 W GR GS TGSM NP 230 650 12.000 5.000 40 50 TGAT 1 SG CP F 0 SG NP 230 650 12.000 5.000 40 50 TGAT CP F GR GR tgifsavedpage restore end showpage %%Trailer %MatchingCreationDate: Fri Oct 6 17:47:38 2006 %%DocumentFonts: Times-Italic %%+ Helvetica-Oblique %%EOF %%EndDocument @endspecial 2647 1865 a(Fig.) j(2:) f(Analytic) g(model.) 2000 2208 y(by) p Fl 2563 2445 a(R) p Fi 2626 2457 a(N) p Fk 2712 2445 a(=) p Fi 2830 2341 a(N) p Fh 2800 2366 a(X) p Fi 2806 2543 a(i) p Fg(=1) p Fi 2964 2341 a(N) p Fh 2933 2366 a(X) p Fi 2936 2543 a(j) p Fg 3 w(=1) p Fl 3067 2445 a(m) p Fi 3140 2457 a(i;j) p Fl 3218 2445 a(d) p Fi 3261 2457 a(i;j) p Fl 3340 2445 a(:) p Fr 632 w(\(1\)) p Fn 2000 2687 a(B.) 41 b(VPN) 29 b(Construction) e(T) -5 b(ime) p Fr 2083 2821 a(W) e(e) 21 b(\002rst) g(deri) n(v) o(e) e(VPN) i (constructio) n(n) g(time) p Fl 20 w(X) p Fi 3443 2833 a(N) p Fr 3506 2821 a(,) f(which) g(is) i(de\002ne) n(d) 2000 2921 y(as) 27 b(the) f(time) g(required) f(for) g(the) p Fl 27 w(N) p Fr 9 w(-th) g(VPN) i(node) f(to) g(join) g(the) g(VPN.) p Fl 2000 3020 a(N) p Fr 9 w(-th) 38 b(VPN) h(nod) n(e) g(measures) f (round) n(-trip) g(time) h(to) f(each) h(of) p Fl 38 w(N) p Fj 34 w(\000) p Fk 2000 3120 a(1) p Fr 38 w(VPN) f(node) n(s) h (that) f(already) f(particip) n(ated) h(in) g(the) g(VPN.) g(It) g (then) 2000 3220 y(particip) n(ates) 33 b(in) g(and) e(re-b) n(uild) n (s) j(the) e(VPN) h(so) f(that) g(the) h(increa) n(se) g(in) 2000 3319 y(the) 39 b(roun) n(d-trip) g(time) h(beco) n(mes) g(the) g (minimu) n(m.) f(Speci\002cally) -5 b(,) 39 b(let) p Fl 2000 3419 a(r) p Fr 35 w(and) p Fl 32 w(l) p Fr 34 w(deno) n(te) 33 b(the) f(upstream) f(VPN) i(nod) n(e) g(and) e(the) h (do) n(wnstre) n(am) 2000 3518 y(VPN) j(node) g(for) f(a) i(ne) n(w) e (VPN) i(node) p Fl 34 w(N) p Fr 9 w(,) f(respecti) n(v) o(ely) -7 b(.) 35 b(Assuming) 2000 3618 y(that) 29 b(the) h(roun) n(d-trip) f (time) h(between) f(VPN) h(nod) n(e) p Fl 30 w(i) p Fr 30 w(and) f(VPN) i(nod) n(e) p Fl 2000 3718 a(j) p Fr 34 w(can) d(be) h(appr) n(oximated) e(by) p Fk 29 w(2) p Fl 14 w(d) p Fi 3017 3730 a(i;j) p Fr 3124 3718 a(using) h(the) g (transmission) g(delay) 2000 3817 y(between) f(the) i(node) n(s,) p Fl 29 w(d) p Fi 2722 3829 a(i;j) p Fr 2801 3817 a(,) p Fl 29 w(r) p Fr 32 w(and) p Fl 27 w(l) p Fr 31 w(are) f(gi) n(v) o(en) g (by) p Fk 2554 4028 a(min) p Fi 2586 4082 a(l;r) p Fh 2706 3911 a(\022) p Fk 2777 3972 a(2) p Fl(d) p Fi 2862 3984 a(l;N) p Fk 2984 3972 a(+) 18 b(2) p Fl(d) p Fi 3152 3984 a(N) s(;r) p 2777 4009 487 4 v Fl 2945 4085 a(m) p Fi 3018 4097 a(l;r) p Fh 3274 3911 a(\023) p Fl 3349 4028 a(:) p Fr 623 w(\(2\)) 2083 4234 y(On) 37 b(\002nding) g(the) g(nodes) g(to) h(be) g(con) n(nected,) f(VPN) h(node) p Fl 37 w(N) p Fr 47 w(re-) 2000 4334 y(b) n(uilds) e(the) h(VPN) g(as) g (follo) n(ws:) f(\(a\)) h(establish) f(an) h(IPsec) g(tunn) n(el) g(to) 2000 4434 y(VPN) 28 b(node) p Fl 27 w(r) p Fr 2 w(;) i(\(b\)) d (establish) h(another) f(IPsec) i(tunn) n(el) g(to) f(VPN) h(nod) n(e) p Fl 2000 4533 a(l) p Fr 2 w(;) 39 b(and) g(\(c\)) g(termin) n(ate) h (the) f(IPsec) h(tunn) n(el) g(between) f(VPN) g(node) p Fl 39 w(l) p Fr 2000 4633 a(and) c(VPN) i(node) p Fl 35 w(r) p Fr 2 w(.) g(Assume) f(that) h(the) f(rou) n(nd-trip) f(time) h (between) 2000 4733 y(VPN) 25 b(nodes) g(particip) n(ated) g(in) h(the) f(VPN) g(is) h(kno) n(wn) e(\(i.e.,) g(the) i(rou) n(nd-) 2000 4832 y(trip) 41 b(time) h(w) o(as) g(already) e(measured) g(and) h (does) g(not) g(change) f(with) 2000 4932 y(time\).) h(T) -7 b(ypically) i(,) 41 b(for) g(creating) g(an) h(IPsec) g(tunnel,) f(six) i(message) 2000 5031 y(e) o(xch) n(anges) 19 b(between) g(VPN) h(nod) n (es) g(are) g(requ) n(ired) f([6].) g(After) g(message) 2000 5131 y(e) o(xch) n(anges,) 45 b(an) h(encryp) n(tion) g(k) o(e) o(y) f (is) h(generated) n(.) g(Let) p Fk 46 w(\001) p Fr 47 w(be) f(the) 2000 5231 y(time) 29 b(requ) n(ired) g(for) f(a) h(VPN) h (nod) n(e) g(to) f(gener) n(ate) g(an) g(encryp) n(tion) g(k) o(e) o(y) -5 b(.) 2000 5330 y(Pro) o(v) n(ided) 22 b(that) g(VPN) g(node) p Fl 21 w(N) p Fr 31 w(e) o(x) o(ecu) n(tes) h(the) f(abo) o(v) m(e) g (proce) n(ss) h(\(a\)) f(and) 2000 5430 y(\(b\)) 29 b(in) h(this) h (ord) n(er) m(,) f(and) f(\(c\)) h(can) g(be) g(e) o(x) o(ec) n(uted) g (in) g(parallel) g(with) g(\(a\)) p dyy eop end %%Page: 4 4 TeXDict begin 4 3 bop Fm 4055 -99 a(4) p Fr -192 -50 a(and) 28 b(\(b\),) p Fl 28 w(X) p Fi 173 -38 a(N) p Fr 264 -50 a(is) i(gi) n(v) o(e) n(n) f(by) p Fl 187 113 a(X) p Fi 256 125 a(N) p Fk 402 113 a(=) 83 b(\(6) p Fl(d) p Fi 667 125 a(N) s(;r) p Fk 797 113 a(+) 18 b(\001\)) h(+) f (\(6) p Fl 14 w(d) p Fi 1214 125 a(l;N) p Fk 1336 113 a(+) g(\001\)) 402 238 y(=) 83 b(6) 14 b(\() p Fl(d) p Fi 681 250 a(l;N) p Fk 803 238 a(+) p Fl 18 w(d) p Fi 929 250 a(N) s(;r) p Fk 1041 238 a(\)) 19 b(+) f(2\001) p Fl(:) p Fr 494 w(\(3\)) -109 403 y(Note) 31 b(that) p Fl 30 w(X) p Fg 308 415 a(0) p Fk 372 403 a(=) c(0) p Fr 31 w(since) k(the) f(initial) h(node) f(does) g(not) h(establish) -192 503 y(an) o(y) 25 b(IPsec) i(tunn) n(el.) f(Consequen) n(tly) -5 b(,) 26 b(the) g(VPN) h(con) n(struction) f(time) g(is) -192 603 y(gi) n(v) o(en) h(by) p Fl 24 805 a(X) p Fi 93 817 a(N) p Fk 239 805 a(=) p Fh 387 688 a(\032) p Fk 491 754 a(0) p Fr 776 w(if) p Fl 29 w(N) p Fk 32 w(=) c(0) 491 854 y(6) 14 b(\() p Fl(d) p Fi 622 866 a(l;N) p Fk 744 854 a(+) p Fl 18 w(d) p Fi 870 866 a(N) s(;r) p Fk 982 854 a(\)) 19 b(+) f(2\001) p Fr 82 w(otherwise) 1803 805 y(\(4\)) p Fn -192 1005 a(C.) 42 b(VPN) 29 b(Reco) m(very) h(T) -5 b(ime) p Fr -109 1137 a(Ne) o(xt,) 25 b(we) g(deri) n(v) o(e) f(the) h (requ) n(ired) g(time) g(to) h(re-b) l(uild) f(the) g(VPN) h(after) -192 1237 y(the) j(VPN) i(nod) n(e) p Fl 30 w(i) p Fr 30 w(discon) n(nected) e(\(VPN) h(reco) o(v) m(ery) f(time\),) p Fl 29 w(Y) p Fi 1665 1249 a(i) p Fr 1693 1237 a(.) g(Sup-) -192 1337 y(pose) e(the) g(VPN) h(node) p Fl 27 w(i) p Fr 27 w(disconn) n(ects) g (from) e(the) i(VPN) g(due) e(to) i(some) -192 1436 y(f) o(ailure.) 38 b(Then) n(,) h(an) g(IPsec) g(tunn) n(el) g(must) g(be) f(established) h (between) -192 1536 y(its) j(upstream) f(VPN) h(nod) n(e) p Fl 42 w(l) p Fr 43 w(\() p Fl(m) p Fi 855 1548 a(l;i) p Fk 971 1536 a(=) k(1) p Fr(\),) 41 b(and) g(its) h(do) n(wnstream) -192 1635 y(VPN) 37 b(node) p Fl 35 w(r) p Fr 40 w(\() p Fl(m) p Fi 387 1647 a(i;r) p Fk 505 1635 a(=) g(1) p Fr(\).) f(In) g (particular) -5 b(,) 37 b(detection) e(of) h(a) h(VPN) -192 1735 y(node) 26 b(f) o(ailure) g(and) h(establishmen) n(t) h(of) f(a) g (ne) n(w) g(IPsec) h(tunn) n(el,) f(as) h(well) -192 1835 y(as) 41 b(terminatio) n(n) g(of) f(no) g(longer) f(required) g (IPsec) i(tunnel,) e(proceed) -192 1934 y(as) g(follo) n(ws:) f(\(a\)) g (VPN) h(nod) n(e) p Fl 39 w(l) p Fr 40 w(detects) g(a) f(f) o(ailure) g (of) g(VPN) h(nod) n(e) p Fl -192 2034 a(i) p Fr 32 w(by) 32 b(non) n(-return) f(of) h(the) g(ackn) n(o) n(wledgin) n(g) g(pack) o (et.) g(\(b\)) f(VPN) i(nod) n(e) p Fl -192 2134 a(l) p Fr 37 w(establishes) h(an) h(IPsec) g(tunne) n(l) h(to) e(VPN) i(nod) n (e) p Fl 35 w(r) p Fr 2 w(.) g(\(c\)) e(The) g(IPsec) -192 2233 y(tunne) n(l) h(between) f(VPN) g(node) p Fl 33 w(l) p Fr 37 w(and) f(VPN) i(nod) n(e) p Fl 35 w(i) p Fr 34 w(is) g(terminated) n(.) -192 2333 y(\(d\)) 24 b(The) h(IPsec) g(tunn) n(el) h(between) d(VPN) j(nod) n(e) p Fl 26 w(i) p Fr 24 w(and) f(VPN) g(node) p Fl 24 w(r) p Fr 28 w(is) -192 2432 y(terminated) n(.) k(In) f(ef) n(fect,) g(both) g (\(c\)) g(and) g(\(d\)) g(can) h(pro) n(ceed) f(in) h(parallel) -192 2532 y(with) g(\(b\)) n(.) g(Therefo) n(re,) f(the) h(VPN) g(reco) o(v) m(ery) f(time) h(is) g(gi) n(v) o(en) e(by) p Fl 375 2696 a(Y) p Fi 423 2708 a(i) p Fk 533 2696 a(=) 83 b(2) p Fl(d) p Fi 766 2708 a(l;i) p Fk 853 2696 a(+) 18 b(6) p Fl(d) p Fi 1021 2708 a(l;r) p Fk 1117 2696 a(+) g(2\001) p Fl(:) p Fr 469 w(\(5\)) p Fn -192 2861 a(D.) 41 b(Minimum) 30 b(Thr) l(ough) n(put,) g(Roun) n(d-T) -5 b(rip) 31 b(T) -5 b(ime) o(,) 31 b(and) e(P) -7 b(ac) n(k) o(et) 31 b(Loss) -192 2961 y(Pr) l(obab) n(ility) f(of) e(TCP) i(Flows) p Fr -109 3093 a(W) -7 b(e) 24 b(deri) n(v) m(e) f(the) f(minimu) n(m) h (throu) n(ghpu) n(t,) p Fl 23 w(T) p Fi 1177 3105 a(min) p Fr 1304 3093 a(,) g(of) f(the) g(TCP) h(\003o) n(w) -5 b(,) -192 3192 y(which) 31 b(has) g(the) g(minimum) f(throu) n(ghpu) n (t) i(among) e(all) i(TCP) g(\003o) n(ws) g(in) -192 3292 y(the) 19 b(VPN.) h(Hereafter) -5 b(,) 20 b(all) g(TCP) g(\003o) n (ws) g(are) f(assumed) g(to) g(continu) n(ously) -192 3392 y(send) 35 b(data.) g(The) g(num) n(ber) g(of) g(TCP) h(\003o) n (ws,) p Fl 35 w(n) p Fi 1222 3404 a(i;j) p Fr 1300 3392 a(,) g(passing) f(throu) n(gh) -192 3491 y(VPN) 29 b(node) p Fl 28 w(i) p Fr 28 w(and) f(VPN) h(node) p Fl 28 w(j) p Fr 34 w(is) g(gi) n(v) o(en) e(by) p Fl 298 3726 a(n) p Fi 348 3738 a(i;j) p Fk 449 3726 a(=) p Fi 537 3622 a(N) p Ff 6 w(\000) p Fg(1) p Fh 549 3647 a(X) p Fi 556 3826 a(l) p Fg(=0) p Fi 695 3622 a(N) p Ff 6 w(\000) p Fi(l) p Ff(\000) p Fg(2) p Fh 743 3647 a(X) p Fi 743 3826 a(k) p Fg 1 w(=0) p Fl 926 3726 a(f) p Fi 967 3738 a(i) p Ff(\000) p Fi(k) q(;j) p Fg 3 w(+) p Fi(k) p Fl 1221 3726 a(;) p Fr 559 w(\(6\)) -192 3956 y(where) p Fl 34 w(f) p Fi 87 3968 a(i;j) p Fr 200 3956 a(is) 35 b(the) g(num) n(ber) f(of) g(TCP) i(\003o) n(ws) f(established) f(between) -192 4055 y(VPN) 29 b(node) p Fl 28 w(i) p Fr 28 w(and) f(VPN) h(node) p Fl 28 w(j) p Fr 5 w(.) -109 4157 y(If) 37 b(the) f(link) h(between) f (VPN) h(node) p Fl 36 w(i) p Fr 37 w(and) f(VPN) h(node) p Fl 36 w(j) p Fr 42 w(is) h(the) -192 4256 y(bottlene) n(ck,) 29 b(VPN) g(nod) n(e) p Fl 29 w(i) p Fr 29 w(and) f(VPN) h(nod) n(e) p Fl 29 w(j) p Fr 34 w(satisfy) p Fk 466 4459 a(min) p Fi 498 4511 a(i;j) p Fh 618 4342 a(\022) p Fl 772 4403 a(b) p Fi 808 4415 a(i;j) p 689 4440 280 4 v Fl 689 4516 a(n) p Fi 739 4528 a(i;j) p Fl 817 4516 a(m) p Fi 890 4528 a(i;j) p Fh 978 4342 a(\023) p Fl 1053 4459 a(:) p Fr 727 w(\(7\)) -192 4660 y(It) d(should) f(be) h(noted) f(that,) h (since) g(all) g(of) g(links) g(between) f(VPN) h(nodes) -192 4760 y(are) 32 b(unidir) n(ectional,) f(the) i(rou) n(nd-trip) e(time) h (of) g(the) g(TCP) h(\003o) n(w) f(from) -192 4859 y(VPN) 21 b(nod) n(e) p Fl 21 w(i) p Fr 20 w(to) g(VPN) g(nod) n(e) p Fl 21 w(j) p Fr 5 w(,) p Fl 20 w(R) p Fi 824 4871 a(i;j) p Fr 902 4859 a(,) g(is) g(a) g(constan) n(t.) g(In) f(other) f(w) o (ords,) p Fl 594 5023 a(R) p Fi 657 5035 a(i;j) p Fk 818 5023 a(=) p Fl 82 w(R) p Fi 1028 5035 a(N) p Fl 1091 5023 a(:) p Fr 689 w(\(8\)) -192 5187 y(Theref) n(ore,) p Fl 28 w(T) p Fi 234 5199 a(min) p Fr 390 5187 a(is) 30 b(gi) n(v) o(e) n(n) f(by) p Fl 489 5382 a(T) p Fi 538 5394 a(min) p Fk 748 5382 a(=) 83 b(min) p Fi 928 5435 a(i;j) p Fl 1065 5326 a(b) p Fi 1101 5338 a(i;j) p 1058 5363 129 4 v Fl 1058 5439 a(n) p Fi 1108 5451 a(i;j) p Fl 1196 5382 a(:) p Fr 584 w(\(9\)) 2083 -50 y(Let) p Fl 35 w(p) p Fr 35 w(be) 35 b(the) g(pack) o(et) g(loss) h(pro) n (bability) f(of) g(TCP) g(\003o) n(ws.) h(Then) n(,) 2000 49 y(it) k(is) h(kno) l(wn) f(that) g(the) f(throug) n(hput) g(of) g(a) h(TCP) h(\003o) n(w) -5 b(,) p Fl 39 w(T) p Fr 12 w(,) 39 b(can) h(be) 2000 149 y(appr) n(oximated) 27 b(by) h(the) h(follo) n (win) n(g) g(equatio) n(n) g([15) n(].) p Fl 2455 349 a(T) p Fj 35 w(') p Fk 2706 293 a(1) p 2636 330 182 4 v 2636 406 a(2) p Fl 14 w(R) p Fi 2755 418 a(N) p Fk 2827 349 a(\() p Fj(\000) p Fk(3) 18 b(+) p Fj 3077 233 a(p) p 3146 233 282 4 v Fk 3146 293 a(6) g(+) g(21) p Fl 14 w(p) p 3077 330 351 4 v Fj 3197 355 a(p) p 3266 355 42 4 v Fl 3266 406 a(p) p Fk 3438 349 a(\)) p Fr 484 w(\(10) n(\)) 2000 550 y(By) k(letting) p Fl 22 w(T) p Fk 35 w(=) p Fl 22 w(T) p Fi 2574 562 a(min) p Fr 2701 550 a(,) h(the) f(pack) o(et) g(loss) h(prob) n(ability) f(of) g(TCP) h (\003o) n(ws) 2000 650 y(is) 29 b(obtained) e(as) p Fl 2346 820 a(p) p Fj 23 w(') p Fk 3007 764 a(3) p 2509 801 1038 4 v 2509 877 a(2) p Fl 14 w(R) p Fi 2628 889 a(N) p Fl 2704 877 a(T) p Fi 2753 889 a(min) p Fk 2880 877 a(\(3) 18 b(+) p Fl 18 w(R) p Fi 3118 889 a(N) p Fl 3195 877 a(T) p Fi 3244 889 a(min) p Fk 3371 877 a(\)) p Fj 19 w(\000) p Fk 18 w(6) p Fl 3556 820 a(:) p Fr 375 w(\(11) n(\)) p Fn 2000 1014 a(E.) 41 b(Numerical) 28 b(Examples) p Fr 2083 1142 a(The) 39 b(sensiti) n(vity) g(of) g(the) g (perfo) n(rmance) g(metrics) g(such) g(as) h(VPN) 2000 1242 y(constru) n(ction) 49 b(time,) g(VPN) g(reco) o(v) m(ery) g (time,) g(and) f(the) h(minimu) n(m) 2000 1342 y(throu) n(ghpu) n(t,) 21 b(round) n(-trip) g(time) g(and) f(pack) o(et) g(loss) i(prob) n (ability) f(of) g(TCP) 2000 1441 y(\003o) n(ws) g(re) o(ga) n(rding) e (se) n(v) o(eral) h(parameter) n(s) i(such) e(as) h(the) g(num) n(ber) g (of) f(VPN) 2000 1541 y(nod) n(es,) g(link) f(band) n(width,) g(link) g (transmission) f(delay) -5 b(,) 18 b(and) h(the) g(numb) n(er) 2000 1641 y(of) 28 b(TCP) h(\003o) n(ws) g(is) h(of) e(our) g(interest.) 2083 1741 y(In) 44 b(particu) n(lar) m(,) g(transmission) g(delay) g(and) g (thro) n(ughp) n(ut) h(are) f(e) o(x-) 2000 1841 y(pected) 39 b(to) i(decrea) n(se) g(as) g(the) g(num) n(ber) f(of) g(VPN) h(nodes) f (increa) n(ses) 2000 1940 y(for) 21 b(ring-) n(based) g(netw) o(orks) g ([12,) g(13]) n(.) h(Therefo) n(re,) g(we) g(in) m(v) m(estigate) f (the) 2000 2040 y(impact) i(of) g(the) h(num) n(ber) f(of) g(VPN) i (nod) n(es) f(participatin) n(g) g(in) g(the) f(VPN,) p Fl 2000 2139 a(N) p Fr 9 w(,) 28 b(on) g(VPN) h(constructio) n(n) g (time,) p Fl 28 w(X) p Fi 3138 2151 a(N) p Fr 3201 2139 a(,) g(VPN) g(reco) o(v) m(ery) f(time,) p Fl 28 w(Y) p Fi 4008 2151 a(N) p Fr 4071 2139 a(,) 2000 2239 y(and) 40 b(minimu) n(m) i(TCP) f(throu) n(ghput,) p Fl 40 w(T) p Fi 3195 2251 a(min) p Fr 3322 2239 a(,) g(and) f(round) n(-trip) h (time,) p Fl 2000 2339 a(R) p Fi 2063 2351 a(N) p Fr 2126 2339 a(,) 36 b(by) f(chang) n(ing) p Fl 36 w(N) p Fr 9 w(.) h(The) f(transmission) g(delay) g(between) g(VPN) 2000 2438 y(nod) n(es,) p Fl 37 w(d) p Fi 2294 2450 a(i;j) p Fr 2372 2438 a(,) h(are) g(set) g(to) g(be) g(unif) n(ormly) f(distrib) n(uted) g(in) h(the) g(rang) n(e) 2000 2538 y(of) i(0\226) p Fl(D) p Fi 2261 2550 a(max) p Fr 2397 2538 a(.) g(The) h(link) f(band) n (width) h(between) f(VPN) h(nod) n(es,) p Fl 39 w(b) p Fi 3993 2550 a(i;j) p Fr 4071 2538 a(,) 2000 2638 y(is) 31 b(\002x) o(ed) e(at) i(10) f([Mbit/s].) g(T) -7 b(able) 30 b(I) g(sho) n(ws) g(the) g(parameter) n(s) h(used) f(in) 2000 2737 y(num) n(erical) f(e) o(xam) n(ples) g(and) f(simulation.) 2083 2837 y(F) o(or) 40 b(simulation,) f(we) i(implemen) n(ted) g(the) f (RING-VPN) h(mod) n(ule) 2000 2937 y(in) 35 b(OPNET) f(modeler) g(v) o (ersio) n(n) h(10.0A) f([16]) n(.) h(F) o(or) g(each) f(param) n(eter) 2000 3037 y(set,) 47 b(simulation) e(is) j(repe) n(ated) f(5) f(times) h (with) g(v) n(ar) n(ying) f(the) g(seed) 2000 3136 y(of) h(a) i(rand) n (om) f(num) n(ber) g(gener) n(ator) m(,) f(and) h(the) g(a) n(v) o(era) n(ge) g(of) g(VPN) 2000 3236 y(constru) n(ction) 26 b(times,) h(VPN) g (reco) o(v) m(ery) f(times,) h(and) f(roun) n(d-trip) g(times) 2000 3336 y(of) i(TCP) h(\003o) n(ws) g(are) g(measur) n(ed.) 2083 3436 y(Figures) c(3) h(thro) n(ugh) f(6) h(sho) n(w) f(the) h(chang) n (es) g(in) g(VPN) g(constructio) n(n) 2000 3536 y(time,) p Fl 19 w(X) p Fi 2257 3548 a(N) p Fr 2319 3536 a(,) 20 b(VPN) f(reco) o(v) o(e) n(ry) g(time,) p Fl 19 w(Y) p Fi 3089 3548 a(N) p Fr 3152 3536 a(,) g(minimum) f(TCP) i(throu) n (ghpu) n(t,) p Fl 2000 3635 a(T) p Fi 2049 3647 a(min) p Fr 2176 3635 a(,) 39 b(and) f(roun) n(d-trip) g(time,) p Fl 39 w(R) p Fi 3042 3647 a(N) p Fr 3105 3635 a(,) h(when) f(the) h (num) n(ber) f(of) h(VPN) 2000 3735 y(nod) n(es,) p Fl 29 w(N) p Fr 9 w(,) 29 b(is) g(change) n(d.) 2083 3835 y(It) 23 b(can) g(be) g(seen) h(fro) n(m) g(Fig.) f(3) g(that) g(VPN) h (construc) n(tion) f(time,) p Fl 23 w(X) p Fi 4008 3847 a(N) p Fr 4071 3835 a(,) 2000 3935 y(decrea) n(ses) 28 b(as) g(the) f(numb) n(er) g(of) g(VPN) h(nod) n(es,) p Fl 28 w(N) p Fr 9 w(,) f(increases.) f(This) i(is) 2000 4034 y(becau) n(se) 21 b(of) f(the) g(increased) f(density) h(of) g (VPN) h(nod) n(es.) g(Namely) -5 b(,) 19 b(as) h(the) 2000 4134 y(num) n(ber) k(of) h(VPN) g(nod) n(es) g(increases,) f(the) h (density) f(of) g(VPN) h(nod) n(es) g(in) 2000 4234 y(the) j(netw) o (or) n(k) g(become) n(s) h(high.) e(Hence,) g(a) h(ne) n(w) g(VPN) g (node) f(is) i(lik) o(ely) 2000 4333 y(to) 37 b(be) g(conn) n(ected) g (to) g(VPN) g(nodes) g(with) g(short) f(roun) n(d-trip) g(times,) 2000 4433 y(leading) 25 b(short) h(VPN) h(constructio) n(n) g(time.) f (Moreo) m(v) o(er) m(,) f(Fig.) i(3) f(sho) n(ws) 2000 4533 y(goo) n(d) 31 b(agreeme) n(nt) h(between) e(num) n(erical) h(e) o (xamp) n(les) h(and) e(simulation) 2000 4632 y(results,) e(indicating) f (v) n(alidity) h(of) g(our) g(appro) n(ximate) g(analysis.) 2083 4733 y(Figure) 35 b(4) i(sho) n(ws) f(that) g(VPN) h(reco) o(v) m(ery) e (time) i(decrea) n(ses) h(as) e(the) 2000 4832 y(num) n(ber) 23 b(of) g(VPN) h(nod) n(es) g(increases.) f(This) g(can) g(be) g(e) o (xplaine) n(d) h(by) e(the) 2000 4932 y(decrea) n(se) 27 b(in) f(the) g(a) n(v) o(erag) n(e) h(delay) e(between) g(each) h(VPN) g (node) f(due) g(to) 2000 5031 y(the) 34 b(increased) f(numb) n(er) h (of) g(VPN) h(nod) n(es.) g(The) f(\002gure) f(also) h(sho) n(ws) 2000 5131 y(that) 40 b(VPN) i(reco) m(v) o(ery) e(time) g(increases) h(with) g(the) f(increase) g(of) g(the) 2000 5231 y(transmission) 24 b(delay) g(between) g(VPN) i(nod) n(es.) g(This) f(may) f(be) h (because) 2000 5330 y(the) 44 b(requir) n(ed) g(time) h(to) f (establish) g(and) g(terminate) f(IPsec) i(tunnels) 2000 5430 y(increases) 36 b(as) h(the) f(transmission) f(delay) h(between) f (node) n(s) i(becomes) p dyy eop end %%Page: 5 5 TeXDict begin 5 4 bop Fm 4055 -99 a(5) p Fo 1823 -106 a(T) -6 b(ABLE) 22 b(I) 1292 -6 y(P) p Fe -1 w(A) t(R) t(A) r(M) t(E) t (T) t(E) t(R) t(S) c(U) t(S) t(E) r(D) j(I) t(N) e(N) t(U) t(M) t(E) r (R) t(I) t(C) t(A) r(L) i(E) t(X) t(A) t(M) r(P) t(L) t(E) t(S) p 744 48 2389 4 v Fo 794 100 a(Number) j(of) f(VPN) g(nodes) p Fd 852 w(N) p Fo 302 w(8\22640) 794 175 y(Maximum) h(transmission) h (delay) g(betwe) r(en) e(VPN) h(nodes) p Fd 100 w(D) p Fc 2333 183 a(max) p Fo 2560 175 a(10,) f(100) 100 b([ms]) 794 250 y(Link) 23 b(band) r(width) h(betwe) r(en) g(VPN) f(nodes) p Fd 474 w(b) p Fc 2305 260 a(i;j) p Fo 2699 250 a(10) 100 b([Mbit/) r(s]) 794 324 y(T) n(ime) 23 b(requir) r(ed) g(for) h(gene) r (rating) h(an) f(encrypt) r(ion) g(k) o(e) o(y) p Fb 185 w(\001) p Fo 332 w(100) 100 b([ms]) 794 399 y(Number) 24 b(of) f(TCP) g(\003o) n(ws) h(betwee) r(n) f(VPN) g(node) r(s) p Fd 295 w(f) p Fc 2309 409 a(i;j) p Fo 2732 399 a(3) -189 2080 y @beginspecial 50 @llx 50 @lly 230 @urx 176 @ury 2467 @rwi @setspecial %%BeginDocument: figure/scatter-n-time.eps %!PS-Adobe-2.0 EPSF-2.0 %%Creator: gnuplot 4.0 patchlevel 0 %%CreationDate: Fri Oct 6 18:26:56 2006 %%DocumentFonts: (atend) %%BoundingBox: 50 50 230 176 %%Orientation: Portrait %%EndComments /gnudict 256 dict def gnudict begin /Color true def /Solid false def /gnulinewidth 10.000 def /userlinewidth gnulinewidth def /vshift -46 def /dl {10.0 mul} def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def /Rounded false def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /N {newpath moveto} bind def /C {setrgbcolor} bind def /f {rlineto fill} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop 0 setgray Solid {pop []} if 0 setdash} ifelse } def /BL { stroke userlinewidth 2 mul setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /AL { stroke userlinewidth 2 div setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /UL { dup gnulinewidth mul /userlinewidth exch def dup 1 lt {pop 1} if 10 mul /udl exch def } def /PL { stroke userlinewidth setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /LTw { PL [] 1 setgray } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 0.6 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 0.6 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 0.6 DL } def /LT3 { PL [1 dl 1.5 dl] 0.6 0 0.6 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 0.6 0.6 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 0.6 0.6 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.6 0.18 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.3 0.3 0.3 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def /BoxColFill { gsave Rec /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor fill grestore } def % % PostScript Level 1 Pattern Fill routine % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill { gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi { PFa 4 get mul 0 M 0 PFs V } for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi { PFa 4 get mul 0 2 1 roll M PFs 0 V } for } if stroke grestore } def % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {show} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} bind def /MFwidth {0 exch {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get stringwidth pop add} {pop} ifelse} forall} bind def /MLshow { currentpoint stroke M 0 exch R MFshow } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R MFshow } def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R MFshow } def end %%EndProlog gnudict begin gsave 50 50 translate 0.050 0.050 scale 0 setgray newpath (Helvetica) findfont 140 scalefont setfont 1.000 UL LTb 798 420 M 63 0 V 2501 0 R -63 0 V stroke 714 420 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0)] ] -46.7 MRshow 1.000 UL LTb 798 742 M 63 0 V 2501 0 R -63 0 V stroke 714 742 M [ [(Helvetica) 140.0 0.0 true true 0 ( 500)] ] -46.7 MRshow 1.000 UL LTb 798 1064 M 63 0 V 2501 0 R -63 0 V stroke 714 1064 M [ [(Helvetica) 140.0 0.0 true true 0 ( 1000)] ] -46.7 MRshow 1.000 UL LTb 798 1386 M 63 0 V 2501 0 R -63 0 V stroke 714 1386 M [ [(Helvetica) 140.0 0.0 true true 0 ( 1500)] ] -46.7 MRshow 1.000 UL LTb 798 1708 M 63 0 V 2501 0 R -63 0 V stroke 714 1708 M [ [(Helvetica) 140.0 0.0 true true 0 ( 2000)] ] -46.7 MRshow 1.000 UL LTb 798 2030 M 63 0 V 2501 0 R -63 0 V stroke 714 2030 M [ [(Helvetica) 140.0 0.0 true true 0 ( 2500)] ] -46.7 MRshow 1.000 UL LTb 798 2352 M 63 0 V 2501 0 R -63 0 V stroke 714 2352 M [ [(Helvetica) 140.0 0.0 true true 0 ( 3000)] ] -46.7 MRshow 1.000 UL LTb 798 420 M 0 63 V 0 1869 R 0 -63 V stroke 798 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0)] ] -46.7 MCshow 1.000 UL LTb 1103 420 M 0 63 V 0 1869 R 0 -63 V stroke 1103 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 5)] ] -46.7 MCshow 1.000 UL LTb 1408 420 M 0 63 V 0 1869 R 0 -63 V stroke 1408 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 10)] ] -46.7 MCshow 1.000 UL LTb 1714 420 M 0 63 V 0 1869 R 0 -63 V stroke 1714 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 15)] ] -46.7 MCshow 1.000 UL LTb 2019 420 M 0 63 V 0 1869 R 0 -63 V stroke 2019 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 20)] ] -46.7 MCshow 1.000 UL LTb 2324 420 M 0 63 V 0 1869 R 0 -63 V stroke 2324 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 25)] ] -46.7 MCshow 1.000 UL LTb 2629 420 M 0 63 V 0 1869 R 0 -63 V stroke 2629 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 30)] ] -46.7 MCshow 1.000 UL LTb 2935 420 M 0 63 V 0 1869 R 0 -63 V stroke 2935 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 35)] ] -46.7 MCshow 1.000 UL LTb 3240 420 M 0 63 V 0 1869 R 0 -63 V stroke 3240 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 40)] ] -46.7 MCshow 1.000 UL LTb 1.000 UL LTb 798 420 M 2564 0 V 0 1932 V -2564 0 V 798 420 L LTb 140 1386 M currentpoint gsave translate 90 rotate 0 0 moveto [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (VPN construction time [ms])] ] -46.7 MCshow grestore LTb 2080 70 M [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (Number of VPN nodes)] ] -46.7 MCshow 1.500 UP 1.000 UL LT0 LTb 2680 2219 M [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (analysis)] [(Helvetica) 140.0 0.0 true true 0 (\()] [(Helvetica-Oblique) 140.0 0.0 true true 0 (Dmax)] [(Helvetica) 140.0 0.0 true true 0 (=10\))] ] -46.7 MRshow LT0 2764 2219 M 430 0 V 1286 613 M 245 -10 V 244 13 V 244 -28 V 244 23 V 244 -17 V 245 11 V 244 -19 V 244 4 V 1.500 UP 1.000 UL LT1 1286 604 M 0 17 V -31 -17 R 62 0 V -62 17 R 62 0 V 214 -30 R 0 24 V -31 -24 R 62 0 V -62 24 R 62 0 V 213 -9 R 0 19 V -31 -19 R 62 0 V -62 19 R 62 0 V 213 -43 R 0 12 V -31 -12 R 62 0 V -62 12 R 62 0 V 213 4 R 0 25 V -31 -25 R 62 0 V -62 25 R 62 0 V 213 -37 R 0 16 V -31 -16 R 62 0 V -62 16 R 62 0 V 214 -6 R 0 18 V -31 -18 R 62 0 V -62 18 R 62 0 V 213 -36 R 0 15 V -31 -15 R 62 0 V -62 15 R 62 0 V 213 -13 R 0 19 V -31 -19 R 62 0 V -62 19 R 62 0 V 1286 613 BoxF 1531 603 BoxF 1775 616 BoxF 2019 588 BoxF 2263 611 BoxF 2507 594 BoxF 2752 605 BoxF 2996 586 BoxF 3240 590 BoxF 1.000 UL LT2 LTb 2680 2079 M [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (analysis)] [(Helvetica) 140.0 0.0 true true 0 (\()] [(Helvetica-Oblique) 140.0 0.0 true true 0 (Dmax)] [(Helvetica) 140.0 0.0 true true 0 (=100\))] ] -46.7 MRshow LT2 2764 2079 M 430 0 V 1286 1294 M 245 -34 V 244 -70 V 244 -51 V 244 -32 V 244 -42 V 245 -47 V 244 -12 V 244 -22 V 1.500 UP 1.000 UL LT3 1286 1247 M 0 95 V -31 -95 R 62 0 V -62 95 R 62 0 V 214 -116 R 0 68 V -31 -68 R 62 0 V -62 68 R 62 0 V 213 -133 R 0 59 V -31 -59 R 62 0 V -62 59 R 62 0 V 213 -108 R 0 53 V -31 -53 R 62 0 V -62 53 R 62 0 V 213 -82 R 0 49 V -31 -49 R 62 0 V -62 49 R 62 0 V 213 -86 R 0 38 V -31 -38 R 62 0 V -62 38 R 62 0 V 2752 981 M 0 75 V -31 -75 R 62 0 V -62 75 R 62 0 V 213 -76 R 0 52 V -31 -52 R 62 0 V -62 52 R 62 0 V 213 -71 R 0 46 V -31 -46 R 62 0 V -62 46 R 62 0 V 1286 1294 DiaF 1531 1260 DiaF 1775 1190 DiaF 2019 1139 DiaF 2263 1107 DiaF 2507 1065 DiaF 2752 1018 DiaF 2996 1006 DiaF 3240 984 DiaF 1.000 UL LT4 LTb 2680 1939 M [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (simulation)] [(Helvetica) 140.0 0.0 true true 0 (\()] [(Helvetica-Oblique) 140.0 0.0 true true 0 (Dmax)] [(Helvetica) 140.0 0.0 true true 0 (=10\))] ] -46.7 MRshow LT4 2764 1939 M 430 0 V 1408 597 M 611 1 V 610 -5 V 611 0 V 1.500 UP 1.000 UL LT5 1408 597 M -31 0 R 62 0 V -62 0 R 62 0 V 580 1 R -31 0 R 62 0 V -62 0 R 62 0 V 579 -5 R -31 0 R 62 0 V -62 0 R 62 0 V 580 0 R -31 0 R 62 0 V -62 0 R 62 0 V 1408 597 TriUF 2019 598 TriUF 2629 593 TriUF 3240 593 TriUF 1.000 UL LT6 LTb 2680 1799 M [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (simulation)] [(Helvetica) 140.0 0.0 true true 0 (\()] [(Helvetica-Oblique) 140.0 0.0 true true 0 (Dmax)] [(Helvetica) 140.0 0.0 true true 0 (=100\))] ] -46.7 MRshow LT6 2764 1799 M 430 0 V 1408 1251 M 611 -45 V 610 -150 V 611 -99 V 1.500 UP 1.000 UL LT7 1408 1251 M -31 0 R 62 0 V -62 0 R 62 0 V 580 -45 R -31 0 R 62 0 V -62 0 R 62 0 V 579 -151 R 0 1 V -31 -1 R 62 0 V -62 1 R 62 0 V 580 -99 R 0 1 V -31 -1 R 62 0 V -62 1 R 62 0 V 1408 1251 TriDF 2019 1206 TriDF 2629 1056 TriDF 3240 957 TriDF 1.000 UL LTb 798 420 M 2564 0 V 0 1932 V -2564 0 V 798 420 L 1.500 UP stroke grestore end showpage %%Trailer %%DocumentFonts: Helvetica-Oblique Helvetica %%EndDocument @endspecial Fr -192 2263 a(Fig.) 29 b(3:) f(Number) h(of) g(VPN) h (nodes) p Fl 29 w(N) p Fr 40 w(vs.) f(VPN) i(constru) n(ction) f(time) p Fl 62 2362 a(X) p Fi 131 2374 a(N) p Fr 194 2362 a(.) -189 3982 y @beginspecial 50 @llx 50 @lly 230 @urx 176 @ury 2467 @rwi @setspecial %%BeginDocument: figure/scatter-n-Y.eps %!PS-Adobe-2.0 EPSF-2.0 %%Creator: gnuplot 4.0 patchlevel 0 %%CreationDate: Fri Oct 6 18:29:15 2006 %%DocumentFonts: (atend) %%BoundingBox: 50 50 230 176 %%Orientation: Portrait %%EndComments /gnudict 256 dict def gnudict begin /Color true def /Solid false def /gnulinewidth 10.000 def /userlinewidth gnulinewidth def /vshift -46 def /dl {10.0 mul} def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def /Rounded false def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /N {newpath moveto} bind def /C {setrgbcolor} bind def /f {rlineto fill} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop 0 setgray Solid {pop []} if 0 setdash} ifelse } def /BL { stroke userlinewidth 2 mul setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /AL { stroke userlinewidth 2 div setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /UL { dup gnulinewidth mul /userlinewidth exch def dup 1 lt {pop 1} if 10 mul /udl exch def } def /PL { stroke userlinewidth setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /LTw { PL [] 1 setgray } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 0.6 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 0.6 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 0.6 DL } def /LT3 { PL [1 dl 1.5 dl] 0.6 0 0.6 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 0.6 0.6 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 0.6 0.6 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.6 0.18 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.3 0.3 0.3 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def /BoxColFill { gsave Rec /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor fill grestore } def % % PostScript Level 1 Pattern Fill routine % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill { gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi { PFa 4 get mul 0 M 0 PFs V } for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi { PFa 4 get mul 0 2 1 roll M PFs 0 V } for } if stroke grestore } def % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {show} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} bind def /MFwidth {0 exch {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get stringwidth pop add} {pop} ifelse} forall} bind def /MLshow { currentpoint stroke M 0 exch R MFshow } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R MFshow } def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R MFshow } def end %%EndProlog gnudict begin gsave 50 50 translate 0.050 0.050 scale 0 setgray newpath (Helvetica) findfont 140 scalefont setfont 1.000 UL LTb 798 420 M 63 0 V 2501 0 R -63 0 V stroke 714 420 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0)] ] -46.7 MRshow 1.000 UL LTb 798 806 M 63 0 V 2501 0 R -63 0 V stroke 714 806 M [ [(Helvetica) 140.0 0.0 true true 0 ( 200)] ] -46.7 MRshow 1.000 UL LTb 798 1193 M 63 0 V 2501 0 R -63 0 V stroke 714 1193 M [ [(Helvetica) 140.0 0.0 true true 0 ( 400)] ] -46.7 MRshow 1.000 UL LTb 798 1579 M 63 0 V 2501 0 R -63 0 V stroke 714 1579 M [ [(Helvetica) 140.0 0.0 true true 0 ( 600)] ] -46.7 MRshow 1.000 UL LTb 798 1966 M 63 0 V 2501 0 R -63 0 V stroke 714 1966 M [ [(Helvetica) 140.0 0.0 true true 0 ( 800)] ] -46.7 MRshow 1.000 UL LTb 798 2352 M 63 0 V 2501 0 R -63 0 V stroke 714 2352 M [ [(Helvetica) 140.0 0.0 true true 0 ( 1000)] ] -46.7 MRshow 1.000 UL LTb 1061 420 M 0 63 V 0 1869 R 0 -63 V stroke 1061 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 5)] ] -46.7 MCshow 1.000 UL LTb 1390 420 M 0 63 V 0 1869 R 0 -63 V stroke 1390 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 10)] ] -46.7 MCshow 1.000 UL LTb 1718 420 M 0 63 V 0 1869 R 0 -63 V stroke 1718 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 15)] ] -46.7 MCshow 1.000 UL LTb 2047 420 M 0 63 V 0 1869 R 0 -63 V stroke 2047 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 20)] ] -46.7 MCshow 1.000 UL LTb 2376 420 M 0 63 V 0 1869 R 0 -63 V stroke 2376 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 25)] ] -46.7 MCshow 1.000 UL LTb 2705 420 M 0 63 V 0 1869 R 0 -63 V stroke 2705 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 30)] ] -46.7 MCshow 1.000 UL LTb 3033 420 M 0 63 V 0 1869 R 0 -63 V stroke 3033 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 35)] ] -46.7 MCshow 1.000 UL LTb 3362 420 M 0 63 V 0 1869 R 0 -63 V stroke 3362 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 40)] ] -46.7 MCshow 1.000 UL LTb 1.000 UL LTb 798 420 M 2564 0 V 0 1932 V -2564 0 V 798 420 L LTb 140 1386 M currentpoint gsave translate 90 rotate 0 0 moveto [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (VPN recovery time [ms])] ] -46.7 MCshow grestore LTb 2080 70 M [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (Number of VPN nodes)] ] -46.7 MCshow 1.500 UP 1.000 UL LT0 LTb 2680 2219 M [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (analysis)] [(Helvetica) 140.0 0.0 true true 0 (\()] [(Helvetica-Oblique) 140.0 0.0 true true 0 (Dmax)] [(Helvetica) 140.0 0.0 true true 0 (=10\))] ] -46.7 MRshow LT0 2764 2219 M 430 0 V 1258 672 M 263 -13 V 263 -2 V 263 -3 V 263 3 V 263 -3 V 263 2 V 263 -5 V 263 0 V 1.500 UP 1.000 UL LT1 1258 668 M 0 8 V -31 -8 R 62 0 V -62 8 R 62 0 V 232 -20 R 0 6 V -31 -6 R 62 0 V -62 6 R 62 0 V 232 -6 R 0 2 V -31 -2 R 62 0 V -62 2 R 62 0 V 232 -7 R 0 5 V -31 -5 R 62 0 V -62 5 R 62 0 V 232 -1 R 0 4 V -31 -4 R 62 0 V -62 4 R 62 0 V 232 -7 R 0 4 V -31 -4 R 62 0 V -62 4 R 62 0 V 232 -2 R 0 5 V -31 -5 R 62 0 V -62 5 R 62 0 V 232 -10 R 0 4 V -31 -4 R 62 0 V -62 4 R 62 0 V 232 -3 R 0 3 V -31 -3 R 62 0 V -62 3 R 62 0 V 1258 672 BoxF 1521 659 BoxF 1784 657 BoxF 2047 654 BoxF 2310 657 BoxF 2573 654 BoxF 2836 656 BoxF 3099 651 BoxF 3362 651 BoxF 1.000 UL LT2 LTb 2680 2079 M [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (analysis)] [(Helvetica) 140.0 0.0 true true 0 (\()] [(Helvetica-Oblique) 140.0 0.0 true true 0 (Dmax)] [(Helvetica) 140.0 0.0 true true 0 (=100\))] ] -46.7 MRshow LT2 2764 2079 M 430 0 V 1258 1214 M 263 -87 V 263 -42 V 263 -39 V 263 -12 V 263 -4 V 263 -7 V 263 -16 V 263 -21 V 1.500 UP 1.000 UL LT3 1258 1200 M 0 29 V -31 -29 R 62 0 V -62 29 R 62 0 V 232 -114 R 0 24 V -31 -24 R 62 0 V -62 24 R 62 0 V 232 -58 R 0 9 V -31 -9 R 62 0 V -62 9 R 62 0 V 232 -50 R 0 13 V -31 -13 R 62 0 V -62 13 R 62 0 V 232 -25 R 0 13 V -31 -13 R 62 0 V -62 13 R 62 0 V 232 -18 R 0 14 V -31 -14 R 62 0 V -62 14 R 62 0 V 232 -22 R 0 16 V -31 -16 R 62 0 V -62 16 R 62 0 V 232 -31 R 0 14 V -31 -14 R 62 0 V -62 14 R 62 0 V 232 -32 R 0 9 V -31 -9 R 62 0 V -62 9 R 62 0 V 1258 1214 DiaF 1521 1127 DiaF 1784 1085 DiaF 2047 1046 DiaF 2310 1034 DiaF 2573 1030 DiaF 2836 1023 DiaF 3099 1007 DiaF 3362 986 DiaF 1.000 UL LT4 LTb 2680 1939 M [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (simulation)] [(Helvetica) 140.0 0.0 true true 0 (\()] [(Helvetica-Oblique) 140.0 0.0 true true 0 (Dmax)] [(Helvetica) 140.0 0.0 true true 0 (=10\))] ] -46.7 MRshow LT4 2764 1939 M 430 0 V 1390 632 M 657 -10 V 658 7 V 657 14 V 1.500 UP 1.000 UL LT5 1390 627 M 0 11 V -31 -11 R 62 0 V -62 11 R 62 0 V 626 -24 R 0 16 V -31 -16 R 62 0 V -62 16 R 62 0 V 627 -4 R 0 7 V -31 -7 R 62 0 V -62 7 R 62 0 V 626 -4 R 0 28 V -31 -28 R 62 0 V -62 28 R 62 0 V 1390 632 TriUF 2047 622 TriUF 2705 629 TriUF 3362 643 TriUF 1.000 UL LT6 LTb 2680 1799 M [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (simulation)] [(Helvetica) 140.0 0.0 true true 0 (\()] [(Helvetica-Oblique) 140.0 0.0 true true 0 (Dmax)] [(Helvetica) 140.0 0.0 true true 0 (=100\))] ] -46.7 MRshow LT6 2764 1799 M 430 0 V 1390 1225 M 657 -103 V 658 -73 V 657 -65 V 1.500 UP 1.000 UL LT7 1390 1213 M 0 23 V -31 -23 R 62 0 V -62 23 R 62 0 V 626 -120 R 0 11 V -31 -11 R 62 0 V -62 11 R 62 0 V 627 -83 R 0 11 V -31 -11 R 62 0 V -62 11 R 62 0 V 626 -76 R 0 9 V -31 -9 R 62 0 V -62 9 R 62 0 V 1390 1225 TriDF 2047 1122 TriDF 2705 1049 TriDF 3362 984 TriDF 1.000 UL LTb 798 420 M 2564 0 V 0 1932 V -2564 0 V 798 420 L 1.500 UP stroke grestore end showpage %%Trailer %%DocumentFonts: Helvetica-Oblique Helvetica %%EndDocument @endspecial -192 4165 a(Fig.) f(4:) f(Number) c(of) h(VPN) h(nodes) p Fl 25 w(N) p Fr 34 w(vs.) g(VPN) g(reco) o(v) m(ery) f(time) p Fl 25 w(Y) p Fi 1816 4177 a(N) p Fr 1879 4165 a(.) -192 4520 y(lar) o(ge) n(r) m(,) 30 b(as) h(can) f(be) g(seen) g(from) g (Eq.) f(\(5\).) h(Aga) n(in,) h(this) f(\002gure) g(sho) n(ws) -192 4619 y(good) g(agre) n(ement) h(between) f(nume) n(rical) h(e) o(xamp) n (les) h(and) f(simulation) -192 4719 y(results,) e(indica) n(ting) g(v) n(alidity) e(of) i(our) e(appro) n(ximate) h(analysis.) -109 4825 y(From) 34 b(these) i(obser) n(v) n(ations,) e(we) i(conc) n(lude) f(that) g(both) f(the) h(VPN) -192 4925 y(constru) n(ction) 47 b(time) h(and) e(the) h(VPN) h(reco) o(v) m(ery) f(time) g(are) g(not) g (so) -192 5025 y(sensiti) n(v) o(e) 28 b(to) h(the) f(numbe) n(r) h(of) f(VPN) h(nodes.) -109 5131 y(Figure) g(5) h(sho) n(ws) h(that) f(the) g (minim) n(um) g(TCP) h(throu) n(ghpu) n(t) g(rapidly) -192 5231 y(decreases) 25 b(as) g(the) g(numb) n(er) g(of) g(VPN) g(nodes) f (increases.) h(This) g(can) g(be) -192 5330 y(e) o(xplain) n(ed) 30 b(by) f(the) h(increased) f(numb) n(er) h(of) g(TCP) h(\003o) n(ws) f (sharing) f(the) -192 5430 y(band) n(width) f(of) f(the) h(bottlen) n (eck) g(link.) f(Also,) h(this) g(\002gure) f(sho) n(ws) h(that) 2003 2080 y @beginspecial 50 @llx 50 @lly 230 @urx 176 @ury 2467 @rwi @setspecial %%BeginDocument: figure/scatter-n-T.eps %!PS-Adobe-2.0 EPSF-2.0 %%Creator: gnuplot 4.0 patchlevel 0 %%CreationDate: Fri Oct 6 18:30:28 2006 %%DocumentFonts: (atend) %%BoundingBox: 50 50 230 176 %%Orientation: Portrait %%EndComments /gnudict 256 dict def gnudict begin /Color true def /Solid false def /gnulinewidth 10.000 def /userlinewidth gnulinewidth def /vshift -46 def /dl {10.0 mul} def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def /Rounded false def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /N {newpath moveto} bind def /C {setrgbcolor} bind def /f {rlineto fill} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop 0 setgray Solid {pop []} if 0 setdash} ifelse } def /BL { stroke userlinewidth 2 mul setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /AL { stroke userlinewidth 2 div setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /UL { dup gnulinewidth mul /userlinewidth exch def dup 1 lt {pop 1} if 10 mul /udl exch def } def /PL { stroke userlinewidth setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /LTw { PL [] 1 setgray } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 0.6 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 0.6 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 0.6 DL } def /LT3 { PL [1 dl 1.5 dl] 0.6 0 0.6 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 0.6 0.6 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 0.6 0.6 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.6 0.18 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.3 0.3 0.3 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def /BoxColFill { gsave Rec /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor fill grestore } def % % PostScript Level 1 Pattern Fill routine % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill { gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi { PFa 4 get mul 0 M 0 PFs V } for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi { PFa 4 get mul 0 2 1 roll M PFs 0 V } for } if stroke grestore } def % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {show} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} bind def /MFwidth {0 exch {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get stringwidth pop add} {pop} ifelse} forall} bind def /MLshow { currentpoint stroke M 0 exch R MFshow } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R MFshow } def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R MFshow } def end %%EndProlog gnudict begin gsave 50 50 translate 0.050 0.050 scale 0 setgray newpath (Helvetica) findfont 140 scalefont setfont 1.000 UL LTb 798 420 M 63 0 V 2501 0 R -63 0 V stroke 714 420 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0)] ] -46.7 MRshow 1.000 UL LTb 798 742 M 63 0 V 2501 0 R -63 0 V stroke 714 742 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0.05)] ] -46.7 MRshow 1.000 UL LTb 798 1064 M 63 0 V 2501 0 R -63 0 V stroke 714 1064 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0.1)] ] -46.7 MRshow 1.000 UL LTb 798 1386 M 63 0 V 2501 0 R -63 0 V stroke 714 1386 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0.15)] ] -46.7 MRshow 1.000 UL LTb 798 1708 M 63 0 V 2501 0 R -63 0 V stroke 714 1708 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0.2)] ] -46.7 MRshow 1.000 UL LTb 798 2030 M 63 0 V 2501 0 R -63 0 V stroke 714 2030 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0.25)] ] -46.7 MRshow 1.000 UL LTb 798 2352 M 63 0 V 2501 0 R -63 0 V stroke 714 2352 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0.3)] ] -46.7 MRshow 1.000 UL LTb 1061 420 M 0 63 V 0 1869 R 0 -63 V stroke 1061 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 5)] ] -46.7 MCshow 1.000 UL LTb 1390 420 M 0 63 V 0 1869 R 0 -63 V stroke 1390 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 10)] ] -46.7 MCshow 1.000 UL LTb 1718 420 M 0 63 V 0 1869 R 0 -63 V stroke 1718 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 15)] ] -46.7 MCshow 1.000 UL LTb 2047 420 M 0 63 V 0 1869 R 0 -63 V stroke 2047 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 20)] ] -46.7 MCshow 1.000 UL LTb 2376 420 M 0 63 V 0 1869 R 0 -63 V stroke 2376 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 25)] ] -46.7 MCshow 1.000 UL LTb 2705 420 M 0 63 V 0 1869 R 0 -63 V stroke 2705 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 30)] ] -46.7 MCshow 1.000 UL LTb 3033 420 M 0 63 V 0 1869 R 0 -63 V stroke 3033 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 35)] ] -46.7 MCshow 1.000 UL LTb 3362 420 M 0 63 V 0 1869 R 0 -63 V stroke 3362 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 40)] ] -46.7 MCshow 1.000 UL LTb 1.000 UL LTb 798 420 M 2564 0 V 0 1932 V -2564 0 V 798 420 L LTb 140 1386 M currentpoint gsave translate 90 rotate 0 0 moveto [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (Minimum TCP throughput [Mbit/s])] ] -46.7 MCshow grestore LTb 2080 70 M [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (Number of VPN nodes)] ] -46.7 MCshow 1.500 UP 1.000 UL LT0 LTb 2680 2219 M [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (Dmax)] [(Helvetica) 140.0 0.0 true true 0 (=10)] ] -46.7 MRshow LT0 2764 2219 M 430 0 V -1936 34 R 1521 1166 L 1784 838 L 2047 680 L 263 -77 V 263 -48 V 263 -33 V 263 -19 V 263 -17 V 1.500 UP 1.000 UL LT1 1258 2188 M 0 129 V -31 -129 R 62 0 V -62 129 R 62 0 V 1521 1151 M 0 31 V -31 -31 R 62 0 V -62 31 R 62 0 V 1784 830 M 0 16 V -31 -16 R 62 0 V -62 16 R 62 0 V 2047 676 M 0 8 V -31 -8 R 62 0 V -62 8 R 62 0 V 232 -83 R 0 4 V -31 -4 R 62 0 V -62 4 R 62 0 V 232 -52 R 0 4 V -31 -4 R 62 0 V -62 4 R 62 0 V 232 -36 R 0 3 V -31 -3 R 62 0 V -62 3 R 62 0 V 232 -22 R 0 2 V -31 -2 R 62 0 V -62 2 R 62 0 V 232 -18 R 0 1 V -31 -1 R 62 0 V -62 1 R 62 0 V 1258 2253 BoxF 1521 1166 BoxF 1784 838 BoxF 2047 680 BoxF 2310 603 BoxF 2573 555 BoxF 2836 522 BoxF 3099 503 BoxF 3362 486 BoxF 1.000 UL LT2 LTb 2680 2079 M [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (Dmax)] [(Helvetica) 140.0 0.0 true true 0 (=100)] ] -46.7 MRshow LT2 2764 2079 M 430 0 V 1258 2242 M 1521 1183 L 1784 837 L 2047 685 L 263 -80 V 263 -49 V 263 -32 V 263 -21 V 263 -16 V 1.500 UP 1.000 UL LT3 1258 2185 M 0 114 V -31 -114 R 62 0 V -62 114 R 62 0 V 1521 1164 M 0 38 V -31 -38 R 62 0 V -62 38 R 62 0 V 1784 830 M 0 15 V -31 -15 R 62 0 V -62 15 R 62 0 V 2047 680 M 0 9 V -31 -9 R 62 0 V -62 9 R 62 0 V 232 -87 R 0 5 V -31 -5 R 62 0 V -62 5 R 62 0 V 232 -52 R 0 2 V -31 -2 R 62 0 V -62 2 R 62 0 V 232 -35 R 0 3 V -31 -3 R 62 0 V -62 3 R 62 0 V 232 -23 R 0 2 V -31 -2 R 62 0 V -62 2 R 62 0 V 232 -18 R 0 2 V -31 -2 R 62 0 V -62 2 R 62 0 V 1258 2242 DiaF 1521 1183 DiaF 1784 837 DiaF 2047 685 DiaF 2310 605 DiaF 2573 556 DiaF 2836 524 DiaF 3099 503 DiaF 3362 487 DiaF 1.000 UL LTb 798 420 M 2564 0 V 0 1932 V -2564 0 V 798 420 L 1.500 UP stroke grestore end showpage %%Trailer %%DocumentFonts: Helvetica-Oblique Helvetica %%EndDocument @endspecial 2000 2263 a(Fig.) g(5:) h(Numbe) n(r) d(of) f(VPN) g(nodes) p Fl 25 w(N) p Fr 34 w(vs.) g(minimum) f(TCP) i(throu) n(gh-) 2254 2362 y(put) p Fl 28 w(T) p Fi 2438 2374 a(min) p Fr 2565 2362 a(.) 2003 3988 y @beginspecial 50 @llx 50 @lly 230 @urx 176 @ury 2467 @rwi @setspecial %%BeginDocument: figure/scatter-n-R.eps %!PS-Adobe-2.0 EPSF-2.0 %%Creator: gnuplot 4.0 patchlevel 0 %%CreationDate: Fri Oct 6 18:30:28 2006 %%DocumentFonts: (atend) %%BoundingBox: 50 50 230 176 %%Orientation: Portrait %%EndComments /gnudict 256 dict def gnudict begin /Color true def /Solid false def /gnulinewidth 10.000 def /userlinewidth gnulinewidth def /vshift -46 def /dl {10.0 mul} def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def /Rounded false def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /N {newpath moveto} bind def /C {setrgbcolor} bind def /f {rlineto fill} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop 0 setgray Solid {pop []} if 0 setdash} ifelse } def /BL { stroke userlinewidth 2 mul setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /AL { stroke userlinewidth 2 div setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /UL { dup gnulinewidth mul /userlinewidth exch def dup 1 lt {pop 1} if 10 mul /udl exch def } def /PL { stroke userlinewidth setlinewidth Rounded { 1 setlinejoin 1 setlinecap } if } def /LTw { PL [] 1 setgray } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 0.6 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 0.6 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 0.6 DL } def /LT3 { PL [1 dl 1.5 dl] 0.6 0 0.6 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 0.6 0.6 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 0.6 0.6 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.6 0.18 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.3 0.3 0.3 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def /BoxColFill { gsave Rec /Fillden exch def currentrgbcolor /ColB exch def /ColG exch def /ColR exch def /ColR ColR Fillden mul Fillden sub 1 add def /ColG ColG Fillden mul Fillden sub 1 add def /ColB ColB Fillden mul Fillden sub 1 add def ColR ColG ColB setrgbcolor fill grestore } def % % PostScript Level 1 Pattern Fill routine % Usage: x y w h s a XX PatternFill % x,y = lower left corner of box to be filled % w,h = width and height of box % a = angle in degrees between lines and x-axis % XX = 0/1 for no/yes cross-hatch % /PatternFill { gsave /PFa [ 9 2 roll ] def PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec gsave 1 setgray fill grestore clip currentlinewidth 0.5 mul setlinewidth /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 0 0 M PFa 5 get rotate PFs -2 div dup translate 0 1 PFs PFa 4 get div 1 add floor cvi { PFa 4 get mul 0 M 0 PFs V } for 0 PFa 6 get ne { 0 1 PFs PFa 4 get div 1 add floor cvi { PFa 4 get mul 0 2 1 roll M PFs 0 V } for } if stroke grestore } def % /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont pop /MFshow { { dup 5 get 3 ge { 5 get 3 eq {gsave} {grestore} ifelse } {dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 get exch 4 get {show} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop pop aload pop M} ifelse }ifelse }ifelse } ifelse } forall} bind def /MFwidth {0 exch {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 6 get stringwidth pop add} {pop} ifelse} forall} bind def /MLshow { currentpoint stroke M 0 exch R MFshow } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R MFshow } def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R MFshow } def end %%EndProlog gnudict begin gsave 50 50 translate 0.050 0.050 scale 0 setgray newpath (Helvetica) findfont 140 scalefont setfont 1.000 UL LTb 798 420 M 63 0 V 2501 0 R -63 0 V stroke 714 420 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0)] ] -46.7 MRshow 1.000 UL LTb 798 806 M 63 0 V 2501 0 R -63 0 V stroke 714 806 M [ [(Helvetica) 140.0 0.0 true true 0 ( 1000)] ] -46.7 MRshow 1.000 UL LTb 798 1193 M 63 0 V 2501 0 R -63 0 V stroke 714 1193 M [ [(Helvetica) 140.0 0.0 true true 0 ( 2000)] ] -46.7 MRshow 1.000 UL LTb 798 1579 M 63 0 V 2501 0 R -63 0 V stroke 714 1579 M [ [(Helvetica) 140.0 0.0 true true 0 ( 3000)] ] -46.7 MRshow 1.000 UL LTb 798 1966 M 63 0 V 2501 0 R -63 0 V stroke 714 1966 M [ [(Helvetica) 140.0 0.0 true true 0 ( 4000)] ] -46.7 MRshow 1.000 UL LTb 798 2352 M 63 0 V 2501 0 R -63 0 V stroke 714 2352 M [ [(Helvetica) 140.0 0.0 true true 0 ( 5000)] ] -46.7 MRshow 1.000 UL LTb 1061 420 M 0 63 V 0 1869 R 0 -63 V stroke 1061 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 5)] ] -46.7 MCshow 1.000 UL LTb 1390 420 M 0 63 V 0 1869 R 0 -63 V stroke 1390 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 10)] ] -46.7 MCshow 1.000 UL LTb 1718 420 M 0 63 V 0 1869 R 0 -63 V stroke 1718 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 15)] ] -46.7 MCshow 1.000 UL LTb 2047 420 M 0 63 V 0 1869 R 0 -63 V stroke 2047 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 20)] ] -46.7 MCshow 1.000 UL LTb 2376 420 M 0 63 V 0 1869 R 0 -63 V stroke 2376 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 25)] ] -46.7 MCshow 1.000 UL LTb 2705 420 M 0 63 V 0 1869 R 0 -63 V stroke 2705 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 30)] ] -46.7 MCshow 1.000 UL LTb 3033 420 M 0 63 V 0 1869 R 0 -63 V stroke 3033 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 35)] ] -46.7 MCshow 1.000 UL LTb 3362 420 M 0 63 V 0 1869 R 0 -63 V stroke 3362 280 M [ [(Helvetica) 140.0 0.0 true true 0 ( 40)] ] -46.7 MCshow 1.000 UL LTb 1.000 UL LTb 798 420 M 2564 0 V 0 1932 V -2564 0 V 798 420 L LTb 140 1386 M 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1784 917 DiaF 2047 1017 DiaF 2310 1162 DiaF 2573 1267 DiaF 2836 1368 DiaF 3099 1429 DiaF 3362 1497 DiaF 1.000 UL LT4 LTb 2680 1939 M [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (simulation)] [(Helvetica) 140.0 0.0 true true 0 (\()] [(Helvetica-Oblique) 140.0 0.0 true true 0 (Dmax)] [(Helvetica) 140.0 0.0 true true 0 (=10\))] ] -46.7 MRshow LT4 2764 1939 M 430 0 V 1390 468 M 657 4 V 658 40 V 657 11 V 1.500 UP 1.000 UL LT5 1390 468 M -31 0 R 62 0 V -62 0 R 62 0 V 626 4 R -31 0 R 62 0 V -62 0 R 62 0 V 627 40 R -31 0 R 62 0 V -62 0 R 62 0 V 626 11 R -31 0 R 62 0 V -62 0 R 62 0 V 1390 468 TriUF 2047 472 TriUF 2705 512 TriUF 3362 523 TriUF 1.000 UL LT6 LTb 2680 1799 M [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (simulation)] [(Helvetica) 140.0 0.0 true true 0 (\()] [(Helvetica-Oblique) 140.0 0.0 true true 0 (Dmax)] [(Helvetica) 140.0 0.0 true true 0 (=100\))] ] -46.7 MRshow LT6 2764 1799 M 430 0 V 1390 851 M 657 162 V 658 337 V 657 172 V 1.500 UP 1.000 UL LT7 1390 851 M -31 0 R 62 0 V -62 0 R 62 0 V 626 162 R -31 0 R 62 0 V -62 0 R 62 0 V 627 337 R -31 0 R 62 0 V -62 0 R 62 0 V 626 172 R -31 0 R 62 0 V -62 0 R 62 0 V 1390 851 TriDF 2047 1013 TriDF 2705 1350 TriDF 3362 1522 TriDF 1.000 UL LTb 798 420 M 2564 0 V 0 1932 V -2564 0 V 798 420 L 1.500 UP stroke grestore end showpage %%Trailer %%DocumentFonts: Helvetica-Oblique Helvetica %%EndDocument @endspecial 2000 4171 a(Fig.) i(6:) h(Numbe) n(r) 20 b(of) g(VPN) g(nodes) p Fl 19 w(N) p Fr 30 w(vs.) g(TCP) g(roun) n (d-trip) f(time) p Fl 20 w(R) p Fi 4008 4183 a(N) p Fr 4071 4171 a(.) 2000 4526 y(the) 38 b(transmission) f(delay) h(between) f (VPN) i(node) n(s) g(does) f(not) g(af) n(fect) 2000 4626 y(the) e(minim) n(um) g(throu) n(ghpu) n(t) h(of) e(TCP) i(\003o) n (ws.) f(This) g(is) h(becau) n(se,) g(as) 2000 4725 y(Eq.) 29 b(\(9\)) g(indicate) n(s,) i(the) e(throu) n(ghpu) n(t) h(of) g(a) f (TCP) i(\003o) n(w) e(is) i(depe) n(ndent) 2000 4825 y(only) 37 b(on) g(the) h(link) g(bandwid) n(th) g(and) g(the) g(num) n (ber) g(of) g(TCP) g(\003o) n(ws.) 2000 4925 y(Note) 26 b(that) h(Fig.) g(5) f(sho) n(ws) h(the) p Fn 27 w(minimum) p Fr 26 w(TCP) g(throug) n(hput,) f(instead) 2000 5024 y(of) i(the) h(a) n(v) o(er) n(age) g(TCP) g(throu) n(ghpu) n(t.) 2083 5131 y(Figure) k(6) h(sho) n(ws) g(that) g(the) f(round) n(-trip) g (time) h(of) g(TCP) g(\003o) n(ws) h(in-) 2000 5231 y(creases) 22 b(almost) f(linearly) g(as) h(the) g(num) n(ber) g(of) f(VPN) h(node) n (s) h(increases.) 2000 5330 y(This) 37 b(is) h(prob) n(ably) f(becau) n (se) h(in) f(our) f(RING-VPN,) h(the) g(roun) n(d-trip) 2000 5430 y(time) c(is) h(the) g(sum) f(of) g(all) h(transmission) e(delays) h(\(see) h(Eq.) e(\(1\).) h(The) p dyy eop end %%Page: 6 6 TeXDict begin 6 5 bop Fm 4055 -99 a(6) p Fr -192 -50 a(\002gure) 40 b(also) i(sho) n(ws) f(that) g(the) g(rou) n(nd-trip) f (time) h(increases) g(as) h(the) -192 49 y(transmission) 28 b(delay) g(between) f(VPN) i(nodes) f(become) n(s) i(lar) o(g) n(er) -5 b(.) -109 149 y(From) 41 b(these) g(observ) n(a) n(tions,) h(we) f (conclud) n(e) h(that) f(the) h(pro) n(posed) -192 249 y(RING-VPN) 20 b(sho) n(ws) g(goo) n(d) g(perf) n(ormanc) n(e) h(in) e (terms) h(of) g(the) f(minimum) -192 348 y(TCP) h(thro) n(ughp) n(ut) f (and) f(round) n(-trip) g(time) h(when) f(the) h(numb) n(er) g(of) f (nodes) -192 448 y(participa) n(ting) 29 b(in) f(the) h(VPN) g(is) g (relati) n(v) o(ely) f(small.) 540 607 y(I) t(V) -7 b(.) 46 b(C) p Fo 4 w(O) t(N) t(C) t(L) t(U) t(S) t(I) t(O) t(N) p Fr -109 735 a(In) 63 b(this) h(pap) n(er) m(,) f(we) h(ha) n(v) o(e) e (prop) n(osed) h(a) h(ring-) n(based) f(VPN) -192 834 y(called) 34 b(RING-VPN,) f(which) g(b) n(uilds) h(VPNs) h(by) e (logically) g(and) g(au-) -192 934 y(tonom) n(ously) k(conn) n(ecting) g (VPN) g(nodes) g(in) g(a) g(ring) g(topo) n(logy) -5 b(.) 36 b(Our) -192 1034 y(RING-VPN) 49 b(can) f(b) n(uild) g(a) h(lar) o(ge) f(numb) n(er) h(of) f(VPNs) i(o) o(v) m(er) f(the) -192 1133 y(e) o(xisting) 39 b(netw) o(or) n(k) h(by) e(reducin) n(g) i(the) f(requir) n(ed) h(cost) f(to) h(maintain) -192 1233 y(IPsec) g(tunne) n (ls.) h(Since) e(each) g(node) g(oper) n(ates) i(auton) n(omou) n(sly) -5 b(,) 39 b(our) -192 1332 y(RING-VPN) f(can) f(realize) g(highly) f (reliable) h(commu) n(nication) g(e) n(v) o(en) -192 1432 y(in) 25 b(case) h(of) f(netw) o(ork) f(f) o(ailures.) h(W) -7 b(e) 26 b(ha) n(v) o(e) e(mathematically) g(analyzed) -192 1532 y(the) 40 b(perfor) n(mance) g(of) g(the) g(RING-VPN.) h(In) f (particula) n(r) m(,) h(we) f(ha) n(v) o(e) -192 1631 y(mode) n(led) 30 b(the) g(RING-VPN) g(and) f(ha) n(v) o(e) g(deri) n (v) o(e) n(d) h(VPN) h(constru) n(ction) -192 1731 y(time,) 53 b(VPN) g(reco) o(v) m(ery) f(time,) g(and) g(the) h(minimu) n(m) g (throu) n(ghpu) n(t,) -192 1831 y(roun) n(d-trip) 26 b(time) i(and) e(pack) o(et) h(loss) h(prob) n(ability) f(of) g(TCP) h (\003o) n(ws.) g(W) -7 b(e) -192 1930 y(ha) n(v) o(e) 28 b(also) h(quan) n(titati) n(v) o(ely) f(demon) n(strated) h(the) f(ef) n (fecti) n(v) o(e) n(ness) h(of) g(the) -192 2030 y(RING-VPN) g(thro) n (ugh) f(se) n(v) o(eral) g(num) n(erical) h(e) o(xam) n(ples.) -109 2130 y(Our) e(future) g(w) o(orks) g(include) g(e) n(v) n(alu) n(ation) h(of) f(the) h(ef) n(fecti) n(v) m(eness) g(of) -192 2229 y(adv) n(an) n(ced) 42 b(commu) n(nication) f(contro) n(l) i (mecha) n(nisms) g(using) e(ad-ho) n(c) -192 2329 y(tunne) n(ls) c(and) d(assessment) i(of) f(the) g(impact) g(of) g(VPN) h(nod) n(e) g(f) o (ailures) -192 2429 y(on,) g(for) h(instance,) f(VPN) i(constru) n (ction) f(time) g(and) g(VPN) g(reco) o(v) m(ery) -192 2528 y(time.) 622 2687 y(R) p Fo 4 w(E) t(F) t(E) t(R) t(E) t(N) t(C) t (E) t(S) -159 2812 y([1]) 42 b(M.) 20 b(Carug) r(i) h(and) g(D.) f (McDysan,) i(\223Servic) r(e) f(require) r(ments) g(for) g(laye) r(r) f (3) h(pro) o(vid) r(er) -40 2887 y(pro) o(visi) r(oned) e(virtua) r(l) f (pri) n(v) n(a) r(te) h(ne) g(tw) o(orks) g(\(PPVPNs\),) -5 b(\224) p Fa 18 w(Request) 19 b(for) g(Comments) -40 2962 y(\(RFC\)) k(4031) p Fo(,) h(Apr) l(.) f(2005.) -159 3037 y([2]) 42 b(B.) 22 b(Gleeson) p Fa 24 w(et) g(al.) p Fo(,) g(\223) -5 b(A) 22 b(frame) n(w) o(o) r(rk) g(for) g(IP) g(based) i(virtual) g(pri) n(v) n(a) r(te) f(netw) o(o) r(rks,) -5 b(\224) p Fa -40 3111 a(Request) 25 b(for) e(Commen) r(ts) g(\(RFC\)) g (2764) p Fo(,) h(Feb) m(.) g(2000.) -159 3186 y([3]) 42 b(A.) 34 b(Nagaraj) r(an,) g(\223Gene) r(ric) h(require) r(ment) g(for) f(pro) o(vide) r(r) g(pro) o(visi) r(oned) h(virtua) r(l) -40 3261 y(pri) n(v) n(a) r(te) 28 b(netw) o(o) r(rks) f(\(PPVPN\),) -5 b(\224) p Fa 27 w(Request) 28 b(for) f(Comment) r(s) g(\(RFC\)) f(3809) p Fo(,) h(June) -40 3336 y(2004.) -159 3411 y([4]) 42 b(R.) 17 b(Call) r(on) g(and) h(M.) f(Suzuki) r(,) f(\223) -5 b(A) 18 b(frame) n(w) o(ork) h(for) e(laye) r(r) g(3) g(pro) o(vi) r (der) h(pro) o(visione) r(d) -40 3485 y(virtu) r(al) 23 b(pric) r(ate) h(netw) o(or) r(ks) e(PPVPNs,) -5 b(\224) p Fa 23 w(Request) 24 b(for) f(Comment) r(s) f(\(RFC\)) h(4110) p Fo(,) -40 3560 y(July) h(2005.) -159 3635 y([5]) 42 b(E.) 24 b(Rosen) i(and) f(Y) -9 b(.) 25 b(Rekhte) r(r) m(,) g(\223BGP/MPLS) g (VPNs,) -5 b(\224) p Fa 25 w(Request) 26 b(for) f(Comments) -40 3710 y(\(RFC\)) e(2547) p Fo(,) h(Mar) l(.) g(1999.) -159 3785 y([6]) 42 b(S.) 25 b(K) n(ent) h(and) g(R.) f(Atkinson) r(,) f (\223Sec) r(urity) i(archi) r(tect) r(ure) g(for) f(the) h(Inte) r (rnet) g(proto-) -40 3859 y(col,) -5 b(\224) p Fa 25 w(Request) 25 b(for) e(Comment) r(s) g(\(RFC\)) g(2401) p Fo(,) h(No) o(v) l(.) e(1998.) -159 3934 y([7]) 42 b(S.) 29 b(K) n(ent) i(and) f(K.) f(Seo,) h(\223Securi) r(ty) g(archi) r(tect) r (ure) g(for) g(the) g(inte) r(rnet) g(proto) r(col,) -5 b(\224) p Fa -40 4009 a(Request) 25 b(for) e(Commen) r(ts) g(\(RFC\)) g (4301) p Fo(,) h(Dec.) g(2005.) -159 4084 y([8]) 42 b(\223Dyna) r(mic) 60 b(VPN) g(control) r(ler) h(\(D) m(VC\)) f(demonst) r(rator) h (projec) r(t) f(report) r(,) -5 b(\224) -40 4159 y(http) r(://www-) t (mic) r(e.cs.ucl.ac.uk/) r(multimed) r(ia/mee) r(tings/vp) r(nw) o (orkshop/) -40 4233 y(documen) r(tat\045i) r(on/proc) r(eedin) r (gs/2003-) t(11) r(-) t(12/VPN-) t(KMS-) t(Issue) r(s.doc,) 62 b(Oct.) -40 4308 y(2003.) -159 4383 y([9]) 42 b(A.) 21 b(Gomez,) h(G.) f(Marti) r(nez,) h(and) g(O.) f(Cano) o(vas,) g(\223Ne) n(w) i(securit) r(y) f(service) r(s) f(based) -40 4458 y(on) g(PKI,) -5 b(\224) p Fa 20 w(Futur) n(e) 21 b(Gener) o(ati) r(on) f(Comput) r(er) g(Systems) p Fo(,) h(v) o(ol.) f(19,) g(no.) g(2,) g (pp.) g(251\226) -40 4532 y(262,) k(Jan.) f(2003.) -192 4607 y([10]) 42 b(J.) 19 b(T) -5 b(ouch,) 18 b(\223Dyna) r(mic) h(inte) r(rnet) h(o) o(v) o(erl) r(ay) f(depl) r(o) o(yment) h(and) g(manageme) r(nt) f(using) -40 4682 y(the) 33 b(X-Bone,) -5 b(\224) p Fa 33 w(Compute) r(r) 31 b(Netw) r(orks) p Fo(,) g(v) o(ol.) h(36,) f (no.) h(2,) f(pp.) h(117\226135,) g(July) -40 4757 y(2001.) -192 4832 y([11]) 42 b(J.) 16 b(T) -5 b(ouch,) 16 b(Y) -9 b(.) 16 b(W) -5 b(ang,) 16 b(V) -9 b(.) 16 b(Pingali) r(,) f(L.) g (Eggert) r(,) g(R.) h(Zhou,) g(and) h(G.) e(Finn,) i(\223) -5 b(A) 16 b(globa) r(l) -40 4906 y(X-Bone) 29 b(for) e(netw) o(o) r(rk) g (e) o(xpe) r(riments,) -5 b(\224) 29 b(in) p Fa 27 w(Pr) m(oceed) r (ing) f(in) g(IEEE) e(T) l(ridentc) r(om) -40 4981 y(2005) p Fo(,) e(Mar) l(.) g(2005,) f(pp.) h(194\226203.) -192 5056 y([12]) 42 b(M.) 31 b(Er) o(gen,) g(D.) f(Lee,) h(R.) g(Atti) r (as,) g(S.) f(T) n(ripakis,) i(A.) e(Puri,) i(R.) e(Sengup) r(ta,) h (and) -40 5131 y(P) -7 b(.) 40 b(V) -7 b(araiya) r(,) 40 b(\223W) m(ire) r(less) h(tok) o(e) r(n) g(ring) g(proto) r(col,) -5 b(\224) 42 b(in) p Fa 41 w(Pr) m(oceed) r(ings) f(of) h(SCI) -40 5206 y(\(Syste) r(ms,) 22 b(Cybe) r(rnetic) r(s) h(and) h(Informati) r (cs\)) p Fo(,) f(v) o(ol.) g(4,) g(July) h(2002.) -192 5280 y([13]) 42 b(R.) 23 b(Jain,) h(\223Performa) r(nce) g(anal) r (ysis) f(of) g(FDDI) h(tok) o(en) h(ring) f(netw) o(ork) r(s:) f(Ef) n (fect) i(of) -40 5355 y(parame) r(ters) c(and) f(guid) r(eline) r(s) f (for) i(setti) r(ng) f(TTR) l(T,) -5 b(\224) p Fa 20 w(IEEE) 18 b(Light) r(wave) j(T) -6 b(elec) r(om-) -40 5430 y(munica) r(tion) 24 b(Syste) r(ms) p Fo(,) e(v) o(ol.) i(20,) f (no.) g(2,) g(pp.) h(16\22622,) g(May) g(1991.) 2000 -50 y([14]) 42 b(J.) 29 b(Postel) r(,) g(\223Inte) r(rnet) i(control) h (message) f(protocol) r(,) -5 b(\224) p Fa 30 w(Request) 31 b(for) g(Comments) 2152 24 y(\(RFC\)) 23 b(792) p Fo(,) g(Sept.) h (1981.) 2000 99 y([15]) 42 b(H.) 21 b(Ohsaki,) i(J.) e(Ujiie) r(,) g (and) i(M.) e(Imase,) h(\223On) h(scala) r(ble) g(modeling) g(of) f (TCP) g(con-) 2152 174 y(gestio) r(n) f(contro) r(l) g(mecha) r(nism) g (for) h(lar) o(ge-sc) r(ale) g(IP) g(netw) o(ork) r(s,) -5 b(\224) 21 b(in) p Fa 22 w(Pr) m(oceedi) r(ngs) 2152 249 y(of) j(IEEE) e(SAINT) h(2005) p Fo(,) h(Feb) m(.) g(2005,) g(pp.) f (361\226369.) 2000 323 y([16]) 42 b(Opnet) 25 b(T) -5 b(echnol) r(ogies,) 24 b(Inc.,) f(\223OPNET,) -5 b(\224) 23 b(http:) r(//www) l(.opnet.c) r(om/.) p dyy eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF