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g(smaller) g(numbe) n(r) h(of) 523 4924 y(VPNs) f(can) f(be) g(b) n(uilt.) p dyy eop end %%Page: 2 2 TeXDict begin 2 1 bop Fx 648 448 a(Se) n(v) o(er) n(al) 22 b(systems) f(to) g(b) n(uild) f(an) h(o) o(v) o(er) n(lay) g(netw) o (ork) f(o) o(v) o(e) n(r) h(an) g(e) o(xisting) f(IP) h(netw) o(ork) f (ha) n(v) o(e) g(been) 523 548 y(prop) n(osed) 28 b([8-1) n(0,) g(10].) f(Such) h(systems) g(include) f(the) h(D) m(VC) h(\(Dyn) n(amic) f(VPN) h(Contro) n(ller\)) f([8],) 523 648 y(which) j(dyn) n(amically) g (establishes) h(and) f(termina) n(tes) i(IPsec) e(tunnels) g(between) g (nod) n(es) h(to) g(b) n(uild) 523 747 y(secure) f(and) f(reliable) h (VPNs.) h(Ho) n(we) n(v) o(e) n(r) m(,) f(the) g(D) m(VC) h(needs) f (to) g(use) h(a) f(full-mesh) f(topolog) n(y) h(to) 523 847 y(establish) 23 b(IPsec) g(tunn) n(els.) h(So,) e(it) i(can) e (only) g(b) n(uild) g(a) h(relati) n(v) o(ely) f(small) h(num) n(ber) g (of) f(VPNs,) h(since) 523 946 y(the) e(numb) n(er) g(of) g(requir) n (ed) g(IPsec) 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n(aluate) f (the) 523 3690 y(impact) 29 b(of) g(the) g(num) n(ber) g(of) g (particip) n(ating) g(node) n(s) h(in) g(a) f(VPN) h(as) g(well) f(as) h (the) f(impact) g(of) g(link) 523 3790 y(band) n(width) c(and) g(prop) n (agation) f(delay) h(on) g(the) g(perf) n(ormanc) n(e) h(of) f (RING-VPN) g(\(e.g.,) g(VPN) g(con-) 523 3890 y(struction) 15 b(time,) g(VPN) h(reco) o(v) m(ery) f(time,) h(and) f(minimu) n(m) h (TCP) g(throu) n(ghpu) n(t\).) g(W) -7 b(e) 17 b(demo) n(nstrate) e (the) 523 3989 y(prop) n(osed) i(RING-VPN) g(sho) n(ws) g(good) f (perfo) n(rmance) g(in) h(terms) g(of) g(se) n(v) o(eral) f(perfor) n (mance) h(metrics) 523 4089 y(includin) n(g) 25 b(VPN) h(constru) n (ction) f(time) g(and) f(minimum) g(TCP) h(throug) n(hput) f(when) h (the) g(num) n(ber) g(of) 523 4189 y(node) n(s) c(participating) e(in) h (the) g(VPN) h(is) g(relati) n(v) o(ely) e(small.) 648 4327 y(The) 31 b(structur) n(e) h(of) g(this) g(paper) e(is) j(as) f (follo) n(ws.) f(First,) h(Section) f(2) h(e) 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(packet) SH GR GR % POLY/OPEN-SPLINE 0 SG GS NP 590 260 M 680 290 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 580 400 M 590 430 L TGSM 1 W S GR GR tgifsavedpage restore end showpage %%Trailer %MatchingCreationDate: Thu Nov 9 20:45:37 2006 %%DocumentFonts: Helvetica %%EOF %%EndDocument @endspecial Fs 1418 1704 a(Fig.) 11 b(1:) 19 b(Ov) o(ervie) n(w) h(of) e (our) i(RING-VPN.) p Fx 523 2117 a(sented) i(for) g(v) n(alidatin) n(g) h(our) e(appro) n(ximate) h(analysis.) g(Finally) -5 b(,) 22 b(Section) f(4) i(conclu) n(des) g(this) g(pap) n(er) 523 2216 y(and) d(discusses) g(future) f(w) o(orks.) p Fm 523 2586 a(2) 99 b(RING-VPN) 24 b(\(Ring-based) i(V) l(irtual) f(Pri) o (v) o(ate) g(Netw) o(ork\)) p Fx 523 2890 a(In) d(this) h(section,) f (we) h(e) o(xp) n(lain) g(our) e(propo) n(sed) i(RING-VPN.) f(The) g(k) o(e) o(y) g(of) g(our) f(RING-VPN) i(is) g(to) 523 2990 y(logically) 18 b(conn) n(ect) h(node) n(s) h(in) f(a) g(ring) e (topolog) n(y) i(for) f(minimizin) n(g) h(the) f(require) n(d) h(numb) n (er) g(of) f(IPsec) 523 3089 y(tunnels.) d(In) g(our) g(prop) n(osed) h (RING-VPN,) f(di) p Fw(\013) p Fx(eren) n(t) i(from) d(other) h(VPN) h (technolo) n(gies) g(with) g(a) g(cen-) 523 3189 y(tral) 21 b(manag) n(ement) g(system) g(such) f(as) i(repre) n(sented) f(by) f (MPLS-VPN,) h(each) g(nod) n(e) g(autono) n(mously) 523 3289 y(\002nds) d(nodes) g(particip) n(ating) g(in) g(a) h(VPN,) g(con) n(nects) g(to) f(the) g(VPN,) h(and) f(then) f(disconn) n(ects) i(from) e(the) 523 3388 y(VPN.) j(Because) f(of) h(this) f(autono) n(my) h(of) f (each) g(nod) n(e,) h(reliable) f(comm) n(unication) n(s) i(can) e(be) g (realized) 523 3488 y(e) n(v) o(en) d(in) h(cases) h(of) f(f) o (ailures) g(such) g(as) h(netw) o(or) n(k) g(de) n(v) n(ices) g(f) o (ailures) f(and) g(rou) n(ting) g(error) n(s.) h(In) f(addition) n(,) 523 3587 y(IPsec) h(tunn) n(els) g(are) f(established) g(between) f (adjacent) h(nod) n(es) h(to) g(realize) f(secure) f(commu) n (nications.) 648 3708 y(Let) 27 b(us) g(de\002ne) g(that) g(the) g (forw) o(ard) f(direction) g(is) i(coun) n(terclockwise) f(in) g(Fig.) g (1.) g(Each) g(VPN) 523 3808 y(node) e(establishes) i(an) f(IPsec) h (tunnel) f(to) g(a) h(do) n(wnstre) n(am) g(VPN) g(nod) n(e,) g(and) f (the) g(IPsec) h(tunnel) f(is) 523 3907 y(used) 18 b(only) g(for) g (unid) n(irectional) g(transmission) f(from) h(an) g(upstream) f(VPN) i (node) f(to) g(a) h(do) n(wnstre) n(am) 523 4007 y(one.) 25 b(Commu) n(nication) g(between) f(VPN) i(nodes) f(is) h(done) f(via) g (VPN) h(nod) n(es) h(along) d(the) h(ring.) g(F) o(or) 523 4106 y(e) o(xamp) n(le,) 19 b(a) g(pack) m(et) h(transfe) n(rred) e (from) g(VPN) h(nod) n(e) g(1) f(to) h(VPN) g(node) e(4) i(passes) g (VPN) g(node) f(2) g(and) 523 4206 y(3) 23 b(in) f(order) f(and) h (\002nally) h(arri) n(v) m(es) g(at) g(VPN) g(node) f(4.) g(It) h(is) g (anticipated) f(that) g(pack) o(ets) g(ha) n(v) o(e) g(to) h(pass) 523 4306 y(a) f(lar) o(g) n(e) g(num) n(ber) f(of) g(nod) n(es) h(in) g (this) f(type) g(of) g(ring-) n(based) g(netw) o(ork) n(.) h(Ther) n (efore,) e(commu) n(nication) 523 4405 y(delay) e(tends) h(to) f(be) h (lar) o(ge) f(and,) g(as) h(a) g(result,) f(TCP) i(throu) n(ghpu) n(t) g (w) o(ould) e(be) g(de) o(gr) n(aded) g([12,) g(13].) g(As) 523 4505 y(we) g(will) g(sho) n(w) f(in) h(Section) f(3,) h(ho) n(w) n(e) n (v) o(er) m(,) f(RING-VPN) g(achie) n(v) o(e) n(s) i(goo) n(d) f(perfo) n(rmance) e(for) h(dozens) 523 4605 y(of) j(users,) g(which) g(is) h (the) f(main) g(tar) o(g) n(et) h(of) f(RING-VPN.) 648 4725 y(In) h(what) h(follo) n(ws,) f(we) i(will) g(e) o(xp) n(lain) f (essential) h(fun) n(ctions) f(of) g(the) g(RING-VPN,) g(i.e.) g(contr) n(ol) 523 4825 y(of) d(commu) n(nication) g(between) f(VPN) i(nodes,) f (contr) n(ol) h(of) f(VPN) h(nod) n(e) g(conne) n(ction) f(to) h(VPNs,) g(and) 523 4924 y(contro) n(l) h(of) f(VPN) h(nod) n(e) g(disconn) n (ection) f(from) f(VPNs.) p dyy eop end %%Page: 4 4 TeXDict begin 4 3 bop Fk 523 448 a(2.1) 82 b(Communication) 20 b(Contr) o(o) n(l) h(between) f(VPN) g(Nodes) p Fx 523 613 a(In) g(our) f(RING-VPN,) i(a) f(VPN) h(node) e(transfers) h(a) g (pack) o(et) g(to) g(a) h(do) n(wnstre) n(am) g(VPN) f(node) g(thro) n (ugh) 523 713 y(an) c(IPsec) h(tunnel) f(using) f(the) i(tunn) n(eling) f(mode) g([6].) f(The) h(destination) g(IP) g(address) g(of) g(the) h (encap) n(su-) 523 812 y(lated) j(pack) m(et) h(is) f(al) o(w) o(ays) g (set) h(to) f(be) f(the) h(IP) g(addre) n(ss) h(of) f(the) f(do) n (wnstream) f(VPN) j(nod) n(e,) f(re) o(ga) n(rdless) 523 912 y(of) g(the) g(destination) f(VPN) i(node) e(of) h(the) g(pack) o (et) g(befor) n(e) h(encap) n(sulation.) 648 1011 y(Upon) d(the) i (arri) n(v) l(al) g(of) f(the) h(encapsu) n(lated) g(pack) o(et) f (from) f(the) i(upstrea) n(m) g(VPN) g(node,) e(the) i(VPN) 523 1111 y(node) 29 b(decapsulates) h(the) g(pack) o(et) g(and) g(comp) n (ares) h(the) f(destination) f(IP) i(addr) n(ess) h(of) e(the) g(pack) o (et) 523 1211 y(befor) n(e) 22 b(encap) n(sulation) f(with) g(its) h(o) n(wn) e(IP) i(addr) n(ess.) g(If) f(the) g(IP) g(addre) n(ss) i(matche) n(s,) f(the) f(VPN) h(nod) n(e) 523 1310 y(recei) n(v) o(e) n(s) k(it.) f(If) g(it) g(does) g(not) f(match,) g(the) h(VPN) g(nod) n(e) h(comp) n (ares) f(the) g(source) f(IP) h(addr) n(ess) h(of) e(the) 523 1410 y(pack) o(et) g(befo) n(re) h(encap) n(sulation) f(with) h(its) g (o) n(wn) f(IP) g(address,) g(and) g(if) g(it) i(match) n(es,) f(the) g (VPN) g(nod) n(e) 523 1510 y(discards) 30 b(the) g(encapsu) n(lated) h (pack) m(et.) g(The) f(VPN) h(nod) n(e) g(check) n(s) g(if) g(the) f (source) f(IP) i(addre) n(ss) h(of) 523 1609 y(the) 21 b(pack) o(et) g(matches) g(its) h(o) n(wn) f(IP) h(add) n(ress.) g(It) g (is) g(becau) n(se) g(the) g(encap) n(sulated) f(pack) o(et) g(will) h (come) 523 1709 y(back) e(after) h(circulating) f(the) h(ring-) n(netw) o(ork,) f(i.e.,) h(there) g(migh) n(t) h(e) o(xist) f(no) g(VPN) h(nod) n(e) g(designa) n(ted) 523 1808 y(to) 16 b(recei) n(v) 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g(already) e(participatin) n(g) i(in) f(the) g(VPN) h(and) 523 2818 y(the) 24 b(infor) n(mation) f(of) h (the) g(ring) f(con\002gu) n(ration) g(from) g(the) h(VPN) g(manager) -7 b(.) 25 b(The) e(ne) n(w) h(VPN) h(nod) n(e) 523 2918 y(then) i(measure) n(s) i(a) n(v) o(era) n(ge) f(rou) n(nd-trip) e (time) i(to) f(each) g(VPN) h(node) e(in) i(VPN) g(using) e(ICMP) i (Echo) 523 3018 y(message) 20 b([14]) n(.) 648 3117 y(Based) g(on) g (the) g(measured) f(roun) n(d-trip) g(time,) h(the) g(ne) n(w) g(VPN) h (node) e(determin) n(es) i(the) f(position) 523 3217 y(in) 32 b(the) f(ring) g(to) h(which) f(it) i(shou) n(ld) f(conne) n (ct.) g(In) g(particu) n(lar) m(,) f(for) g(each) h(adjacen) n(t) g (node) f(pair) g(in) 523 3317 y(the) 23 b(ring,) f(the) h(ne) n(w) g (VPN) h(nod) n(e) g(measures) f(the) g(rou) n(nd-trip) f(time) h(to) g (each) g(of) g(the) g(upstream) f(and) 523 3416 y(do) n(wn) n(stream) j (VPN) h(nod) n(es) g(of) f(the) g(pair) f(and,) g(by) h(summin) n(g) g (up) g(the) 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g(the) h(ring) f(when) h(the) g(comm) n(uni-) 523 4426 y(cation) c(between) g(VPN) h(nod) n(es) h(termin) n(ated) f (for) f(some) g(reason.) g(Belo) n(w) g(is) i(the) e(control) g(mecha) n (nism) 523 4526 y(of) 20 b(the) g(VPN) h(nod) n(e) g(disconn) n (ection,) f(dur) n(ing) g(the) h(re-estab) n(lishment) f(of) g(the) g (ring.) 648 4625 y(A) 27 b(VPN) g(manag) n(ement) f(pack) o(et) g (circulates) g(throug) n(h) h(VPN) g(node) n(s) h(along) d(the) i (ring.) f(In) g(this) 523 4725 y(manag) n(ement) j(pack) o(et,) g(the) h (list) h(of) e(the) h(VPN) g(nod) n(es) h(and) e(the) g(inform) n (ation) h(of) f(the) g(ring) g(con-) 523 4825 y(\002guratio) n(n) f (are) f(record) n(ed.) h(Each) f(VPN) h(nod) n(e) g(return) n(s) h(the) e(ackno) l(wledgmen) n(t) h(to) g(its) h(upstre) n(am) 523 4924 y(VPN) 20 b(nod) n(e) g(e) n(v) o(e) n(ry) f(time) g(the) g(VPN) h (nod) n(e) g(recei) n(v) o(e) n(s) g(this) g(man) n(agement) e(pack) o (et.) g(Each) h(VPN) h(nod) n(e) p dyy eop end %%Page: 5 5 TeXDict begin 5 4 bop Fx 523 448 a(judges) 24 b(that) i(its) g(do) n (wn) n(stream) f(VPN) h(nod) n(e) g(is) g(not) e(operation) n(al) i(if) f(it) h(does) f(not) f(recei) n(v) o(e) g(an) o(y) h(ac-) 523 548 y(kno) n(w) n(ledgemen) n(t) c(after) f(a) h(certain) e(period) g (of) h(time.) 648 648 y(An) o(y) j(VPN) i(node) f(that) g(detects) h(a) g(non) n(-oper) n(ational) f(do) n(wnstrea) n(m) h(VPN) g(node) e (noti\002es) i(this) 523 747 y(to) i(the) g(fur) n(ther) g(do) n(wn) n (stream) g(VPN) g(nod) n(e) h(con) n(necting) e(to) h(the) g(non) n (-oper) n(ational) g(nod) n(e.) g(It) g(then) 523 847 y(establishes) f(a) f(ne) n(w) g(IPsec) h(tunne) n(l) g(to) g(this) g (fur) n(ther) f(do) n(wnstrea) n(m) h(VPN) g(nod) n(e.) g(In) f (additio) n(n,) g(the) 523 946 y(IPsec) g(tunnels) g(between) f(the) h (VPN) g(node) f(and) h(the) g(non) n(-opera) n(tional) g(one) f(as) i (well) g(as) f(between) 523 1046 y(the) e(furth) n(er) g(do) n(wn) n (stream) g(VPN) g(node) f(and) g(the) h(non-) n(operatio) n(nal) g(one) f(are) h(terminate) n(d.) g(Lastly) -5 b(,) 523 1146 y(the) 26 b(VPN) h(node,) e(which) h(detected) g(the) g(non-) n (operation) n(al) h(nod) n(e,) g(upda) n(tes) h(the) e(list) h(of) f (the) h(VPN) 523 1245 y(node) n(s) 18 b(and) f(the) g(info) n(rmation) f (of) h(the) g(ring) f(con\002gu) n(ration) g(recorde) n(d) h(in) h(the) f(mana) n(gement) f(pack) o(et.) 523 1345 y(Then,) j(it) i(transmits) f (this) h(pack) o(et) f(to) g(do) n(wn) n(stream) g(VPN) h(nodes.) p Fm 523 1585 a(3) 99 b(Analysis) p Fx 523 1758 a(In) 27 b(this) g(section,) g(we) g(\002rst) h(mod) n(el) g(the) f(RING-VPN) g (and) f(deri) n(v) o(e) g(its) i(VPN) g(con) n(struction) f(time,) 523 1857 y(VPN) 17 b(reco) o(v) m(ery) f(time,) g(and) f(the) i(minim) n (um) f(throu) n(ghput,) f(roun) n(d-trip) h(time) g(and) g(pack) m(et) h (loss) g(prob) n(-) 523 1957 y(ability) 28 b(of) h(TCP) g(\003o) n(ws.) g(W) -7 b(e) 30 b(then) e(quan) n(titati) n(v) o(ely) g(e) n(v) n (aluate) g(the) h(perf) 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w(N) p Fx 5 w(-th) g(VPN) h(nod) n(e) g(measur) n(es) g(roun) n (d-trip) e(time) i(to) f(each) 523 4184 y(of) p Fl 28 w(N) p Fi 28 w(\000) p Fx 23 w(1) 27 b(VPN) f(nodes) g(that) g(already) g(particip) n(ated) g(in) h(the) f(VPN.) h(It) f(then) g(participate) n (s) i(in) e(and) 523 4283 y(re-b) n(uild) n(s) i(the) g(VPN) g(so) g (that) f(the) g(increase) g(in) h(the) f(roun) n(d-trip) g(time) g (becomes) g(the) g(minimum) n(.) 523 4383 y(Speci\002cally) -5 b(,) 20 b(let) p Fl 22 w(r) p Fx 24 w(and) p Fl 21 w(l) p Fx 22 w(denote) h(the) g(upstream) f(VPN) i(node) f(and) f(the) i(do) n (wn) n(stream) g(VPN) g(nod) n(e) 523 4483 y(for) g(a) h(ne) n(w) f (VPN) h(nod) n(e) p Fl 25 w(N) p Fx 5 w(,) g(respecti) n(v) o(ely) -7 b(.) 22 b(Assuming) g(that) h(the) f(roun) n(d-trip) g(time) g(between) g(VPN) 523 4582 y(node) p Fl 30 w(i) p Fx 32 w(and) 31 b(VPN) g(node) p Fl 42 w(j) p Fx 33 w(can) g(be) g(app) n(roximated) f (by) h(2) p Fl 14 w(d) p Fg 2337 4594 a(i) p Fh(;) p Fg 9 w(j) p Fx 2429 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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 FF [24 0 0 -24 0 0] MS (VPN node ) TGSW AD /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (i) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [24 0 0 -24 0 0] MS (VPN node ) SH 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (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 FF [24 0 0 -24 0 0] MS (VPN node ) TGSW AD /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (j) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [24 0 0 -24 0 0] MS (VPN node ) SH 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (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 FF [24 0 0 -24 0 0] MS (VPN node 1) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica 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 FF [24 0 0 -24 0 0] MS (VPN node ) TGSW AD /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (N) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [24 0 0 -24 0 0] MS (VPN node ) SH 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (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 FF [24 0 0 -24 0 0] MS (link bandwidth) 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 FF [24 0 0 -24 0 0] MS (link propagation delay) SH GR GR % TEXT NP 0 SG GS 1 W 530 260 M GS GS 0 /Helvetica FF [24 0 0 -24 0 0] MS (IPsec tunnel) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica 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 631 681 M GS 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (=2) SH GR GR % TEXT NP 0 SG GS 1 W 721 86 M GS 0 SG /Times-Italic FF [24 0 0 -24 0 0] MS (=1) SH GR GR % TEXT NP 0 SG GS 1 W 280 680 M GS 0 SG /Helvetica FF [24 0 0 -24 0 0] MS (number of TCP flows) 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 % TEXT NP 0 SG GS 1 W 520 680 M GS 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (f) SH GR GR % TEXT NP 0 SG GS 1 W 530 684 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (i,j) SH GR GR % TEXT NP 0 SG GS 1 W 602 679 M GS 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (f) SH GR GR % TEXT NP 0 SG GS 1 W 612 683 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (i,j) SH GR GR % TEXT NP 0 SG GS 1 W 416 378 M GS 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (d) SH GR GR % TEXT NP 0 SG GS 1 W 430 384 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (i,j) SH GR GR % TEXT NP 0 SG GS 1 W 547 438 M GS 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (b) SH GR GR % TEXT NP 0 SG GS 1 W 560 443 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (i,j) SH GR GR % TEXT NP 0 SG GS 1 W 681 85 M GS 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (f) SH GR GR % TEXT NP 0 SG GS 1 W 691 89 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (i,N) SH GR GR % TEXT NP 0 SG GS 1 W 356 55 M GS 0 SG /Times-Italic FF [24 0 0 -24 0 0] MS (=1) SH GR GR % TEXT NP 0 SG GS 1 W 316 54 M GS 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (f) SH GR GR % TEXT NP 0 SG GS 1 W 326 58 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (N,1) SH GR GR % POLY/OPEN-SPLINE 0 SG GS GS NP 11 93 M 0 -10 atan DU cos 12.000 MU exch sin 12.000 MU RM 1 93 L TGSM 3 W 1 SG S 1 W GR NP 11 93 M 0 -10 atan DU cos 12.000 MU exch sin 12.000 MU RM 1 93 L TGSM 3 W FLAT pat12 8 -8 80 24 24 TGPF 1 W GR GS TGSM NP 11 93 12.000 5.000 10 0 TGAT 1 SG CP F 0 SG NP 11 93 12.000 5.000 10 0 TGAT CP EC NP pat12 8 -8 80 24 24 TGPF GR % TEXT NP 0 SG GS 1 W 57 88 M GS 0 SG /Times-Italic FF [24 0 0 -24 0 0] MS (=1) SH GR GR % TEXT NP 0 SG GS 1 W 17 87 M GS 0 SG /Helvetica-Oblique FF [24 0 0 -24 0 0] MS (f) SH GR GR % TEXT NP 0 SG GS 1 W 27 91 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (N,i) SH GR GR GR tgifsavedpage restore end showpage %%Trailer %MatchingCreationDate: Thu Nov 9 21:01:46 2006 %%DocumentFonts: Times-Italic %%+ Helvetica-Oblique %%+ Helvetica %%EOF %%EndDocument @endspecial Fs 1619 2291 a(Fig.) 12 b(2:) 19 b(Analytic) g(model.) p Fx 648 2660 a(On) k(\002nding) f(the) i(nod) n(es) g(to) g(be) f(conn) n (ected,) g(VPN) h(node) p Fl 25 w(N) p Fx 29 w(re-b) n(u) n(ilds) g (the) g(VPN) g(as) g(follo) n(ws:) 523 2760 y(\(a\)) d(establish) h(an) f(IPsec) h(tunne) n(l) g(to) g(VPN) g(node) p Fl 20 w(r) p Fx 2 w(;) h(\(b\)) d(establish) i(anoth) n(er) g(IPsec) g(tunn) n(el) g (to) g(VPN) 523 2860 y(node) p Fl 15 w(l) p Fx(;) 17 b(and) e(\(c\)) g(terminate) g(the) h(IPsec) h(tunn) n(el) g(between) e (VPN) h(node) p Fl 15 w(l) p Fx 16 w(and) g(VPN) g(node) p Fl 15 w(r) p Fx 2 w(.) g(Assume) 523 2959 y(that) k(the) f(roun) n (d-trip) g(time) g(between) g(VPN) h(nodes) f(participa) n(ted) h(in) g (the) f(VPN) h(is) h(kno) l(wn) f(\(i.e.,) e(the) 523 3059 y(roun) n(d-trip) 26 b(time) h(w) o(as) g(already) f(measur) n(ed) h(and) f(does) g(not) h(chan) n(ge) g(with) g(time\).) f(T) -7 b(ypically) i(,) 25 b(for) 523 3159 y(creating) c(an) h(IPsec) h(tunne) n(l,) g(six) g(message) f(e) o(xch) n(anges) g(between) g(VPN) g(nodes) g(are) g(requ) n(ired) g([6].) 523 3258 y(After) k(message) g(e) o(xch) n(anges,) g(an) g(encry) n(ption) g(k) o(e) o(y) f(is) i(gener) n (ated.) f(Let) p Fj 26 w(\001) p Fx 27 w(be) g(the) g(time) g(require) n (d) 523 3358 y(for) 20 b(a) g(VPN) h(nod) n(e) g(to) f(generate) f(an) h (encryp) n(tion) g(k) o(e) o(y) -5 b(.) 19 b(Pro) o(vid) n(ed) h(that) g (VPN) h(node) p Fl 21 w(N) p Fx 26 w(e) o(x) o(ecute) n(s) g(the) 523 3457 y(abo) o(v) m(e) h(process) f(\(a\)) h(and) f(\(b\)) g(in) h(this) h(ord) n(er) m(,) e(and) h(\(c\)) f(can) h(be) f(e) o(x) o(ecuted) f (in) i(parallel) g(with) g(\(a\)) f(and) 523 3557 y(\(b\),) p Fl 21 w(X) p Fg 715 3569 a(N) p Fx 783 3557 a(is) g(gi) n(v) o(en) e (by) p Fl 1457 3737 a(X) p Fg 1509 3749 a(N) p Fw 1579 3737 a(=) p Fx 23 w(\(6) p Fl(d) p Fg 1766 3749 a(N) p Fh(;) p Fg(r) p Fw 1867 3737 a(+) p Fj 18 w(\001) p Fx(\)) p Fw 18 w(+) p Fx 18 w(\(6) p Fl 14 w(d) p Fg 2230 3749 a(l) p Fh(;) p Fg -1 w(N) p Fw 2326 3737 a(+) p Fj 18 w(\001) p Fx(\)) p Fw 1579 3861 a(=) p Fx 23 w(6) 14 b(\() p Fl(d) p Fg 1779 3873 a(l) p Fh(;) p Fg 1 w(N) p Fw 1876 3861 a(+) p Fl 18 w(d) p Fg 1990 3873 a(N) p Fh(;) p Fg(r) p Fx 2072 3861 a(\)) p Fw 18 w(+) p Fx 18 w(2) p Fj(\001:) p Fx 1007 w(\(3\)) 523 4041 y(Note) 30 b(that) p Fl 32 w(X) p Fv 923 4053 a(0) p Fw 997 4041 a(=) p Fx 41 w(0) g(since) g(the) f(initial) i(nod) n(e) g(doe) n(s) g (not) f(establish) g(an) o(y) f(IPsec) h(tunne) n(l.) h(Conse-) 523 4141 y(quen) n(tly) -5 b(,) 20 b(the) g(VPN) h(constructio) n(n) f (time) h(is) g(gi) n(v) o(en) e(by) p Fl 1341 4369 a(X) p Fg 1393 4381 a(N) p Fw 1462 4369 a(=) p Ff 1538 4252 a(\() p Fx 1597 4318 a(0) 606 b(if) p Fl 23 w(N) p Fw 28 w(=) p Fx 23 w(0) 1597 4418 y(6) 14 b(\() p Fl(d) p Fg 1721 4430 a(l) p Fh(;) p Fg 1 w(N) p Fw 1818 4418 a(+) p Fl 19 w(d) p Fg 1933 4430 a(N) p Fh(;) p Fg(r) p Fx 2014 4418 a(\)) p Fw 18 w(+) p Fx 19 w(2) p Fj(\001) p Fx 22 w(otherwise) 3308 4369 y(\(4\)) p Fk 523 4661 a(3.3) 82 b(VPN) 20 b(Reco) o(v) o(ery) f(T) o(ime) p Fx 523 4825 a(Ne) o(xt,) 30 b(we) h(deri) n(v) m(e) g(the) g(requ) n(ired) f(time) h (to) g(re-b) l(uild) g(the) f(VPN) i(after) e(the) g(VPN) h(node) p Fl 30 w(i) p Fx 31 w(is) g(dis-) 523 4924 y(conn) n(ected) 22 b(\(VPN) h(reco) o(v) m(ery) e(time\),) p Fl 22 w(Y) p Fg 1674 4936 a(i) p Fx 1695 4924 a(.) h(Suppo) n(se) h(the) f(VPN) h (node) p Fl 21 w(i) p Fx 23 w(is) g(disconn) n(ected) f(from) f(the) p dyy eop end %%Page: 7 7 TeXDict begin 7 6 bop Fx 523 448 a(VPN) 28 b(due) e(to) i(some) f(f) o (ailure) n(.) h(Then,) e(an) h(IPsec) h(tunn) n(el) g(must) f(be) g (established) g(between) f(its) i(up-) 523 548 y(stream) 21 b(VPN) g(nod) n(e) p Fl 21 w(l) p Fx 22 w(\() p Fl(m) p Fg 1268 560 a(l) p Fh(;) p Fg(i) p Fw 1342 548 a(=) p Fx 24 w(1\),) f(and) g(its) i(do) n(wn) n(stream) f(VPN) g(node) p Fl 20 w(r) p Fx 23 w(\() p Fl(m) p Fg 2709 560 a(i) p Fh(;) p Fg(r) p Fw 2791 548 a(=) p Fx 24 w(1\).) f(In) g(particular) -5 b(,) 523 648 y(detection) 26 b(of) i(a) f(VPN) h(node) f(f) o(ailure) g (and) g(establishmen) n(t) h(of) f(a) h(ne) n(w) g(IPsec) f(tunnel,) g (as) h(well) g(as) 523 747 y(terminatio) n(n) 21 b(of) g(no) f(longer) g (requ) n(ired) h(IPsec) g(tunn) n(el,) h(pro) n(ceed) f(as) g(follo) n (ws:) g(\(a\)) f(VPN) i(nod) n(e) p Fl 21 w(l) p Fx 22 w(de-) 523 847 y(tects) g(a) g(f) o(ailure) f(of) g(VPN) h(node) p Fl 20 w(i) p Fx 22 w(by) f(absence) g(of) g(the) h(ackno) l(wledgin) n (g) g(pack) o(et.) f(\(b\)) f(VPN) i(node) p Fl 21 w(l) p Fx 523 946 a(establishes) j(an) f(IPsec) h(tunn) n(el) g(to) g(VPN) g (nod) n(e) p Fl 25 w(r) p Fx 2 w(.) g(\(c\)) f(The) g(IPsec) h(tunn) n (el) g(between) f(VPN) g(node) p Fl 24 w(l) p Fx 523 1046 a(and) 17 b(VPN) i(nod) n(e) p Fl 18 w(i) p Fx 19 w(is) f(terminated) n(.) g(\(d\)) f(The) h(IPsec) g(tunne) n(l) h (between) e(VPN) h(node) p Fl 17 w(i) p Fx 18 w(and) f(VPN) i(nod) n(e) p Fl 523 1146 a(r) p Fx 28 w(is) 26 b(termin) n(ated.) f(In) f(e) p Fw(\013) p Fx(ect,) h(both) f(\(c\)) h(and) f(\(d\)) g(can) h(proce) n (ed) g(in) g(parallel) g(with) g(\(b\).) f(Theref) n(ore,) 523 1245 y(the) c(VPN) h(reco) o(v) m(ery) f(time) g(is) h(gi) n(v) o(en) e (by) p Fl 1598 1401 a(Y) p Fg 1644 1413 a(i) p Fw 1688 1401 a(=) p Fx 23 w(2) p Fl(d) p Fg 1848 1413 a(l) p Fh(;) p Fg -2 w(i) p Fw 1916 1401 a(+) p Fx 18 w(6) p Fl(d) p Fg 2071 1413 a(l) p Fh(;) p Fg(r) p Fw 2148 1401 a(+) p Fx 18 w(2) p Fj(\001:) p Fx 977 w(\(5\)) p Fk 523 1629 a(3.4) 82 b(Minimum) 23 b(Thr) o(oughput,) e(Round-T) -6 b(rip) 23 b(T) o(ime,) f(and) g(P) o(ack) o(et) f(Loss) i(Pr) o(o) n (bability) f(of) 710 1728 y(TCP) f(Flo) o(ws) p Fx 523 1873 a(W) -7 b(e) 32 b(deri) n(v) o(e) e(the) h(minimum) f(throu) n (ghpu) n(t) i(of) f(the) g(TCP) h(\003o) n(w) p Fl 31 w(T) p Fg 2428 1885 a(min) p Fx 2519 1873 a(,) g(which) e(has) i(the) f (minimu) n(m) 523 1972 y(throu) n(ghpu) n(t) 24 b(amon) n(g) g(all) f (TCP) h(\003o) n(ws) f(in) g(the) g(VPN.) h(Hereafter) -5 b(,) 23 b(all) h(TCP) g(\003o) n(ws) f(are) g(assumed) f(to) 523 2072 y(continu) n(ously) e(send) g(data.) g(F) o(or) f(compact) g (notation,) g(we) i(use) p Fl 1697 2228 a(f) p Fg 1720 2240 a(i) p Fh(;) p Fg 9 w(j) p Fe 1803 2228 a(,) p Fl 35 w(f) p Fg 1914 2240 a(i) p Fu(+) p Fg(k) r(N) p Fh(;) p Fg 9 w(j) p Fu(+) p Fg(l) q(N) p Fj 2176 2228 a(;) p Fx 1111 w(\(6\)) 523 2384 y(where) p Fl 20 w(k) p Fx 22 w(and) p Fl 19 w(l) p Fx 21 w(are) f(inte) o(ger) n(s.) h(The) f (numb) n(er) g(of) g(TCP) h(\003o) n(ws,) p Fl 21 w(n) p Fg 2364 2396 a(i) p Fh(;) p Fg 9 w(j) p Fx 2423 2384 a(,) f(passing) g(throu) n(gh) g(VPN) h(nod) n(e) p Fl 21 w(i) p Fx 523 2483 a(and) f(VPN) g(node) p Fl 32 w(j) p Fx 21 w(is) h(gi) n(v) o(en) e(by) p Fl 1569 2715 a(n) p Fg 1611 2727 a(i) p Fh(;) p Fg 9 w(j) p Fw 1693 2715 a(=) p Fg 1770 2613 a(N) p Fd 3 w(\000) p Fv(1) p Ff 1769 2630 a(X) p Fg 1783 2810 a(l) p Fu(=) p Fv(0) p Fg 1894 2613 a(N) p Fd 3 w(\000) p Fg(l) p Fd(\000) p Fv(2) p Ff 1919 2630 a(X) p Fg 1928 2810 a(k) p Fu 1 w(=) p Fv(0) p Fl 2081 2715 a(f) p Fg 2104 2727 a(i) p Fd(\000) p Fg(k) p Fh 1 w(;) p Fg 9 w(j) p Fu(+) p Fg(k) p Fj 2292 2715 a(;) p Fx 995 w(\(7\)) 523 2940 y(where) p Fl 33 w(f) p Fg 783 2952 a(i) p Fh(;) p Fg 9 w(j) p Fx 865 2940 a(is) k(the) e(numb) n(er) h(of) f(TCP) h(\003o) n(ws) g (established) f(between) g(VPN) h(nod) n(e) p Fl 22 w(i) p Fx 23 w(and) e(VPN) j(nod) n(e) p Fl 535 3040 a(j) p Fx(.) 648 3140 y(If) d(the) i(link) e(between) h(VPN) g(node) p Fl 20 w(i) p Fx 22 w(and) g(VPN) g(node) p Fl 32 w(j) p Fx 22 w(is) h(the) f(bottleneck) n(,) h(VPN) f(node) p Fl 20 w(i) p Fx 22 w(and) 523 3239 y(VPN) g(nod) n(e) p Fl 33 w(j) p Fx 21 w(satisfy) 1700 3444 y(min) p Fg 1737 3495 a(i) p Fh(;) p Fg 9 w(j) p Ff 1843 3326 a( ) p Fl 1944 3382 a(b) p Fg 1986 3394 a(i) p Fh(;) p Fg 9 w(j) p 1885 3425 221 5 v Fl 1885 3501 a(n) p Fg 1927 3513 a(i) p Fh(;) p Fg 9 w(j) p Fl 1986 3501 a(m) p Fg 2046 3513 a(i) p Fh(;) p Fg 9 w(j) p Ff 2115 3326 a(!) p Fj 2161 3444 a(:) p Fx 1126 w(\(8\)) 523 3646 y(It) 28 b(should) f(be) g(noted) g(that,) h(since) g(all) g(of) g(links) f(between) g(VPN) i(nod) n(es) g (are) e(unidire) n(ctional,) g(the) 523 3746 y(roun) n(d-trip) 20 b(time) g(of) h(the) f(TCP) h(\003o) n(w) g(from) e(VPN) j(nod) n(e) p Fl 21 w(i) p Fx 21 w(to) f(VPN) g(nod) n(e) p Fl 33 w(j) p Fx(,) p Fl 22 w(R) p Fg 2782 3758 a(i) p Fh(;) p Fg 9 w(j) p Fx 2841 3746 a(,) g(is) g(a) g(constant.) f(In) 523 3845 y(other) f(w) o(ords,) p Fl 1799 4001 a(R) p Fg 1850 4013 a(i) p Fh(;) p Fg 9 w(j) p Fw 1933 4001 a(=) p Fl 23 w(R) p Fg 2061 4013 a(N) p Fj 2108 4001 a(:) p Fx 1179 w(\(9\)) 523 4157 y(Theref) n(ore,) p Fl 20 w(T) p Fg 941 4169 a(min) p Fx 1053 4157 a(is) j(gi) n(v) o(e) n(n) f(by) p Fl 1701 4358 a(T) p Fg 1751 4370 a(min) p Fw 1866 4358 a(=) p Fx 23 w(min) p Fg 1978 4409 a(i) p Fh(;) p Fg 9 w(j) p Fl 2095 4295 a(b) p Fg 2137 4307 a(i) p Fh(;) p Fg 9 w(j) p 2095 4339 102 5 v Fl 2095 4414 a(n) p Fg 2137 4426 a(i) p Fh(;) p Fg 9 w(j) p Fj 2206 4358 a(:) p Fx 1040 w(\(10) n(\)) 648 4560 y(Let) p Fl 22 w(p) p Fx 16 w(be) 15 b(the) h(pack) o(et) f(loss) i(pro) n(bability) e(of) h (TCP) g(\003o) n(ws.) g(Then,) f(it) h(is) h(kno) n(wn) d(that) i(the) g (throu) n(gh-) 523 4660 y(put) k(of) g(a) g(TCP) h(\003o) n(w) -5 b(,) p Fl 20 w(T) p Fx 10 w(,) 21 b(can) f(be) g(appr) n(oximated) f (by) h(the) g(follo) n(win) n(g) h(equ) n(ation) f([15].) p Fl 1469 4882 a(T) p Fi 33 w(') p Fx 1690 4826 a(1) p 1633 4863 154 5 v 1633 4939 a(2) p Fl 14 w(R) p Fg 1741 4951 a(N) p Ff 1797 4785 a(\022) p Fi 1828 4882 a(\000) p Fx(3) p Fw 18 w(+) p Ff 2036 4751 a(p) p 2097 4751 276 5 v Fx 2097 4821 a(6) p Fw 17 w(+) p Fx 19 w(21) p Fl 20 w(p) p 2022 4863 351 5 v Fi 2151 4887 a(p) p 2209 4887 48 5 v Fl 2215 4939 a(p) p Ff 2382 4785 a(\023) p Fx 3267 4882 a(\(11) n(\)) p dyy eop end %%Page: 8 8 TeXDict begin 8 7 bop Fo 1239 417 a(T) -7 b(able) 19 b(1.) p Fs 18 w(P) o(arameters) g(used) g(in) g(numerical) h(e) o (xamples) p 842 527 2225 4 v 854 591 a(Number) g(of) f(VPN) f(nodes) p Fn 856 w(N) p Fs 192 w(8\22640) 854 683 y(Maximum) i(transmission) g (delay) f(between) h(VPN) e(nodes) p Fn 26 w(D) p Fa 2450 694 a(ma) r(x) p Fs 2563 683 a(10,) h(100) 25 b([ms]) 854 774 y(Link) 19 b(bandwidth) h(between) g(VPN) e(nodes) p Fn 437 w(b) p Fa 2431 785 a(i) p Fb(;) p Fa 7 w(j) p Fs 2713 774 a(10) 24 b([Mbit) p Fr(/) p Fs(s]) 854 865 y(T) m(ime) 19 b(required) h(for) e(generating) i(an) g(encryption) g (k) o(e) o(y) p Fc 126 w(\001) p Fs 237 w(100) 25 b([ms]) 854 957 y(Number) 20 b(of) f(TCP) e(\003o) n(ws) i(between) h(VPN) e(nodes) p Fn 263 w(f) p Fa 2426 968 a(i) p Fb(;) p Fa 7 w(j) p Fs 2750 957 a(3) p Fx 523 1341 a(By) j(letting) p Fl 20 w(T) p Fw 33 w(=) p Fl 23 w(T) p Fg 1078 1353 a(min) p Fx 1169 1341 a(,) g(the) f(pack) o(et) g(loss) h(pro) n(bability) f(of) g(TCP) h(\003o) n(ws) f(is) h(obtained) e(as) p Fl 1413 1565 a(p) p Fi 23 w(') p Fx 1983 1509 a(3) p 1564 1546 880 5 v 1564 1622 a(2) p Fl 14 w(R) p Fg 1672 1634 a(N) p Fl 1732 1622 a(T) p Fg 1781 1634 a(min) p Fx 1873 1622 a(\(3) p Fw 17 w(+) p Fl 18 w(R) p Fg 2083 1634 a(N) p Fl 2144 1622 a(T) p Fg 2193 1634 a(min) p Fx 2285 1622 a(\)) p Fi 18 w(\000) p Fx 18 w(6) p Fj 2453 1565 a(:) p Fx 793 w(\(12) n(\)) p Fk 523 1857 a(3.5) 82 b(Numerical) 20 b(Examples) p Fx 523 2029 a(The) f(sensiti) n(vity) g(of) g(the) g (perf) n(orman) n(ce) h(metrics) f(such) g(as) h(VPN) f(constructio) n (n) g(time,) g(VPN) h(reco) o(v) n(-) 523 2129 y(ery) k(time,) g(and) f (the) h(minimum) f(throu) n(ghpu) n(t,) i(rou) n(nd-trip) e(time) h (and) g(pack) m(et) h(loss) g(pro) n(bability) f(of) 523 2229 y(TCP) f(\003o) n(ws) g(re) o(g) n(ardin) n(g) g(se) n(v) o(era) n (l) g(paramete) n(rs) g(such) f(as) h(the) f(numb) n(er) g(of) g(VPN) h (nod) n(es,) g(link) f(band) n(-) 523 2328 y(width,) e(link) g (transmission) f(delay) -5 b(,) 19 b(and) h(the) g(numb) n(er) g(of) g (TCP) h(\003o) n(ws) g(is) g(of) f(our) f(interest.) 648 2429 y(In) 31 b(particu) n(lar) m(,) g(transmission) g(delay) g(and) g (throu) n(ghpu) n(t) h(are) g(e) o(xpe) n(cted) g(to) f(decrease) g(as) h(the) 523 2529 y(numb) n(er) 22 b(of) g(VPN) g(nodes) g(increases) g (in) g(ring) n(-based) g(netw) o(or) n(ks) h([12) n(,) g(13]) n(.) g (Ther) n(efore,) e(we) i(in) m(v) m(es-) 523 2628 y(tigate) k(the) g (impac) n(t) h(of) f(the) g(num) n(ber) g(of) f(VPN) i(node) n(s) g (participatin) n(g) f(in) g(the) g(VPN,) p Fl 30 w(N) p Fx 5 w(,) g(on) g(VPN) 523 2728 y(constru) n(ction) g(time,) p Fl 29 w(X) p Fg 1211 2740 a(N) p Fx 1258 2728 a(,) g(VPN) g(reco) o(v) o (e) n(ry) g(time,) p Fl 27 w(Y) p Fg 2058 2740 a(N) p Fx 2105 2728 a(,) g(and) f(minimum) g(TCP) i(thro) n(ughp) n(ut,) p Fl 27 w(T) p Fg 3293 2740 a(min) p Fx 3384 2728 a(,) 523 2827 y(and) 22 b(round) n(-trip) g(time,) p Fl 23 w(R) p Fg 1270 2839 a(N) p Fx 1317 2827 a(,) h(by) g(chan) n(ging) p Fl 24 w(N) p Fx 5 w(.) h(The) e(transmission) h(delay) f(between) g (VPN) h(nodes,) p Fl 523 2927 a(d) p Fg 565 2939 a(i) p Fh(;) p Fg 9 w(j) p Fx 624 2927 a(,) f(are) g(set) g(to) g(be) g(unif) n (ormly) f(distrib) n(uted) g(in) h(the) f(range) g(of) g(0\226) p Fl 2 w(D) p Fg 2477 2939 a(ma) s(x) p Fx 2580 2927 a(.) h(The) g(link) f (bandw) n(idth) h(be-) 523 3027 y(tween) 27 b(VPN) g(nodes,) p Fl 27 w(b) p Fg 1227 3039 a(i) p Fh(;) p Fg 9 w(j) p Fx 1286 3027 a(,) g(is) h(\002x) o(ed) e(at) i(10) f([Mbit) p Fw(/) p Fx -2 w(s].) h(T) -7 b(able) 27 b(1) g(sho) n(ws) g(the) g (param) n(eters) h(used) e(in) 523 3126 y(numer) n(ical) 21 b(e) o(xam) n(ples) g(and) f(simulation) n(.) 648 3227 y(F) o(or) 25 b(simulation) n(,) h(we) g(implem) n(ented) f(the) h (RING-VPN) f(modu) n(le) h(in) g(OPNET) f(modeler) f(v) o(er) n(-) 523 3327 y(sion) 18 b(10.0) n(A) h([16) n(].) f(F) o(or) g(each) f (parameter) g(set,) h(simulation) f(is) i(repeated) e(5) h(times) g (with) g(v) n(aryin) n(g) g(the) 523 3426 y(seed) 23 b(of) f(a) h(rando) n(m) g(numb) n(er) g(gene) n(rator) m(,) f(and) g (the) g(a) n(v) o(erage) g(of) g(VPN) h(constructio) n(n) g(times,) g (VPN) 523 3526 y(reco) o(v) m(ery) d(times,) g(and) g(rou) n(nd-trip) f (times) i(of) f(TCP) h(\003o) n(ws) f(are) g(measured.) 648 3627 y(Figur) n(es) 29 b(3) f(throu) n(gh) g(6) g(sho) n(w) f(changes) g (in) h(VPN) h(constru) n(ction) f(time,) p Fl 30 w(X) p Fg 2827 3639 a(N) p Fx 2873 3627 a(,) h(VPN) f(reco) o(v) m(ery) 523 3726 y(time,) p Fl 24 w(Y) p Fg 763 3738 a(N) p Fx 810 3726 a(,) d(minimu) n(m) g(TCP) g(thro) n(ughp) n(ut,) p Fl 25 w(T) p Fg 1840 3738 a(min) p Fx 1931 3726 a(,) g(and) f(rou) n (nd-trip) f(time,) p Fl 24 w(R) p Fg 2728 3738 a(N) p Fx 2775 3726 a(,) h(when) g(the) g(numb) n(er) 523 3826 y(of) c(VPN) h(nod) n(es,) p Fl 23 w(N) p Fx 5 w(,) g(is) g(chang) n (ed.) 648 3927 y(It) e(can) g(be) g(seen) h(from) e(Fig.) i(3) f(that) g (VPN) h(construc) n(tion) g(time,) p Fl 21 w(X) p Fg 2516 3939 a(N) p Fx 2562 3927 a(,) g(decreases) f(as) h(the) f(numb) n (er) 523 4027 y(of) 27 b(VPN) g(nodes,) p Fl 28 w(N) p Fx 5 w(,) h(increases.) e(This) h(is) h(because) e(of) h(the) g (increased) f(density) g(of) h(VPN) g(nodes.) 523 4126 y(Namely) -5 b(,) 22 b(as) i(the) g(numb) n(er) g(of) f(VPN) h(nod) n (es) g(increases,) g(the) f(density) g(of) g(VPN) h(node) n(s) h(in) e (the) h(net-) 523 4226 y(w) o(ork) g(beco) n(mes) h(high.) e(Hence,) h (a) g(ne) n(w) h(VPN) f(node) g(is) h(lik) o(ely) f(to) g(be) h(con) n (nected) f(to) g(VPN) h(nodes) 523 4325 y(with) 32 b(short) g(roun) n (d-trip) g(times,) g(leading) f(short) h(VPN) h(constru) n(ction) f (time.) g(Moreo) m(v) o(er) m(,) f(Fig.) h(3) 523 4425 y(sho) n(ws) 22 b(good) f(agreem) n(ent) h(between) f(numeric) n(al) i (e) o(xamp) n(les) g(and) e(simulation) h(results,) g(indicatin) n(g) 523 4525 y(v) n(alidity) d(of) h(our) g(appr) n(oximate) g(analy) n (sis.) 648 4625 y(Figur) n(e) 31 b(4) f(sho) n(ws) g(that) g(VPN) g (reco) o(v) m(ery) g(time) g(decrea) n(ses) h(as) g(the) f(numb) n(er) g (of) g(VPN) g(nodes) 523 4725 y(increases.) f(This) h(can) g(be) g(e) o (xp) n(lained) f(by) h(the) f(decrease) h(in) f(the) h(a) n(v) o(erage) f(delay) g(between) g(each) 523 4825 y(VPN) 20 b(node) e(due) h(to) h (the) f(increased) g(num) n(ber) g(of) g(VPN) h(nodes.) f(The) g (\002gur) n(e) h(also) g(sho) n(ws) f(that) h(VPN) 523 4924 y(reco) o(v) m(ery) 15 b(time) h(increases) f(with) h(the) g (increa) n(se) h(of) e(the) h(transmission) f(delay) g(between) f(VPN) i (nodes.) p dyy eop end %%Page: 9 9 TeXDict begin 9 8 bop 993 2038 a @beginspecial 50 @llx 50 @lly 230 @urx 176 @ury 2351 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} 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 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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) 140.0 0.0 true true 0 (VPN construction time [ms])] ] -46.7 MCshow grestore LTb 2080 70 M [ [(Helvetica) 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=10)] [(Helvetica) 140.0 0.0 true true 0 ([ms]\(analysis\))] ] -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 (Dmax=100)] [(Helvetica) 140.0 0.0 true true 0 ([ms]\(analysis\))] ] -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 (Dmax=10)] [(Helvetica) 140.0 0.0 true true 0 ([ms]\(simulation\))] ] -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 (Dmax=100)] [(Helvetica) 140.0 0.0 true true 0 ([ms]\(simulation\))] ] -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 Fs 1010 2212 a(Fig.) 12 b(3:) 19 b(Number) g(of) g(VPN) f (nod) r(es) p Fn 20 w(N) p Fs 23 w(vs.) h(VPN) f(construction) i(time) p Fn 21 w(X) p Fa 2859 2223 a(N) p Fs 2899 2212 a(.) 993 4350 y @beginspecial 50 @llx 50 @lly 230 @urx 176 @ury 2351 @rwi @setspecial %%BeginDocument: figure/scatter-n-Y.eps %!PS-Adobe-2.0 EPSF-2.0 %%Creator: gnuplot 4.0 patchlevel 0 %%CreationDate: Thu Nov 9 21:06:13 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) 140.0 0.0 true true 0 (VPN recovery time [ms])] ] -46.7 MCshow grestore LTb 2080 70 M [ [(Helvetica) 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=10)] [(Helvetica) 140.0 0.0 true true 0 ([ms]\(analysis\))] ] -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 (Dmax=100)] [(Helvetica) 140.0 0.0 true true 0 ([ms]\(analysis\))] ] -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 (Dmax=10)] [(Helvetica) 140.0 0.0 true true 0 ([ms]\(simulation\))] ] -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 (Dmax=100)] [(Helvetica) 140.0 0.0 true true 0 ([ms]\(simulation\))] ] -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 1068 4525 a(Fig.) 12 b(4:) 19 b(Number) h(of) e(VPN) h (nodes) p Fn 22 w(N) p Fs 22 w(vs.) g(VPN) f(reco) o(v) o(ery) i(time) p Fn 19 w(Y) p Fa 2801 4536 a(N) p Fs 2841 4525 a(.) p dyy eop end %%Page: 10 10 TeXDict begin 10 9 bop 993 1737 a @beginspecial 50 @llx 50 @lly 230 @urx 176 @ury 2351 @rwi @setspecial %%BeginDocument: figure/scatter-n-T.eps %!PS-Adobe-2.0 EPSF-2.0 %%Creator: gnuplot 4.0 patchlevel 0 %%CreationDate: Thu Nov 9 21:08:04 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 798 681 M 63 0 V 2501 0 R -63 0 V stroke 714 681 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0.05)] ] -46.7 MRshow 1.000 UL LTb 798 942 M 63 0 V 2501 0 R -63 0 V stroke 714 942 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0.1)] ] -46.7 MRshow 1.000 UL LTb 798 1203 M 63 0 V 2501 0 R -63 0 V stroke 714 1203 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0.15)] ] -46.7 MRshow 1.000 UL LTb 798 1464 M 63 0 V 2501 0 R -63 0 V stroke 714 1464 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0.2)] ] -46.7 MRshow 1.000 UL LTb 798 1725 M 63 0 V 2501 0 R -63 0 V stroke 714 1725 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0.25)] ] -46.7 MRshow 1.000 UL LTb 798 1986 M 63 0 V 2501 0 R -63 0 V stroke 714 1986 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0.3)] ] -46.7 MRshow 1.000 UL LTb 798 2248 M 63 0 V 2501 0 R -63 0 V stroke 714 2248 M [ [(Helvetica) 140.0 0.0 true true 0 ( 0.35)] ] -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=10)] [(Helvetica) 140.0 0.0 true true 0 ([ms]\(analysis\))] ] -46.7 MRshow LT0 2764 2219 M 430 0 V 1258 1906 M 263 -881 V 1784 759 L 2047 631 L 263 -63 V 263 -39 V 263 -26 V 263 -16 V 263 -13 V 1.500 UP 1.000 UL LT1 1258 1854 M 0 104 V -31 -104 R 62 0 V -62 104 R 62 0 V 232 -945 R 0 25 V -31 -25 R 62 0 V -62 25 R 62 0 V 1784 753 M 0 12 V -31 -12 R 62 0 V -62 12 R 62 0 V 2047 628 M 0 6 V -31 -6 R 62 0 V -62 6 R 62 0 V 232 -67 R 0 3 V -31 -3 R 62 0 V -62 3 R 62 0 V 232 -42 R 0 3 V -31 -3 R 62 0 V -62 3 R 62 0 V 232 -29 R 0 2 V -31 -2 R 62 0 V -62 2 R 62 0 V 232 -17 R 0 1 V -31 -1 R 62 0 V -62 1 R 62 0 V 232 -15 R 0 1 V -31 -1 R 62 0 V -62 1 R 62 0 V 1258 1906 BoxF 1521 1025 BoxF 1784 759 BoxF 2047 631 BoxF 2310 568 BoxF 2573 529 BoxF 2836 503 BoxF 3099 487 BoxF 3362 474 BoxF 1.000 UL LT2 LTb 2680 2079 M [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (Dmax=100)] [(Helvetica) 140.0 0.0 true true 0 ([ms]\(analysis\))] ] -46.7 MRshow LT2 2764 2079 M 430 0 V 1258 1897 M 263 -858 V 1784 758 L 2047 635 L 263 -65 V 263 -40 V 263 -26 V 263 -17 V 263 -13 V 1.500 UP 1.000 UL LT3 1258 1851 M 0 92 V -31 -92 R 62 0 V -62 92 R 62 0 V 232 -920 R 0 31 V -31 -31 R 62 0 V -62 31 R 62 0 V 1784 752 M 0 13 V -31 -13 R 62 0 V -62 13 R 62 0 V 2047 631 M 0 7 V -31 -7 R 62 0 V -62 7 R 62 0 V 232 -70 R 0 4 V -31 -4 R 62 0 V -62 4 R 62 0 V 232 -43 R 0 2 V -31 -2 R 62 0 V -62 2 R 62 0 V 232 -28 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 232 -14 R 0 1 V -31 -1 R 62 0 V -62 1 R 62 0 V 1258 1897 DiaF 1521 1039 DiaF 1784 758 DiaF 2047 635 DiaF 2310 570 DiaF 2573 530 DiaF 2836 504 DiaF 3099 487 DiaF 3362 474 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 Fs 941 1911 a(Fig.) 12 b(5:) 19 b(Number) g(of) g(VPN) f (node) r(s) p Fn 20 w(N) p Fs 23 w(vs.) h(minimum) g(TCP) f(through) r (put) p Fn 19 w(T) p Fa 2889 1922 a(min) p Fs 2968 1911 a(.) p Fx 523 2278 a(This) 32 b(is) h(pro) n(bably) e(because) g(the) h (requ) n(ired) g(time) f(to) h(establish) g(and) f(terminate) g(IPsec) h (tunnels) 523 2377 y(increases) 20 b(as) g(the) g(transmission) f (delay) h(between) f(nod) n(es) i(beco) n(mes) g(lar) o(g) n(er) m(,) f (as) g(can) g(be) g(seen) g(fro) n(m) 523 2477 y(Eq.) 31 b(\(5\).) g(Again,) g(this) h(\002gure) f(sho) n(ws) h(good) f(agree) n (ment) h(between) f(nume) n(rical) h(e) o(xamp) n(les) h(and) 523 2577 y(simulation) 19 b(results,) i(indicatin) n(g) g(v) n(alid) n(ity) g(of) f(our) f(appro) n(ximate) h(analysis.) 648 2676 y(From) g(these) g(observ) n(a) n(tions,) h(we) g(con) n(clude) f(that) h(both) f(the) g(VPN) h(constructio) n(n) g(time) g(and) e(the) 523 2776 y(VPN) i(reco) o(v) m(ery) f(time) g(are) g(not) g(so) g(sensiti) n (v) o(e) g(to) h(the) f(numb) n(er) g(of) g(VPN) h(node) n(s) h(in) e (RING-VPN.) 648 2875 y(Figur) n(e) h(5) g(sho) n(ws) f(that) g(the) h (minimu) n(m) g(TCP) g(thro) n(ughp) n(ut) g(rapidly) e(decreases) h (as) h(the) f(numb) n(er) 523 2975 y(of) i(VPN) g(nodes) f(increases.) h (This) g(can) g(be) f(e) o(xplaine) n(d) h(by) g(the) g(increased) f (num) n(ber) h(of) f(TCP) i(\003o) n(ws) 523 3075 y(sharing) e(the) g (bandw) n(idth) h(of) f(the) h(bottlen) n(eck) g(link.) f(Also,) g (this) h(\002gure) f(sho) n(ws) h(that) f(the) h(transmis-) 523 3174 y(sion) f(delay) f(between) g(VPN) h(node) n(s) h(does) f(not) f (a) p Fw(\013) p Fx(ect) h(the) f(minimum) g(thro) n(ughp) n(ut) h(of) g (TCP) g(\003o) n(ws.) 523 3274 y(This) 16 b(is) h(becau) n(se,) g(as) f (Eq.) g(\(10) n(\)) g(indicates,) g(the) f(throug) n(hput) g(of) h(a) g (TCP) h(\003o) n(w) f(is) g(depend) n(ent) g(only) f(on) 523 3374 y(the) 22 b(link) f(band) n(width) g(and) g(the) h(num) n(ber) g (of) f(TCP) h(\003o) n(ws.) g(Note) f(that) h(Fig.) f(5) h(sho) n(ws) f (the) p Fl 22 w(minimum) p Fx 523 3473 a(TCP) g(throu) n(ghpu) n(t,) g (instead) f(of) g(the) g(a) n(v) o(erag) n(e) h(TCP) g(throu) n(ghpu) n (t.) 648 3573 y(Figur) n(e) 26 b(6) f(sho) n(ws) h(that) f(the) g (round) n(-trip) g(time) g(of) g(TCP) h(\003o) n(ws) g(increases) f (almost) g(linearly) g(as) 523 3672 y(the) f(numb) n(er) g(of) g(VPN) g (nodes) f(increases.) h(This) g(is) h(pro) n(bably) e(because) g(in) i (our) e(RING-VPN,) g(the) 523 3772 y(roun) n(d-trip) 16 b(time) i(is) g(the) f(sum) g(of) f(all) i(transmission) f(delay) n(s) h (\(see) g(Eq.) e(\(1\)\).) g(The) h(\002gure) f(also) h(sho) n(ws) 523 3872 y(that) 29 b(the) g(roun) n(d-trip) f(time) i(increa) n(ses) g(as) g(the) f(transmission) f(delay) h(between) f(VPN) i(nod) n(es) g(be-) 523 3971 y(comes) 20 b(lar) o(ge) n(r) -5 b(.) 648 4071 y(From) 26 b(these) h(observ) l(ations,) f(we) i(conc) n(lude) f(that) g (the) f(propo) n(sed) h(RING-VPN) g(sho) n(ws) g(goo) n(d) 523 4171 y(perfo) n(rmance) e(in) h(terms) g(of) g(the) g(minim) n(um) g (TCP) h(thro) n(ughpu) n(t) g(and) e(roun) n(d-trip) g(time) h(when) f (the) 523 4270 y(numb) n(er) 20 b(of) g(nodes) g(particip) n(ating) g (in) h(the) f(VPN) h(is) g(relati) n(v) o(e) n(ly) g(small.) p Fm 523 4531 a(4) 99 b(Conclusion) p Fx 523 4725 a(In) 29 b(this) i(pape) n(r) m(,) f(we) g(ha) n(v) o(e) f(pro) n(posed) g(a) h (ring-b) n(ased) g(VPN) g(called) g(RING-VPN,) f(which) h(b) n(uilds) 523 4825 y(VPNs) d(by) f(logically) f(and) h(auton) n(omou) n(sly) h (conn) n(ecting) f(VPN) h(nod) n(es) g(in) f(a) h(ring) f(topo) n(logy) -5 b(.) 25 b(Our) 523 4924 y(RING-VPN) g(can) f(b) n(uild) g(a) h(lar) o (ge) e(numbe) n(r) i(of) f(VPNs) i(o) o(v) o(e) n(r) f(the) f(e) o (xisting) g(netw) o(ork) f(by) h(reducin) n(g) p dyy eop end %%Page: 11 11 TeXDict begin 11 10 bop 993 1737 a @beginspecial 50 @llx 50 @lly 230 @urx 176 @ury 2351 @rwi @setspecial %%BeginDocument: figure/scatter-n-R.eps %!PS-Adobe-2.0 EPSF-2.0 %%Creator: gnuplot 4.0 patchlevel 0 %%CreationDate: Thu Nov 9 21:06:10 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 currentpoint gsave translate 90 rotate 0 0 moveto [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (TCP round-trip 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 (Dmax=10)] [(Helvetica) 140.0 0.0 true true 0 ([ms]\(analysis\))] ] -46.7 MRshow LT0 2764 2219 M 430 0 V 1258 451 M 263 9 V 263 11 V 263 5 V 263 19 V 263 9 V 263 16 V 263 -1 V 263 9 V 1.500 UP 1.000 UL LT1 1258 448 M 0 5 V -31 -5 R 62 0 V -62 5 R 62 0 V 232 4 R 0 5 V -31 -5 R 62 0 V -62 5 R 62 0 V 232 6 R 0 6 V -31 -6 R 62 0 V -62 6 R 62 0 V 232 -5 R 0 13 V -31 -13 R 62 0 V -62 13 R 62 0 V 232 11 R 0 5 V -31 -5 R 62 0 V -62 5 R 62 0 V 232 3 R 0 5 V -31 -5 R 62 0 V -62 5 R 62 0 V 232 10 R 0 8 V -31 -8 R 62 0 V -62 8 R 62 0 V 232 -9 R 0 7 V -31 -7 R 62 0 V -62 7 R 62 0 V 232 4 R 0 5 V -31 -5 R 62 0 V -62 5 R 62 0 V 1258 451 BoxF 1521 460 BoxF 1784 471 BoxF 2047 476 BoxF 2310 495 BoxF 2573 504 BoxF 2836 520 BoxF 3099 519 BoxF 3362 528 BoxF 1.000 UL LT2 LTb 2680 2079 M [ [(Helvetica-Oblique) 140.0 0.0 true true 0 (Dmax=100)] [(Helvetica) 140.0 0.0 true true 0 ([ms]\(analysis\))] ] -46.7 MRshow LT2 2764 2079 M 430 0 V 1258 739 M 263 80 V 263 98 V 263 100 V 263 145 V 263 105 V 263 101 V 263 61 V 263 68 V 1.500 UP 1.000 UL LT3 1258 731 M 0 17 V -31 -17 R 62 0 V -62 17 R 62 0 V 232 62 R 0 17 V -31 -17 R 62 0 V -62 17 R 62 0 V 232 80 R 0 20 V -31 -20 R 62 0 V -62 20 R 62 0 V 232 74 R 0 32 V -31 -32 R 62 0 V -62 32 R 62 0 V 232 120 R 0 17 V -31 -17 R 62 0 V -62 17 R 62 0 V 232 90 R 0 15 V -31 -15 R 62 0 V -62 15 R 62 0 V 232 79 R 0 28 V -31 -28 R 62 0 V -62 28 R 62 0 V 232 34 R 0 26 V -31 -26 R 62 0 V -62 26 R 62 0 V 232 47 R 0 17 V -31 -17 R 62 0 V -62 17 R 62 0 V 1258 739 DiaF 1521 819 DiaF 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 (Dmax=10)] [(Helvetica) 140.0 0.0 true true 0 ([ms]\(simulation\))] ] -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 (Dmax=100)] [(Helvetica) 140.0 0.0 true true 0 ([ms]\(simulation\))] ] -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 Fs 1051 1911 a(Fig.) 11 b(6:) 19 b(Number) h(of) f(VPN) f (nodes) p Fn 22 w(N) p Fs 23 w(vs.) g(TCP) g(round) r(-trip) g(time) p Fn 18 w(R) p Fa 2818 1922 a(N) p Fs 2859 1911 a(.) p Fx 523 2293 a(the) e(required) f(cost) i(to) f(maintain) g(IPsec) h (tunn) n(els.) g(Since) g(each) f(nod) n(e) h(oper) n(ates) g(autono) n (mously) -5 b(,) 15 b(our) 523 2393 y(RING-VPN) j(can) f(realize) h (highly) e(reliable) i(comm) n(unication) e(e) n(v) o(en) h(in) h(case) g(of) g(netw) o(or) n(k) g(f) o(ailures.) 523 2493 y(W) -7 b(e) 19 b(ha) n(v) o(e) e(mathematica) n(lly) h(analyzed) f(the) h (perf) n(ormanc) n(e) h(of) e(the) h(RING-VPN.) g(In) f(particular) -5 b(,) 18 b(we) 523 2592 y(ha) n(v) o(e) h(modeled) g(the) h(RING-VPN) g (and) f(ha) n(v) o(e) h(deri) n(v) m(ed) g(VPN) h(con) n(struction) f (time,) f(VPN) i(reco) o(v) m(ery) 523 2692 y(time,) f(and) g(the) g (minimu) n(m) h(thro) n(ughpu) n(t,) g(rou) n(nd-trip) e(time) h(and) g (pack) o(et) g(loss) h(pro) n(bability) f(of) g(TCP) 523 2791 y(\003o) n(ws.) 29 b(W) -7 b(e) 30 b(ha) n(v) o(e) e(also) h (quantitati) n(v) m(ely) g(demo) n(nstrated) f(the) h(e) p Fw(\013) p Fx(ecti) n(v) o(en) n(ess) h(of) f(the) f(RING-VPN) 523 2891 y(throu) n(gh) 20 b(se) n(v) o(eral) g(num) n(erical) g(e) o(xamp) n(les.) 648 2996 y(Our) k(futur) n(e) h(w) o(orks) f(include) g(e) n(v) n(alu) n(ation) h(of) f(the) g(e) p Fw(\013) p Fx(ecti) n(v) o(ene) n (ss) i(of) e(adv) n(anc) n(ed) h(comm) n(unica-) 523 3096 y(tion) 17 b(con) n(trol) g(mechan) n(isms) h(such) e(as) i(ad-h) n (oc) f(tunnelin) n(g) g(and) f(assessment) i(of) e(the) h(impact) f(of) h(VPN) 523 3195 y(node) i(f) o(ailures) h(on,) g(for) f(instance,) h (VPN) h(con) n(struction) f(time) g(and) g(VPN) h(reco) m(v) o(ery) e (time.) p Fm 523 3488 a(Refer) n(en) r(ces) p Fs 560 3705 a(1.) 42 b(M.) 21 b(Carugi) g(and) h(D.) e(McDysan,) i (\223Service) f(requirements) h(for) e(layer) i(3) f(pro) o(vider) g (pro) o(vision) r(ed) g(virtual) 658 3797 y(pri) n(v) n(ate) e(ne) h (tw) o(orks) f(\(PPVP) n(Ns\),) -5 b(\224) 19 b(Request) g(for) g (Comments) g(\(RFC\)) f(4031,) i(April) e(2005) r(.) 560 3893 y(2.) 42 b(B.) 24 b(Gleeson) p Fn 25 w(et) g(al.) p Fs(,) f(\223) -6 b(A) 24 b(frame) n(w) o(ork) i(for) e(IP) f(based) j (virtual) e(pri) n(v) n(ate) h(netw) o(orks,) -5 b(\224) 25 b(Request) f(for) h(Com-) 658 3984 y(ments) 19 b(\(RFC\)) f(2764,) i (Feb) m(.) e(2000.) 560 4081 y(3.) 42 b(A.) d(Nagarajan,) h (\223Generic) g(requirement) h(for) e(pro) o(vider) i(pro) o(visioned) g (virtual) f(pri) n(v) n(ate) g(netw) o(orks) 658 4172 y(\(PPVP) n(N\),) -5 b(\224) 19 b(Request) g(for) g(Comments) g (\(RFC\)) f(3809,) i(June) f(2004) r(.) 560 4269 y(4.) 42 b(R.) 29 b(Callon) g(and) h(M.) f(Suzuki,) g(\223) -6 b(A) 29 b(frame) n(w) o(ork) i(for) e(layer) g(3) h(pro) o(vider) g (pro) o(visioned) g(virtual) g(pricate) 658 4360 y(netw) o(orks) 20 b(PPVP) n(Ns,) -5 b(\224) 19 b(Request) g(for) g(Comments) g(\(RFC\)) f (4110) r(,) g(July) h(2005) r(.) 560 4457 y(5.) 42 b(E.) 20 b(Rosen) h(and) h(Y) -10 b(.) 21 b(Rekhter) m(,) f(\223BGP) p Fr(/) p Fs(MPLS) g(VPNs,) -5 b(\224) 20 b(Request) h(for) g(Comments) h (\(RFC\)) d(2547) r(,) h(March) 658 4548 y(1999.) 560 4645 y(6.) 42 b(S.) 17 b(K) n(ent) i(and) g(R.) e(Atkinson,) i (\223Security) f(architecture) h(for) f(the) h(Internet) f(protocol,) -5 b(\224) 19 b(Request) g(for) f(Com-) 658 4736 y(ments) h(\(RFC\)) f (2401,) i(No) o(v) -5 b(.) 19 b(1998.) 560 4833 y(7.) 42 b(S.) 18 b(K) n(ent) h(and) h(K.) e(Seo,) g(\223Security) h (architecture) h(for) e(the) h(internet) g(protoco) r(l,) -5 b(\224) 18 b(Request) h(for) g(Comments) 658 4924 y(\(RFC\)) f(4301,) h (Dec.) g(2005) r(.) p dyy eop end %%Page: 12 12 TeXDict begin 12 11 bop Fs 560 448 a(8.) 42 b(\223Dynamic) 32 b(VPN) f(controller) h(\(D) m(VC\)) f(demonstrator) h(project) g (report.) -5 b(\224) p Fp 31 w(http://www-) t(mice.cs.) 658 540 y(ucl.ac.uk/multimedia/meetings) q(/vpnw) q(orks) q(hop/) q(docum) q (enta) q(t\045ion) q(/pro) q(ceed) q(ings/) 658 631 y(2003-) t(11-) t (12/VPN-) t(KMS-) t(Issues.d) q(oc) p Fs(,) 25 b(Oct.) 18 b(2003.) 560 722 y(9.) 42 b(A.) 28 b(Gomez,) h(G.) f(Martinez,) h(and) g (O.) f(Cano) o(v) n(as,) h(\223Ne) n(w) g(security) g(services) g (based) g(on) g(PKI,) -5 b(\224) 28 b(Future) 658 814 y(Generation) 20 b(Computer) f(Systems,) g(v) o(ol.19,) f(no.2,) i (pp.251\2262) r(62,) f(Jan.) g(2003.) 523 905 y(10.) 42 b(J.) 17 b(T) -6 b(ouch,) 18 b(\223Dynamic) g(internet) g(o) o(v) o (erlay) g(deplo) o(y) r(ment) f(and) h(manag) r(ement) f(using) i(the) e (X-Bone,) -5 b(\224) 18 b(Com-) 658 996 y(puter) h(Netw) o(orks,) g(v) o (ol.36,) g(no.2,) g(pp.117) r(\226135,) g(July) h(2001.) 523 1088 y(11.) 42 b(J.) 14 b(T) -6 b(ouch,) 16 b(Y) -10 b(.) 14 b(W) -6 b(ang,) 15 b(V) -10 b(.) 15 b(Pingali,) e(L.) h (Eggert,) h(R.) f(Zhou,) h(and) h(G.) e(Finn,) h(\223) -6 b(A) 14 b(global) i(X-Bone) f(for) g(netw) o(ork) 658 1179 y(e) o(xperiments,) -5 b(\224) 19 b(Proceeding) h(in) f(IEEE) f(T) m(ridentcom) h(2005) r(,) f(pp.194) r(\226203,) h(March) h(2005.) 523 1270 y(12.) 42 b(M.) 26 b(Er) o(gen,) g(D.) g(Lee,) g(R.) f(Attias,) h (S.) f(T) m(ripakis,) h(A.) g(Puri,) g(R.) f(Sengupta,) i(and) g(P) -8 b(.) 25 b(V) -8 b(araiya,) 26 b(\223W) m(ireless) 658 1362 y(tok) o(en) 18 b(ring) f(protocol,) -5 b(\224) 17 b(Proceeding) r(s) f(of) h(SCI) f(\(Systems,) h(Cybernetics) g(and) h (Informatics\),) f(July) g(2002.) 523 1453 y(13.) 42 b(R.) 15 b(Jain,) g(\223Performance) i(analysis) f(of) g(FDDI) f(tok) o (en) h(ring) g(netw) o(orks:) h(E) p Fr(\013) p Fs(ect) e(of) g (parameters) i(and) f(guide-) 658 1544 y(lines) j(for) g(setting) h (TTR) l(T) n(,) -5 b(\224) 19 b(IEEE) f(Lightw) o(a) o(v) o(e) h(T) -5 b(elecommunication) 21 b(Systems,) e(v) o(ol.20,) g(no.2,) g(pp.16) r (\226) 658 1636 y(22,) g(May) h(1991.) 523 1727 y(14.) 42 b(J.) 15 b(Postel,) f(\223Internet) h(control) h(message) g(protocol,) -5 b(\224) 15 b(Request) h(for) f(Comments) h(\(RFC\)) e(792,) h(Sept.) g(1981.) 523 1818 y(15.) 42 b(H.) 19 b(Ohsaki,) g(J.) g(Ujiie,) g(and) h (M.) f(Imase,) g(\223On) h(scalable) g(modeling) h(of) e(TCP) f(cong) r (estion) h(control) h(mech-) 658 1910 y(anism) 27 b(for) g(lar) o (ge-scale) g(IP) f(netw) o(orks,) -5 b(\224) 28 b(Proceedings) g(of) f (IEEE) e(SAINT) h(2005,) i(pp.361\226) r(369,) f(Feb) m(.) 658 2001 y(2005.) 523 2092 y(16.) 42 b(Opnet) 19 b(T) -5 b(echnolog) r(ies,) 18 b(Inc.,) g(\223OPNET.) -5 b(\224) p Fp 18 w(http://www.opnet.com/) p Fs(.) p dyy eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF