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@setspecial %%BeginDocument: figure/model.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 20 642 267 834 %%Title: model %%CreationDate: Tue Dec 18 00:47:58 2001 %%Creator: Tgif-4.1.35 by William Chia-Wei Cheng (william@cs.UCLA.edu) %%ProducedBy: (unknown) %%Pages: 1 %%DocumentFonts: (atend) %%EndComments %%BeginProlog /tgifdict 58 dict def tgifdict begin /tgifellipsedict 6 dict def tgifellipsedict /mtrx matrix put /TGEL % tgifellipse { tgifellipsedict begin /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y translate xrad yrad scale 0 0 1 0 360 arc savematrix setmatrix end } def /tgifarrowtipdict 8 dict def tgifarrowtipdict /mtrx matrix put /TGAT % tgifarrowtip { tgifarrowtipdict begin /dy exch def /dx exch def /h exch def /w exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y translate dy dx atan rotate 0 0 moveto w neg h lineto w neg h neg lineto savematrix setmatrix end } def /tgifarcdict 8 dict def tgifarcdict /mtrx matrix put /TGAN % tgifarcn { tgifarcdict begin /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y translate xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix end } def /TGAR % tgifarc { tgifarcdict begin /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y translate xrad yrad scale 0 0 1 startangle endangle arcn savematrix setmatrix end } def /TGMAX { exch dup 3 1 roll exch dup 3 1 roll gt { pop } { exch pop } ifelse } def /TGMIN { exch dup 3 1 roll exch dup 3 1 roll lt { pop } { exch pop } ifelse } def /TGSW { stringwidth pop } def /bd { bind def } bind def /GS { gsave } bd /GR { grestore } bd /NP { newpath } bd /CP { closepath } bd /CHP { charpath } bd /CT { curveto } bd /L { lineto } bd /RL { rlineto } bd /M { moveto } bd /RM { rmoveto } bd /S { stroke } bd /F { fill } bd /TR { translate } bd /RO { rotate } bd /SC { scale } bd /MU { mul } bd /DI { div } bd /DU { dup } bd /NE { neg } bd /AD { add } bd /SU { sub } bd /PO { pop } bd /EX { exch } bd /CO { concat } bd /CL { clip } bd /EC { eoclip } bd /EF { eofill } bd /IM { image } bd /IMM { imagemask } bd /ARY { array } bd /SG { setgray } bd /RG { setrgbcolor } bd /SD { setdash } bd /W { setlinewidth } bd /SM { setmiterlimit } bd /SLC { setlinecap } bd /SLJ { setlinejoin } bd /SH { show } bd /FF { findfont } bd /MS { makefont setfont } bd /AR { arcto 4 {pop} repeat } bd /CURP { currentpoint } bd /FLAT { flattenpath strokepath clip newpath } bd /TGSM { tgiforigctm setmatrix } def /TGRM { savematrix setmatrix } def end %%EndProlog %%Page: 1 1 %%PageBoundingBox: 20 642 267 834 tgifdict begin /tgifsavedpage save def 1 SM 1 W 0 SG 72 0 MU 72 11.602 MU TR 72 128 DI 100.000 MU 100 DI DU NE SC GS /tgiforigctm matrix currentmatrix def % POLY/OPEN-SPLINE 0 SG GS NP 130 50 M 190 150 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 130 200 M 190 175 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 130 265 M 190 190 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 305 190 M 370 270 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 305 160 M 370 60 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 310 165 M 370 100 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 310 175 M 370 200 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS [4 4] 0 SD NP 385 125 M 385 180 L TGSM 1 W S [] 0 SD GR % TEXT NP 0 SG GS 1 W 185 115 M GS 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (RED Gateway) SH GR GR % TEXT NP 0 SG GS 1 W 165 70 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (w\(k\)) SH GR GR % TEXT NP 0 SG GS 1 W 155 280 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (w\(k\)) SH GR GR % BOX 0 SG NP 375 55 M 405 55 L 405 80 L 375 80 L CP F GS 10 SM GS NP 375 55 M 405 55 L 405 80 L 375 80 L CP 2 W S GR GR % BOX 0 SG NP 370 50 M 400 50 L 400 75 L 370 75 L CP 1 SG F 0 SG GS 10 SM GS NP 370 50 M 400 50 L 400 75 L 370 75 L CP 2 W S GR GR % BOX 0 SG NP 375 95 M 405 95 L 405 120 L 375 120 L CP F GS 10 SM GS NP 375 95 M 405 95 L 405 120 L 375 120 L CP 2 W S GR GR % BOX 0 SG NP 375 190 M 405 190 L 405 215 L 375 215 L CP F GS 10 SM GS NP 375 190 M 405 190 L 405 215 L 375 215 L CP 2 W S GR GR % BOX 0 SG NP 375 260 M 405 260 L 405 285 L 375 285 L CP F GS 10 SM GS NP 375 260 M 405 260 L 405 285 L 375 285 L CP 2 W S GR GR % BOX 0 SG NP 370 90 M 400 90 L 400 115 L 370 115 L CP 1 SG F 0 SG GS 10 SM GS NP 370 90 M 400 90 L 400 115 L 370 115 L CP 2 W S GR GR % BOX 0 SG NP 370 185 M 400 185 L 400 210 L 370 210 L CP 1 SG F 0 SG GS 10 SM GS NP 370 185 M 400 185 L 400 210 L 370 210 L CP 2 W S GR GR % BOX 0 SG NP 370 255 M 400 255 L 400 280 L 370 280 L CP 1 SG F 0 SG GS 10 SM GS NP 370 255 M 400 255 L 400 280 L 370 280 L CP 2 W S GR GR % OVAL 0 SG NP 290 180 25 30 TGEL F GS GS NP 290 180 25 30 TGEL 2 W S GR GR % OVAL 0 SG NP 290 180 25 30 TGEL F GS GS NP 290 180 25 30 TGEL 2 W S GR GR % BOX 0 SG NP 105 45 M 135 45 L 135 70 L 105 70 L CP F GS 10 SM GS NP 105 45 M 135 45 L 135 70 L 105 70 L CP 2 W S GR GR % BOX 0 SG NP 105 90 M 135 90 L 135 115 L 105 115 L CP F GS 10 SM GS NP 105 90 M 135 90 L 135 115 L 105 115 L CP 2 W S GR GR % BOX 0 SG NP 105 260 M 135 260 L 135 285 L 105 285 L CP F GS 10 SM GS NP 105 260 M 135 260 L 135 285 L 105 285 L CP 2 W S GR GR % BOX 0 SG NP 105 195 M 135 195 L 135 220 L 105 220 L CP F GS 10 SM GS NP 105 195 M 135 195 L 135 220 L 105 220 L CP 2 W S GR GR % BOX 0 SG NP 100 40 M 130 40 L 130 65 L 100 65 L CP 1 SG F 0 SG GS 10 SM GS NP 100 40 M 130 40 L 130 65 L 100 65 L CP 2 W S GR GR % BOX 0 SG NP 100 85 M 130 85 L 130 110 L 100 110 L CP 1 SG F 0 SG GS 10 SM GS NP 100 85 M 130 85 L 130 110 L 100 110 L CP 2 W S GR GR % BOX 0 SG NP 100 255 M 130 255 L 130 280 L 100 280 L CP 1 SG F 0 SG GS 10 SM GS NP 100 255 M 130 255 L 130 280 L 100 280 L CP 2 W S GR GR % BOX 0 SG NP 100 190 M 130 190 L 130 215 L 100 215 L CP 1 SG F 0 SG GS 10 SM GS NP 100 190 M 130 190 L 130 215 L 100 215 L CP 2 W S GR GR % POLY/OPEN-SPLINE 0 SG GS [4 4] 0 SD NP 115 120 M 115 175 L TGSM 1 W S [] 0 SD GR % POLY/OPEN-SPLINE 0 SG GS NP 155 60 M 30 20 atan DU cos 10.000 MU 175 exch SU exch sin 10.000 MU 90 exch SU L TGSM 2 W S 1 W GR GS TGSM NP 175 90 10.000 4.000 20 30 TGAT 1 SG CP F 0 SG NP 175 90 10.000 4.000 20 30 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 160 250 M -25 15 atan DU cos 10.000 MU 175 exch SU exch sin 10.000 MU 225 exch SU L TGSM 2 W S 1 W GR GS TGSM NP 175 225 10.000 4.000 15 -25 TGAT 1 SG CP F 0 SG NP 175 225 10.000 4.000 15 -25 TGAT CP F GR % ARC 0 SG NP 94 190 M 94 190 33 120 138 183 TGAN 94 190 L CP 1 SG F 0 SG GS GS NP 94 190 33 120 138 183 TGAN [8 8] 0 SD S GR GR % ARC 0 SG NP 83 137 M 83 137 23 98 -129 -182 TGAR 83 137 L CP 1 SG F 0 SG GS GS NP 83 137 23 98 -129 -182 TGAR [8 8] 0 SD S GR GR % POLY/OPEN-SPLINE 0 SG NP 120 5 M 385 5 L 385 30 L CP 1 SG EF 0 SG GS NP 120 5 M 385 5 L 385 30 L TGSM 3 W S 1 W GR % POLY/OPEN-SPLINE 0 SG GS NP 385 30 M 0 -265 atan DU cos 12.000 MU 120 exch SU exch sin 12.000 MU 30 exch SU L TGSM 3 W S 1 W GR GS TGSM NP 120 30 12.000 5.000 -265 0 TGAT 1 SG CP F 0 SG NP 120 30 12.000 5.000 -265 0 TGAT CP F GR % TEXT NP 0 SG NP 254 35 M 266 35 L 266 68 L 254 68 L CP 1 SG F 0 SG GS 1 W 255 60 M GS 0 SG /Symbol FF [24 0 0 -24 0 0] MS (t) SH GR GR % TEXT NP 0 SG NP 194 122 M 263 122 L 263 145 L 194 145 L CP 1 SG F 0 SG GS 1 W 195 140 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (q\(k\),q\(k\)) SH GR GR % POLY/OPEN-SPLINE 0 SG GS NP 230 125 M 245 125 L TGSM 1 W S GR % TEXT NP 0 SG NP 39 310 M 174 310 L 174 340 L 39 340 L CP 1 SG F 0 SG GS 1 W 40 335 M GS 0 SG /Helvetica FF [24 0 0 -24 0 0] MS (Source Host) SH GR GR % TEXT NP 0 SG NP 289 310 M 472 310 L 472 340 L 289 340 L CP 1 SG F 0 SG GS 1 W 290 335 M GS 0 SG /Helvetica FF [24 0 0 -24 0 0] MS (Destination Host) SH GR GR % TEXT NP 0 SG NP 44 146 M 78 146 L 78 170 L 44 170 L CP 1 SG F 0 SG GS 1 W 45 165 M GS 0 SG /Helvetica-Oblique FF [20 0 0 -20 0 0] MS (n\(k\)) SH GR GR % TEXT NP 0 SG NP 224 227 M 265 227 L 265 250 L 224 250 L CP 1 SG F 0 SG GS 1 W 225 245 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (min) SH 0 SG /Helvetica-Oblique FF [12 0 0 -12 0 0] MS (th) SH GR GR % TEXT NP 0 SG NP 194 247 M 241 247 L 241 270 L 194 270 L CP 1 SG F 0 SG GS 1 W 195 265 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (max) SH 0 SG /Helvetica-Oblique FF [12 0 0 -12 0 0] MS (th) SH GR GR % POLY/OPEN-SPLINE 0 SG GS NP 325 120 M -35 20 atan DU cos 10.000 MU 345 exch SU exch sin 10.000 MU 85 exch SU L TGSM 2 W S 1 W GR GS TGSM NP 345 85 10.000 4.000 20 -35 TGAT 1 SG CP F 0 SG NP 345 85 10.000 4.000 20 -35 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 330 205 M 40 30 atan DU cos 10.000 MU 360 exch SU exch sin 10.000 MU 245 exch SU L TGSM 2 W S 1 W GR GS TGSM NP 360 245 10.000 4.000 30 40 TGAT 1 SG CP F 0 SG NP 360 245 10.000 4.000 30 40 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 135 105 M 190 160 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 255 155 M 255 205 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 245 155 M 245 205 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 235 155 M 235 205 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 225 155 M 225 205 L TGSM 1 W S GR % BOX 0 SG NP 195 155 M 265 155 L 265 205 L 195 205 L CP F GS 10 SM GS NP 195 155 M 265 155 L 265 205 L 195 205 L CP 2 W S GR GR % POLY/OPEN-SPLINE 0 SG GS NP 250 150 M 250 200 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 240 150 M 240 200 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 230 150 M 230 200 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 220 150 M 220 200 L TGSM 1 W S GR % BOX 0 SG NP 190 150 M 260 150 L 260 200 L 190 200 L CP 1 SG F 0 SG GS 10 SM GS NP 190 150 M 260 150 L 260 200 L 190 200 L CP 2 W S GR GR % OVAL 0 SG NP 285 175 25 30 TGEL CP 1 SG F 0 SG GS GS NP 285 175 25 30 TGEL 2 W S GR GR % POLY/OPEN-SPLINE 0 SG GS NP 250 150 M 250 200 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 240 150 M 240 200 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 230 150 M 230 200 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 220 150 M 220 200 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 220 205 M 220 245 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 240 205 M 240 225 L TGSM 1 W S GR % POLY/OPEN-SPLINE 0 SG GS NP 265 215 M 0 45 atan DU cos 10.000 MU 310 exch SU exch sin 10.000 MU 215 exch SU L TGSM 2 W S 1 W GR GS TGSM NP 310 215 10.000 4.000 45 0 TGAT 1 SG CP F 0 SG NP 310 215 10.000 4.000 45 0 TGAT CP F GR % TEXT NP 0 SG NP 279 216 M 293 216 L 293 239 L 279 239 L CP 1 SG F 0 SG GS 1 W 280 235 M GS 0 SG /Helvetica FF [20 0 0 -20 0 0] MS (B) SH GR GR GR tgifsavedpage restore end showpage %%Trailer %MatchingCreationDate: Tue Dec 18 00:47:58 2001 %%DocumentFonts: Symbol %%+ Helvetica-Oblique %%+ Helvetica %%EOF %%EndDocument @endspecial Fq 322 1067 a(Figur) o(e) p 576 1067 a(1:) p Fr 671 1067 a(Analytic) p 978 1067 a(model.) -222 1407 y(This) p -55 1407 a(paper) p 149 1407 a(is) p 224 1407 a(or) o(ganized) p 569 1407 a(as) p 658 1407 a(follo) n(ws.) p 951 1407 a(In) p 1040 1407 a(Section) p 1309 1407 a(2,) p 1391 1407 a(we) p 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337 4246 a(their) p 513 4246 a(windo) n(w) p 801 4246 a(sizes) p 986 4246 a(synchronously) p 1469 4246 a(,) p 1510 4246 a(and) p 1654 4246 a(\(5\)) -222 4346 y(the) p -91 4346 a(a) n(v) o(erage) p 194 4346 a(queue) p 422 4346 a(length) p 659 4300 41 4 v Fo 659 4346 a(q) p Fr 728 4346 a(is) p 813 4346 a(between) p Fo 1120 4346 a(min) p Fn 1272 4358 a(th) p Fr 1369 4346 a(and) p Fo 1518 4346 a(max) p Fn 1682 4358 a(th) p Fr -222 4445 a(because) p 61 4445 a(control) p 317 4445 a(parameters) p 702 4445 a(of) p 791 4445 a(the) p 913 4445 a(RED) p 1100 4445 a(gate) n(w) o(ay) p 1393 4445 a(are) p 1515 4445 a(con\002g-) -222 4545 y(ured) p -51 4545 a(appropriately) p 390 4545 a(.) p 443 4545 a(Note) p 628 4545 a(that) p 777 4545 a(v) n(alidity) p 1052 4545 a(of) p 1145 4545 a(these) p 1340 4545 a(assumptions) -222 4645 y(is) p -146 4645 a(discussed) p 193 4645 a(in) p 278 4645 a([8].) -222 4827 y(Under) p 22 4827 a(these) p 229 4827 a(assumptions,) p 701 4827 a(the) p 839 4827 a(entire) p 1065 4827 a(netw) o(ork) p 1373 4827 a(is) p 1464 4827 a(modeled) -222 4927 y(by) p -104 4927 a(a) p -32 4927 a(discrete-time) p 437 4927 a(system,) p 727 4927 a(where) p 965 4927 a(a) p 1037 4927 a(time) p 1220 4927 a(slot) p 1376 4927 a(of) p 1480 4927 a(the) p 1617 4927 a(sys-) -222 5027 y(tem) p -78 5027 a(corresponds) p 343 5027 a(to) p 427 5027 a(the) p 549 5027 a(round-trip) p 905 5027 a(time) p 1072 5027 a(of) p 1161 5027 a(TCP) p 1333 5027 a(connections.) -222 5126 y(Namely) p 37 5126 a(,) p 83 5126 a(the) p 211 5126 a(deri) n(v) n(ations) p 602 5126 a(of) p 697 5126 a(the) p 824 5126 a(windo) n(w) p 1116 5126 a(size) p Fo 1271 5126 a(w) p Fm 1332 5126 a(\() p Fo(k) p Fm 1410 5126 a(\)) p Fr(,) p 1491 5126 a(the) p 1618 5126 a(cur) n(-) -222 5226 y(rent) p -67 5226 a(queue) p 157 5226 a(length) p Fo 390 5226 a(q) p Fm 430 5226 a(\() p Fo(k) p Fm 508 5226 a(\)) p Fr(,) p 589 5226 a(and) p 734 5226 a(the) p 862 5226 a(a) n(v) o(erage) p 1143 5226 a(queue) p 1367 5226 a(length) p 1600 5180 V Fo 1600 5226 a(q) p Fm 1640 5226 a(\() p Fo(k) p Fm 1718 5226 a(\)) p Fr -222 5326 a(are) p -100 5326 a(gi) n(v) o(en) p 102 5326 a(by) p 206 5326 a(the) p 328 5326 a(follo) n(wing) p 670 5326 a(equations.) p Fo -89 5540 a(w) p Fm -28 5540 a(\() p Fo(k) p Fm 69 5540 a(+) p 152 5494 39 4 v Fo 152 5540 a(s) p Fm(\() p Fo(k) p Fm 269 5540 a(\)\)) p 417 5540 a(=) p Fo 575 5484 a(w) p Fm 636 5484 a(\() p Fo(k) p Fm 714 5484 a(\)) p 765 5484 a(+) p 848 5438 V Fo 848 5484 a(s) p Fm(\() p Fo(k) p Fm 965 5484 a(\)) p Fs 1016 5484 a(\000) p Fm 1099 5484 a(1) p 575 5521 566 4 v 837 5597 a(2) p Fr 1654 5540 a(\(1\)) p Fo -67 5748 a(q) p Fm -27 5748 a(\() p Fo(k) p Fm 69 5748 a(+) p 152 5703 39 4 v Fo 152 5748 a(s) p Fm(\() p Fo(k) p Fm 269 5748 a(\)\)) p Fs 417 5748 a(') p Fo 575 5692 a(n) p Fm(\() p Fo(k) p Fm 703 5692 a(\)) p 749 5692 a(\() p Fo(w) p Fm 842 5692 a(\() p Fo(k) p Fm 920 5692 a(\)) p 971 5692 a(+) p 1055 5647 V Fo 1055 5692 a(s) p Fm 1093 5692 a(\() p Fo(k) p Fm 1171 5692 a(\)) p Fs 1222 5692 a(\000) p Fm 1305 5692 a(1\)) p 575 5729 805 4 v 956 5805 a(2) p Fs 1408 5748 a(\000) p Fo 1491 5748 a(B) p 1572 5748 a(\034) p Fr 1654 5748 a(\(2\)) p Fq 2429 164 a(T) p 2476 164 a(able) p 2645 164 a(1:) p Fr 2740 164 a(De\002nitions) p 3129 164 a(of) p 3219 164 a(symbols.) p 1987 275 2029 4 v 1987 1321 4 1047 v Fo 2071 370 a(min) p Fn 2223 382 a(th) p Fr 2397 370 a(minimum) p 2740 370 a(threshold) p 3070 370 a(v) n(alue) p Fo 2065 469 a(max) p Fn 2229 481 a(th) p Fr 2397 469 a(maximum) p 2754 469 a(threshold) p 3084 469 a(v) n(alue) p Fo 2080 569 a(max) p Fn 2244 581 a(p) p Fr 2397 569 a(maximum) p 2754 569 a(pack) o(et) p 2991 569 a(marking) p 3288 569 a(probability) p Fo 2135 669 a(q) p Fn 2172 681 a(w) p Fr 2397 669 a(weight) p 2643 669 a(f) o(actor) p 2857 669 a(for) p 2974 669 a(a) n(v) o (eraging) p Fo 2158 768 a(\034) p Fr 2397 768 a(propagation) p 2814 768 a(delay) p 3014 768 a(of) p 3104 768 a(TCP) p 3277 768 a(connections) p Fo 2147 868 a(B) p Fr 2397 868 a(processing) p 2772 868 a(speed) p 2982 868 a(of) p 3072 868 a(the) p 3194 868 a(RED) p 3381 868 a(gate) n(w) o(ay) p Fo 2095 968 a(w) p Fm 2156 968 a(\() p Fo(k) p Fm 2234 968 a(\)) p Fr 2397 968 a(windo) n(w) p 2683 968 a(size) p 2833 968 a(at) p 2913 968 a(slot) p Fo 3054 968 a(k) 2106 1067 y(q) p Fm 2146 1067 a(\() p Fo(k) p Fm 2224 1067 a(\)) p Fr 2397 1067 a(current) p 2652 1067 a(queue) p 2871 1067 a(length) p 3100 1067 a(at) p 3180 1067 a(slot) p Fo 3321 1067 a(k) p 2106 1121 41 4 v 2106 1167 a(q) p Fm 2146 1167 a(\() p Fo(k) p Fm 2224 1167 a(\)) p Fr 2397 1167 a(a) n(v) o(erage) p 2673 1167 a(queue) p 2892 1167 a(length) p 3120 1167 a(at) p 3201 1167 a(slot) p Fo 3341 1167 a(k) 2101 1266 y(n) p Fm(\() p Fo(k) p Fm 2229 1266 a(\)) p Fr 2397 1266 a(the) p 2519 1266 a(number) p 2793 1266 a(of) p 2883 1266 a(TCP) p 3056 1266 a(connections) p 3473 1266 a(at) p 3554 1266 a(slot) p Fo 3695 1266 a(k) p 4012 1321 4 1047 v 1987 1324 2029 4 v 2141 1630 41 4 v 2141 1676 a(q) p Fm 2181 1676 a(\() p Fo(k) p Fm 2278 1676 a(+) p 2361 1630 39 4 v Fo 2361 1676 a(s) p Fm(\() p Fo(k) p Fm 2478 1676 a(\)\)) p Fs 2626 1676 a(') p Fm 2773 1676 a(\(1) p Fs 2866 1676 a(\000) p Fo 2949 1676 a(q) p Fn 2986 1688 a(w) p Fm 3039 1676 a(\)) p 3071 1592 59 4 v Fn 3071 1642 a(X) p Fl 3131 1642 a(\() p Fn(k) p Fl 3193 1642 a(\)) p 3237 1630 41 4 v Fo 3237 1676 a(q) p Fm 3277 1676 a(\() p Fo(k) p Fm 3355 1676 a(\)) 2773 1821 y(+) p Fs(f) p Fm(1) p Fs 2939 1821 a(\000) p Fm 3022 1821 a(\(1) p Fs 3115 1821 a(\000) p Fo 3198 1821 a(q) p Fn 3235 1833 a(w) p Fm 3288 1821 a(\)) p 3320 1737 59 4 v Fn 3320 1786 a(X) p Fl 3380 1786 a(\() p Fn(k) p Fl 3442 1786 a(\)) p Fs 3472 1821 a(g) p Fo 3528 1821 a(q) p Fm 3568 1821 a(\() p Fo(k) p Fm 3646 1821 a(\)) p Fr 3862 1821 a(\(3\)) 1987 2007 y(where) p 2210 1940 76 4 v Fo 2210 2007 a(X) p Fm 2285 2007 a(\() p Fo(k) p Fm 2363 2007 a(\)) p Fr 2417 2007 a(and) p 2557 1961 39 4 v Fo 2557 2007 a(s) p Fm(\() p Fo(k) p Fm 2674 2007 a(\)) p Fr 2727 2007 a(are) p 2849 2007 a(gi) n(v) o(en) p 3051 2007 a(by) p 1987 2176 76 4 v Fo 1987 2243 a(X) p Fm 2062 2243 a(\() p Fo(k) p Fm 2140 2243 a(\)) p 2255 2243 a(=) 2413 2187 y(1) p 2413 2224 42 4 v 2413 2300 a(2) p Fk 2492 2126 a(\022) p Fo 2656 2187 a(max) p Fn 2820 2199 a(th) p Fs 2907 2187 a(\000) p Fo 2990 2187 a(min) p Fn 3142 2199 a(th) p 2563 2224 739 4 v Fo 2563 2300 a(max) p Fn 2727 2312 a(p) p Fm 2766 2300 a(\() p 2798 2254 41 4 v Fo(q) p Fm 2838 2300 a(\() p Fo(k) p Fm 2916 2300 a(\)) p Fs 2967 2300 a(\000) p Fo 3050 2300 a(min) p Fn 3202 2312 a(th) p Fm 3269 2300 a(\)) 3330 2243 y(+) p 3413 2243 a(1) p Fk 3455 2126 a(\023) p 2023 2496 39 4 v Fo 2023 2542 a(s) p Fm(\() p Fo(k) p Fm 2140 2542 a(\)) p 2255 2542 a(=) 2413 2486 y(1) p 2413 2523 42 4 v 2413 2599 a(2) p Fs 2483 2542 a(\000) p Fo 2566 2542 a(w) p Fm 2627 2542 a(\() p Fo(k) p Fm 2705 2542 a(\)) p 2756 2542 a(+) p Fk 2849 2364 a(q) p 2932 2364 1145 4 v Fo 2932 2465 a(n) p Fm(\() p Fo(k) p Fm 3060 2465 a(\)) p Fl 3092 2441 a(2) p Fm 3130 2465 a(\(1) p Fs 3222 2465 a(\000) p Fm 3305 2465 a(2) p Fo(w) p Fm 3408 2465 a(\() p Fo(k) p Fm 3486 2465 a(\)\)) p Fl 3550 2441 a(2) p Fm 3607 2465 a(+) p 3690 2465 a(8) p Fo(n) p Fm(\() p Fo(k) p Fm 3860 2465 a(\)) p 3892 2398 76 4 v Fo(X) p Fm 3967 2465 a(\() p Fo(k) p Fm 4045 2465 a(\)) p 2849 2523 1228 4 v 3362 2599 a(2) p Fo(n) p Fm(\() p Fo(k) p Fm 3532 2599 a(\)) p Fr 1987 2853 a(Refer) p 2192 2853 a(to) p 2277 2853 a([8,) p 2388 2853 a(11]) p 2519 2853 a(for) p 2637 2853 a(the) p 2759 2853 a(detail) p 2964 2853 a(of) p 3054 2853 a(the) p 3176 2853 a(deri) n(v) n(ation.) p Fq 2430 3200 a(3) p 2513 3200 a(T) p 2562 3200 a(ransient) p 2874 3200 a(Beha) n(vior) p 3215 3200 a(Analysis) p Fr 1987 3414 a(In) p 2086 3414 a(what) p 2278 3414 a(follo) n(ws,) p 2579 3414 a(we) p 2706 3414 a(analyze) p 2990 3414 a(the) p 3122 3414 a(transient) p 3439 3414 a(beha) n(vior) p 3758 3414 a(of) p 3858 3414 a(the) 1987 3513 y(RED) p 2183 3513 a(gate) n(w) o(ay) p 2486 3513 a(for) p 2613 3513 a(v) n(arious) p 2886 3513 a(types) p 3091 3513 a(of) p 3191 3513 a(TCP) p 3373 3513 a(connection) p 3768 3513 a(v) n(aria-) 1987 3613 y(tions) p 2180 3613 a(by) p 2295 3613 a(utilizing) p 2603 3613 a(the) p 2737 3613 a(state) p 2921 3613 a(transition) p 3266 3613 a(equations) p 3616 3613 a(\(Eqs.) p 3821 3613 a(\(1\)\226) 1987 3713 y(\(3\)\).) p 2187 3713 a(The) p 2347 3713 a(congestion) p 2737 3713 a(control) p 3003 3713 a(mechanism) p 3412 3713 a(of) p 3511 3713 a(TCP) p 3694 3713 a(has) p 3835 3713 a(tw) o(o) 1987 3812 y(operation) p 2327 3812 a(phases:) p 2609 3812 a(the) p Fp 2737 3812 a(cong) o(estion) p 3123 3812 a(avoidance) p 3491 3812 a(phase) p Fr 3711 3812 a(and) p 3858 3812 a(the) p Fp 1987 3912 a(slow) p 2161 3912 a(start) p 2335 3912 a(phase) p Fr(.) p 2579 3912 a(Similar) p 2845 3912 a(to) p 2932 3912 a([11],) p 3113 3912 a(we) p 3232 3912 a(use) p 3365 3912 a(tw) o(o) p 3510 3912 a(dif) n(ferent) p 3816 3912 a(ana-) 1987 4012 y(lytic) p 2154 4012 a(methods) p 2455 4012 a(according) p 2802 4012 a(to) p 2887 4012 a(the) p 3008 4012 a(operation) p 3342 4012 a(phase) p 3550 4012 a(of) p 3639 4012 a(TCP) p 3812 4012 a(con-) 1987 4111 y(nections.) 1987 4294 y(W) p 2058 4294 a(e) p 2125 4294 a(\002rst) p 2284 4294 a(classify) p 2568 4294 a(types) p 2773 4294 a(of) p 2872 4294 a(TCP) p 3055 4294 a(connection) p 3449 4294 a(v) n(ariations.) p 3848 4294 a(Let) p Fo 1987 4393 a(N) p Fr 2097 4393 a(be) p 2210 4393 a(the) p 2346 4393 a(number) p 2634 4393 a(of) p 2737 4393 a(TCP) p 2924 4393 a(connections) p 3355 4393 a(established) p 3759 4393 a(in) p 3858 4393 a(the) 1987 4493 y(netw) o(ork.) p 2341 4493 a(There) p 2568 4493 a(are) p 2703 4493 a(four) p 2874 4493 a(types) p 3082 4493 a(of) p 3185 4493 a(TCP) p 3370 4493 a(connection) p 3768 4493 a(v) n(aria-) 1987 4593 y(tions) p 2169 4593 a([11]:) p Fq 1987 4845 a(C1:) p Fm 2157 4845 a(\001) p Fo(N) p Fr 2339 4845 a(of) p Fo 2445 4845 a(N) p Fr 2557 4845 a(TCP) p 2747 4845 a(connections) p 3180 4845 a(terminate) p 3530 4845 a(\(or) p 3664 4845 a(suspend\)) 2153 4945 y(their) p 2326 4945 a(data) p 2485 4945 a(transmissions.) p Fq 1987 5118 a(C2:) p Fm 2157 5118 a(\001) p Fo(N) p Fr 2323 5118 a(TCP) p 2496 5118 a(connections) p 2914 5118 a(resume) p 3175 5118 a(their) p 3348 5118 a(data) p 3507 5118 a(transmissions) 2153 5218 y(after) p 2326 5218 a(a) p 2383 5218 a(short) p 2570 5218 a(idle) p 2715 5218 a(period.) p Fq 1987 5391 a(C3:) p Fm 2157 5391 a(\001) p Fo(N) p Fr 2323 5391 a(TCP) p 2496 5391 a(connections) p 2914 5391 a(resume) p 3175 5391 a(their) p 3348 5391 a(data) p 3507 5391 a(transmissions) 2153 5491 y(after) p 2326 5491 a(a) p 2383 5491 a(long) p 2551 5491 a(idle) p 2697 5491 a(period.) p Fq 1987 5664 a(C4:) p Fm 2157 5664 a(\001) p Fo(N) p Fr 2326 5664 a(TCP) p 2501 5664 a(connections) p 2922 5664 a(ne) n(wly) p 3146 5664 a(start) p 3312 5664 a(their) p 3488 5664 a(data) p 3650 5664 a(transmis-) 2153 5764 y(sions.) 3830 6013 y(p.) p 3918 6013 a(2) p 90 rotate dyy eop %%Page: 3 3 3 2 bop Fr -222 107 a(In) p -134 107 a(the) p -14 107 a(case) p 148 107 a(of) p 236 107 a(C1) p 352 107 a(\(or) p 468 107 a(C2\),) p Fo 633 107 a(N) p Fs 720 107 a(\000) p Fm 797 107 a(\001) p Fo(N) p Fr 960 107 a(\(or) p Fo 1076 107 a(N) p Fm 1164 107 a(+) p 1241 107 a(\001) p Fo(N) p Fr 1386 107 a(\)) p 1432 107 a(TCP) p 1603 107 a(con-) -222 206 y(nections) p 77 206 a(will) p 228 206 a(operate) p 494 206 a(in) p 581 206 a(the) p 705 206 a(congestion) p 1086 206 a(a) n(v) n(oidance) p 1442 206 a(phase.) p 1681 206 a(In) -222 306 y(the) p -98 306 a(cases) p 99 306 a(of) p 191 306 a(C3) p 310 306 a(and) p 453 306 a(C4,) p Fm 593 306 a(\001) p Fo(N) p Fr 761 306 a(TCP) p 935 306 a(connections) p 1354 306 a(will) p 1506 306 a(operate) -222 406 y(in) p -138 406 a(the) p -17 406 a(slo) n(w) p 157 406 a(start) p 320 406 a(phase) p 529 406 a(while) p Fo 733 406 a(N) p Fr 828 406 a(TCP) p 1000 406 a(connections) p 1416 406 a(will) p 1565 406 a(in) p 1649 406 a(the) -222 505 y(congestion) p 158 505 a(a) n(v) n(oidance) p 512 505 a(phase.) -222 688 y(In) p -131 688 a(what) p 53 688 a(follo) n(ws,) p 343 688 a(the) p 467 688 a(equilibrium) p 877 688 a(v) n(alue) p 1077 688 a(of) p 1168 688 a(a) p 1227 688 a(v) n(ariable) p Fo 1515 688 a(x) p Fm(\() p Fo(k) p Fm 1640 688 a(\)) p Fr 1695 688 a(is) -222 788 y(denoted) p 62 788 a(by) p Fo 166 788 a(x) p Fj 213 757 a(\003) p Fr 252 788 a(.) p 300 788 a(F) o(or) p 436 788 a(enabling) p 743 788 a(the) p 866 788 a(transient) p 1173 788 a(beha) n(vior) p 1483 788 a(analysis) -222 887 y(of) p -131 887 a(the) p -8 887 a(RED) p 180 887 a(gate) n(w) o(ay) p 450 887 a(,) p 491 887 a(the) p 615 887 a(state) p 789 887 a(transition) p 1124 887 a(equations) p 1464 887 a(gi) n(v) o(en) p 1667 887 a(by) -222 987 y(Eqs.) p -59 987 a(\(1\)\226\(3\)) p 194 987 a(are) p 313 987 a(linearly) p 584 987 a(approximated) p 1059 987 a(around) p 1307 987 a(a) n(v) o(erage) p 1580 987 a(equi-) -222 1086 y(librium) p 42 1086 a(v) n(alues) p Fo 271 1086 a(w) p Fj 332 1056 a(\003) p Fr 371 1086 a(,) p Fo 411 1086 a(q) p Fj 451 1056 a(\003) p Fr 489 1086 a(,) p 529 1041 41 4 v Fo 529 1086 a(q) p Fj 569 1055 a(\003) p Fr 607 1086 a(,) p 648 1086 a(and) p Fo 786 1086 a(n) p Fj 836 1056 a(\003) p Fr 874 1086 a(.) p 920 1086 a(Then,) p 1131 1086 a(the) p 1252 1086 a(linearized) p 1598 1086 a(state) -222 1186 y(transition) p 112 1186 a(equations) p 451 1186 a(can) p 587 1186 a(be) p 686 1186 a(written) p 942 1186 a(in) p 1028 1186 a(a) p 1085 1186 a(matrix) p 1323 1186 a(form) p 1505 1186 a([8,) p 1616 1186 a(11]:) p 327 1315 51 4 v Fi 327 1362 a(x) p Fm(\() p Fo(k) p Fm 474 1362 a(+) p 557 1316 39 4 v Fo 557 1362 a(s) p Fm 595 1362 a(\() p Fo(k) p Fm 673 1362 a(\)\)) p Fs 821 1362 a(') p Fi 969 1362 a(A) p 1041 1315 51 4 v(x) p Fm(\() p Fo(k) p Fm 1169 1362 a(\)) p Fr 1654 1362 a(\(4\)) -222 1537 y(where) p Fq 5 1537 a(A) p Fr 89 1537 a(is) p 168 1537 a(called) p 391 1537 a(a) p Fp 452 1537 a(state) p 632 1537 a(tr) o(ansition) p 978 1537 a(matrix) p Fr(,) p 1241 1537 a(and) p 1385 1490 V Fi 1385 1537 a(x) p Fm(\() p Fo(k) p Fm 1513 1537 a(\)) p Fr 1569 1537 a(is) p 1649 1537 a(the) -222 1637 y(dif) n(ference) p 146 1637 a(between) p 457 1637 a(the) p 593 1637 a(state) p 779 1637 a(v) o(ector) p Fq 1020 1637 a(x) p Fm 1061 1637 a(\() p Fo(k) p Fm 1139 1637 a(\)) p Fr 1206 1637 a(and) p 1360 1637 a(the) p 1495 1637 a(a) n(v) o(erage) -222 1737 y(equilibrium) p 186 1737 a(v) n(alues.) p 443 1737 a(Namely) p 702 1737 a(,) p 742 1690 V Fi 742 1737 a(x) p Fm(\() p Fo(k) p Fm 870 1737 a(\)) p Fr 923 1737 a(is) p 999 1737 a(de\002ned) p 1265 1737 a(as) p 285 2015 V Fi 285 2062 a(x) p Fm(\() p Fo(k) p Fm 413 2062 a(\)) p Fs 529 2062 a(\021) p Fk 676 1845 a(2) 676 1991 y(6) 676 2041 y(6) 676 2094 y(4) p Fo 773 1911 a(w) p Fm 834 1911 a(\() p Fo(k) p Fm 912 1911 a(\)) p Fs 964 1911 a(\000) p Fo 1047 1911 a(w) p Fj 1108 1881 a(\003) p Fo 795 2011 a(q) p Fm 835 2011 a(\() p Fo(k) p Fm 913 2011 a(\)) p Fs 964 2011 a(\000) p Fo 1047 2011 a(q) p Fj 1087 1981 a(\003) p 795 2065 41 4 v Fo 795 2111 a(q) p Fm 835 2111 a(\() p Fo(k) p Fm 913 2111 a(\)) p Fs 964 2111 a(\000) p 1047 2065 V Fo 1047 2111 a(q) p Fj 1087 2079 a(\003) p Fo 785 2210 a(n) p Fm(\() p Fo(k) p Fm 913 2210 a(\)) p Fs 964 2210 a(\000) p Fo 1047 2210 a(n) p Fj 1097 2180 a(\003) p Fk 1188 1845 a(3) 1188 1991 y(7) 1188 2041 y(7) 1188 2094 y(5) p Fr -222 2381 a(As) p -108 2381 a(can) p 30 2381 a(be) p 131 2381 a(found) p 347 2381 a(from) p 530 2381 a(Eq.) p 665 2381 a(\(4\),) p 806 2381 a(the) p 929 2381 a(system) p 1182 2381 a(state) p 1357 2381 a(changes) p 1646 2381 a(e) n(v-) -222 2481 y(ery) p -96 2435 39 4 v Fo -96 2481 a(s) p Fm(\() p Fo(k) p Fm 21 2481 a(\)) p Fr 74 2481 a(slot,) p 235 2481 a(which) p 459 2481 a(represents) p 816 2481 a(the) p 937 2481 a(number) p 1212 2481 a(of) p 1301 2481 a(adjacent) p 1598 2481 a(slots) -222 2580 y(in) p -136 2580 a(which) p 89 2580 a(all) p 193 2580 a(pack) o(ets) p 463 2580 a(ha) n(v) o(e) p 638 2580 a(been) p 817 2580 a(unmark) o(ed) p 1170 2580 a(by) p 1274 2580 a(the) p 1397 2580 a(RED) p 1585 2580 a(gate-) -222 2680 y(w) o(ay) p -61 2680 a([8].) p 90 2680 a(In) p 183 2680 a(what) p 368 2680 a(follo) n(ws,) p 660 2680 a(we) p 780 2680 a(de\002ne) p Fp 1007 2680 a(sequence) p Fo 1334 2680 a(k) p Fr 1404 2680 a(as) p 1496 2680 a(a) p 1557 2680 a(group) -222 2780 y(of) p -132 2734 V Fo -132 2780 a(s) p Fm -94 2780 a(\() p Fo(k) p Fm -16 2780 a(\)) p Fr 37 2780 a(slots.) p 236 2780 a(W) p 307 2780 a(e) p 365 2780 a(also) p 519 2780 a(de\002ne) p Fo 743 2780 a(S) p Fn 794 2792 a(k) p Fr 855 2780 a(as) p 945 2780 a(the) p 1066 2780 a(\002rst) p 1216 2780 a(slot) p 1356 2780 a(of) p 1446 2780 a(sequence) p Fo -222 2879 a(k) p Fr -176 2879 a(.) -222 3062 y(First,) p -14 3062 a(the) p 120 3062 a(cases) p 328 3062 a(\(C1) p 485 3062 a(and) p 637 3062 a(C2\),) p 818 3062 a(where) p 1054 3062 a(all) p 1169 3062 a(TCP) p 1354 3062 a(connections) -222 3161 y(will) p -77 3161 a(operate) p 184 3161 a(in) p 264 3161 a(the) p 382 3161 a(congestion) p 758 3161 a(a) n(v) n(oidance) p 1107 3161 a(phase) p 1312 3161 a(after) p 1481 3161 a(the) p 1598 3161 a(TCP) -222 3261 y(connection) p 161 3261 a(v) n(ariation,) p 494 3261 a(are) p 614 3261 a(considered.) p 1019 3261 a(Let) p Fo 1148 3261 a(u) p Fm(\() p Fo(k) p Fm 1274 3261 a(\)) p Fr 1325 3261 a(be) p 1422 3261 a(the) p 1542 3261 a(dif) n(fer) n(-) -222 3361 y(ence) p -44 3361 a(in) p 46 3361 a(the) p 173 3361 a(numbers) p 484 3361 a(of) p 579 3361 a(TCP) p 756 3361 a(connections) p 1178 3361 a(at) p 1264 3361 a(slot) p Fo 1409 3361 a(k) p Fs 1477 3361 a(\000) p Fm 1564 3361 a(1) p Fr 1631 3361 a(and) -222 3460 y(slot) p Fo -78 3460 a(k) p Fr -32 3460 a(.) p 25 3460 a(Also) p 206 3460 a(let) p Fo 314 3460 a(y) p Fm 358 3460 a(\() p Fo(k) p Fm 436 3460 a(\)) p Fr 492 3460 a(be) p 595 3460 a(the) p 721 3460 a(queue) p 943 3460 a(length) p 1175 3460 a(of) p 1269 3460 a(the) p 1394 3460 a(RED) p 1585 3460 a(gate-) 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a(start) p 1435 4667 a(phase) p 1658 4667 a(af-) -222 4766 y(ter) p -111 4766 a(the) p 15 4766 a(TCP) p 191 4766 a(connection) p 579 4766 a(v) n(ariation,) p 917 4766 a(are) p 1043 4766 a(considered.) p 1458 4766 a(Let) p Fo 1592 4766 a(u) p Fm(\() p Fo(k) p Fm 1718 4766 a(\)) p Fr -222 4866 a(be) p -119 4866 a(the) p 7 4866 a(dif) n(ference) p 366 4866 a(in) p 455 4866 a(the) p 581 4866 a(total) p 754 4866 a(numbers) p 1064 4866 a(of) p 1158 4866 a(pack) o(ets) p 1431 4866 a(sent) p 1589 4866 a(from) -222 4966 y(source) p 19 4966 a(hosts) p 214 4966 a(operating) p 552 4966 a(in) p 641 4966 a(the) p 767 4966 a(slo) n(w) p 946 4966 a(start) p 1114 4966 a(phase) p 1327 4966 a(at) p 1412 4966 a(slot) p Fo 1556 4966 a(k) p Fs 1623 4966 a(\000) p Fm 1709 4966 a(1) p Fr -222 5065 a(and) p -77 5065 a(slot) p Fo 68 5065 a(k) p Fr 114 5065 a(.) p 173 5065 a(Let) p Fo 309 5065 a(y) p Fm 353 5065 a(\() p Fo(k) p Fm 431 5065 a(\)) p Fr 488 5065 a(be) p 591 5065 a(the) p 717 5065 a(queue) p 941 5065 a(length) p 1173 5065 a(of) p 1267 5065 a(the) p 1394 5065 a(RED) p 1585 5065 a(gate-) -222 5165 y(w) o(ay) p -54 5165 a(at) p 37 5165 a(slot) p Fo 188 5165 a(k) p Fr 265 5165 a(\(Fig.) p 455 5165 a(3\).) p 601 5165 a(Similar) p 877 5165 a(to) p 972 5165 a(the) p 1105 5165 a(pre) n(vious) p 1420 5165 a(cases,) p 1649 5165 a(the) -222 5264 y(linearized) p 127 5264 a(state) p 300 5264 a(transition) p 636 5264 a(equations) p 975 5264 a(gi) n(v) o(en) p 1178 5264 a(by) p 1283 5264 a(Eq.) p 1417 5264 a(\(4\)) p 1535 5264 a(can) p 1672 5264 a(be) -222 5364 y(e) o(xtended) p 98 5364 a(to) p 184 5364 a(include) p Fo 450 5364 a(u) p Fm(\() p Fo(k) p Fm 576 5364 a(\)) p Fr 629 5364 a(and) p Fo 771 5364 a(y) p Fm 815 5364 a(\() p Fo(k) p Fm 893 5364 a(\)) p Fr 946 5364 a(as) p 1037 5364 a(the) p 1160 5364 a(input) p 1352 5364 a(and) p 1494 5364 a(the) p 1617 5364 a(out-) -222 5464 y(put,) p -74 5464 a(respecti) n(v) o(ely) p 321 5464 a(.) p 163 5592 V Fi 163 5639 a(x) p Fm(\() p Fo(k) p Fm 310 5639 a(+) p 393 5594 39 4 v Fo 393 5639 a(s) p Fm(\() p Fo(k) p Fm 510 5639 a(\)\)) p 658 5639 a(=) p Fi 805 5639 a(A) p 877 5592 51 4 v(x) p Fm 928 5639 a(\() p Fo(k) p Fm 1006 5639 a(\)) p 1057 5639 a(+) p Fi 1140 5639 a(B) p Fo(u) p Fm(\() p Fo(k) p Fm 1334 5639 a(\)) p Fr 1654 5639 a(\(6\)) p Fo 420 5764 a(y) p Fm 464 5764 a(\() p Fo(k) p Fm 542 5764 a(\)) p 658 5764 a(=) p Fi 805 5764 a(C) p 874 5717 V(x) p Fm(\() p Fo(k) p Fm 1002 5764 a(\)) 2032 885 y @beginspecial 26 @llx 555 @lly 498 @urx 803 @ury 2257 @rwi 1033 @rhi @setspecial %%BeginDocument: figure/model-ca.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 26 555 498 803 %%Title: model-ca %%CreationDate: Sat Jun 8 07:29:56 2002 %%Creator: Tgif-4.1.35 by William Chia-Wei Cheng (william@cs.UCLA.edu) %%ProducedBy: (unknown) %%Pages: 1 %%DocumentFonts: (atend) %%EndComments %%BeginProlog /tgifdict 53 dict def tgifdict begin /tgifarrowtipdict 8 dict def tgifarrowtipdict /mtrx matrix put /TGAT % tgifarrowtip { tgifarrowtipdict begin /dy exch def /dx exch def /h exch def /w exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y translate dy dx atan rotate 0 0 moveto w neg h lineto w neg h neg lineto savematrix setmatrix end } def /TGMAX { exch dup 3 1 roll exch dup 3 1 roll gt { pop } { exch pop } ifelse } def /TGMIN { exch dup 3 1 roll exch dup 3 1 roll lt { pop } { exch pop } ifelse } def /TGSW { stringwidth pop } def /bd { bind def } bind def /GS { gsave } bd /GR { grestore } bd /NP { newpath } bd /CP { closepath } bd /CHP { charpath } bd /CT { curveto } bd /L { lineto } bd /RL { rlineto } bd /M { moveto } bd /RM { rmoveto } bd /S { stroke } bd /F { fill } bd /TR { translate } bd /RO { rotate } bd /SC { scale } bd /MU { mul } bd /DI { div } bd /DU { dup } bd /NE { neg } bd /AD { add } bd /SU { sub } bd /PO { pop } bd /EX { exch } bd /CO { concat } bd /CL { clip } bd /EC { eoclip } bd /EF { eofill } bd /IM { image } bd /IMM { imagemask } bd /ARY { array } bd /SG { setgray } bd /RG { setrgbcolor } bd /SD { setdash } bd /W { setlinewidth } bd /SM { setmiterlimit } bd /SLC { setlinecap } bd /SLJ { setlinejoin } bd /SH { show } bd /FF { findfont } bd /MS { makefont setfont } bd /AR { arcto 4 {pop} repeat } bd /CURP { currentpoint } bd /FLAT { flattenpath strokepath clip newpath } bd /TGSM { tgiforigctm setmatrix } def /TGRM { savematrix setmatrix } def end %%EndProlog %%Page: 1 1 %%PageBoundingBox: 26 555 498 803 tgifdict begin /tgifsavedpage save def 1 SM 1 W 0 SG 72 0 MU 72 11.602 MU TR 72 128 DI 100.000 MU 100 DI DU NE SC GS /tgiforigctm matrix currentmatrix def % POLY/OPEN-SPLINE 0 SG GS NP 605 255 M 715 255 L 715 95 L 215 95 L 215 255 L 0 90 atan DU cos 22.000 MU 305 exch SU exch sin 22.000 MU 255 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 305 255 22.000 9.000 90 0 TGAT 1 SG CP F 0 SG NP 305 255 22.000 9.000 90 0 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 605 305 M 715 305 L 715 465 L 215 465 L 215 305 L 0 90 atan DU cos 22.000 MU 305 exch SU exch sin 22.000 MU 305 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 305 305 22.000 9.000 90 0 TGAT 1 SG CP F 0 SG NP 305 305 22.000 9.000 90 0 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 605 205 M 655 205 L 655 135 L 255 135 L 255 205 L 0 50 atan DU cos 22.000 MU 305 exch SU exch sin 22.000 MU 205 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 305 205 22.000 9.000 50 0 TGAT 1 SG CP F 0 SG NP 305 205 22.000 9.000 50 0 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 605 355 M 655 355 L 655 425 L 255 425 L 255 355 L 0 50 atan DU cos 22.000 MU 305 exch SU exch sin 22.000 MU 355 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 305 355 22.000 9.000 50 0 TGAT 1 SG CP F 0 SG NP 305 355 22.000 9.000 50 0 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 715 255 M 0 160 atan DU cos 22.000 MU 875 exch SU exch sin 22.000 MU 255 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 875 255 22.000 9.000 160 0 TGAT 1 SG CP F 0 SG NP 875 255 22.000 9.000 160 0 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 65 355 M 0 190 atan DU cos 22.000 MU 255 exch SU exch sin 22.000 MU 355 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 255 355 22.000 9.000 190 0 TGAT 1 SG CP F 0 SG NP 255 355 22.000 9.000 190 0 TGAT CP F GR % BOX 0 SG NP 310 160 M 610 160 L 610 400 L 310 400 L CP F GS 10 SM GS NP 310 160 M 610 160 L 610 400 L 310 400 L CP 2 W S GR GR % BOX 0 SG NP 300 150 M 600 150 L 600 390 L 300 390 L CP 1 SG F 0 SG GS 10 SM GS NP 300 150 M 600 150 L 600 390 L 300 390 L CP 2 W S GR GR % TEXT NP 0 SG GS 1 W 442 283 M GS 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (A) SH GR GR % TEXT NP 0 SG GS 1 W 522 204 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (w\(k+s\(k\)\)) SH GR GR % TEXT NP 0 SG GS 1 W 522 254 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (q\(k+s\(k\)\)) SH GR GR % TEXT NP 0 SG GS 1 W 522 304 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (q\(k+s\(k\)\)) SH GR GR % TEXT NP 0 SG GS 1 W 522 354 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (n\(k+s\(k\)\)) SH GR GR % TEXT NP 0 SG GS 1 W 306 204 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (w\(k\)) SH GR GR % TEXT NP 0 SG GS 1 W 306 254 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (q\(k\)) SH GR GR % TEXT NP 0 SG GS 1 W 306 304 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (q\(k\)) SH GR GR % TEXT NP 0 SG GS 1 W 306 354 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (n\(k\)) SH GR GR % TEXT NP 0 SG GS 1 W 230 339 M GS 0 SG /Helvetica FF [17 0 0 -17 0 0] MS (+) SH GR GR % TEXT NP 0 SG GS 1 W 261 371 M GS 0 SG /Helvetica FF [17 0 0 -17 0 0] MS (+) SH GR GR % TEXT NP 0 SG NP 109 322 M 142 322 L 142 345 L 109 345 L CP 1 SG F 0 SG GS 1 W 110 340 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (u\(k\)) SH GR GR % TEXT NP 0 SG NP 779 222 M 812 222 L 812 245 L 779 245 L CP 1 SG F 0 SG GS 1 W 780 240 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (y\(k\)) SH GR GR % TEXT NP 0 SG NP 719 202 M 883 202 L 883 223 L 719 223 L CP 1 SG F 0 SG GS 1 W 720 219 M GS 0 SG /Helvetica FF [17 0 0 -17 0 0] MS (Current Queue Length) SH GR GR % TEXT NP 0 SG GS 124 277 TR [1.000 0.000 0.000 0.977 0 1] CO 124 NE 277 NE TR NP 49 276 M 198 276 L 198 321 L 49 321 L CP 1 SG F 0 SG GR GS 1 W 124 277 TR [1.000 0.000 0.000 0.977 0 1] CO 0 18 M GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (Variation in # of ) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (Variation in # of ) SH GR 0 22 RM GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (TCP Connections) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (TCP Connections) SH GR GR % POLY/OPEN-SPLINE 0.159 0.302 0.286 RG GS NP 600 250 M 710 250 L 710 90 L 210 90 L 210 250 L 0 90 atan DU cos 22.000 MU 300 exch SU exch sin 22.000 MU 250 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 300 250 22.000 9.000 90 0 TGAT 1 SG CP F 0.159 0.302 0.286 RG NP 300 250 22.000 9.000 90 0 TGAT CP F GR % POLY/OPEN-SPLINE 0.159 0.302 0.286 RG GS NP 600 300 M 710 300 L 710 460 L 210 460 L 210 300 L 0 90 atan DU cos 22.000 MU 300 exch SU exch sin 22.000 MU 300 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 300 300 22.000 9.000 90 0 TGAT 1 SG CP F 0.159 0.302 0.286 RG NP 300 300 22.000 9.000 90 0 TGAT CP F GR % POLY/OPEN-SPLINE 0.159 0.302 0.286 RG GS NP 600 200 M 650 200 L 650 130 L 250 130 L 250 200 L 0 50 atan DU cos 22.000 MU 300 exch SU exch sin 22.000 MU 200 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 300 200 22.000 9.000 50 0 TGAT 1 SG CP F 0.159 0.302 0.286 RG NP 300 200 22.000 9.000 50 0 TGAT CP F GR % POLY/OPEN-SPLINE 0.159 0.302 0.286 RG GS NP 600 350 M 650 350 L 650 420 L 250 420 L 250 350 L 0 50 atan DU cos 22.000 MU 300 exch SU exch sin 22.000 MU 350 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 300 350 22.000 9.000 50 0 TGAT 1 SG CP F 0.159 0.302 0.286 RG NP 300 350 22.000 9.000 50 0 TGAT CP F GR % POLY/OPEN-SPLINE 0.159 0.302 0.286 RG GS NP 710 250 M 0 160 atan DU cos 22.000 MU 870 exch SU exch sin 22.000 MU 250 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 870 250 22.000 9.000 160 0 TGAT 1 SG CP F 0.159 0.302 0.286 RG NP 870 250 22.000 9.000 160 0 TGAT CP F GR % POLY/OPEN-SPLINE 0.159 0.302 0.286 RG GS NP 60 350 M 0 190 atan DU cos 22.000 MU 250 exch SU exch sin 22.000 MU 350 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 250 350 22.000 9.000 190 0 TGAT 1 SG CP F 0.159 0.302 0.286 RG NP 250 350 22.000 9.000 190 0 TGAT CP F GR % TEXT NP 0 SG NP 375 313 M 512 313 L 512 380 L 375 380 L CP 1 SG F 0 SG GS 1 W 444 332 M GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (State Transition ) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (State Transition ) SH GR 0 22 RM GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (Matrix) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (Matrix) SH GR 0 22 RM GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (of RED and TCP) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (of RED and TCP) SH GR GR % TEXT NP 0 SG NP 305 101 M 600 101 L 600 124 L 305 124 L CP 1 SG F 0 SG GS 1 W 453 120 M GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (Window Size of TCP Connections ) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (Window Size of TCP Connections ) SH GR GR % TEXT NP 0 SG NP 355 59 M 540 59 L 540 82 L 355 82 L CP 1 SG F 0 SG GS 1 W 448 78 M GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (Current Queue Length) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (Current Queue Length) SH GR GR % TEXT NP 0 SG NP 353 471 M 544 471 L 544 494 L 353 494 L CP 1 SG F 0 SG GS 1 W 449 490 M GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (Average Queue Length) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (Average Queue Length) SH GR GR % TEXT NP 0 SG NP 331 428 M 574 428 L 574 451 L 331 451 L CP 1 SG F 0 SG GS 1 W 453 447 M GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (# of Active TCP Connections) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (# of Active TCP Connections) SH GR GR % POLY/OPEN-SPLINE 0 SG GS NP 305 289 M 319 289 L TGSM 2 W S 1 W GR % POLY/OPEN-SPLINE 0 SG GS NP 521 286 M 536 286 L TGSM 2 W S 1 W GR GR tgifsavedpage restore end showpage %%Trailer %MatchingCreationDate: Sat Jun 8 07:29:56 2002 %%DocumentFonts: Helvetica-Oblique %%+ Helvetica %%EOF %%EndDocument @endspecial Fq 1987 1067 a(Figur) o(e) p 2247 1067 a(2:) p Fh 2343 1067 a(Cases) p 2542 1067 a(C1) p 2653 1067 a(and) p 2785 1067 a(C2) p 2896 1067 a(where) p 3103 1067 a(all) p 3202 1067 a(TCP) p 3363 1067 a(connections) p 3744 1067 a(in) p 3826 1067 a(con-) 2331 1159 y(gestion) p 2566 1159 a(a) o(v) o(oidance) p 2884 1159 a(phase.) 2032 2222 y @beginspecial 18 @llx 556 @lly 498 @urx 802 @ury 2257 @rwi 1033 @rhi @setspecial %%BeginDocument: figure/model-ss.eps %!PS-Adobe-3.0 EPSF-3.0 %%BoundingBox: 18 556 498 802 %%Title: model-ss %%CreationDate: Sat Jun 8 07:29:15 2002 %%Creator: Tgif-4.1.35 by William Chia-Wei Cheng (william@cs.UCLA.edu) %%ProducedBy: (unknown) %%Pages: 1 %%DocumentFonts: (atend) %%EndComments %%BeginProlog /tgifdict 53 dict def tgifdict begin /tgifarrowtipdict 8 dict def tgifarrowtipdict /mtrx matrix put /TGAT % tgifarrowtip { tgifarrowtipdict begin /dy exch def /dx exch def /h exch def /w exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y translate dy dx atan rotate 0 0 moveto w neg h lineto w neg h neg lineto savematrix setmatrix end } def /TGMAX { exch dup 3 1 roll exch dup 3 1 roll gt { pop } { exch pop } ifelse } def /TGMIN { exch dup 3 1 roll exch dup 3 1 roll lt { pop } { exch pop } ifelse } def /TGSW { stringwidth pop } def /bd { bind def } bind def /GS { gsave } bd /GR { grestore } bd /NP { newpath } bd /CP { closepath } bd /CHP { charpath } bd /CT { curveto } bd /L { lineto } bd /RL { rlineto } bd /M { moveto } bd /RM { rmoveto } bd /S { stroke } bd /F { fill } bd /TR { translate } bd /RO { rotate } bd /SC { scale } bd /MU { mul } bd /DI { div } bd /DU { dup } bd /NE { neg } bd /AD { add } bd /SU { sub } bd /PO { pop } bd /EX { exch } bd /CO { concat } bd /CL { clip } bd /EC { eoclip } bd /EF { eofill } bd /IM { image } bd /IMM { imagemask } bd /ARY { array } bd /SG { setgray } bd /RG { setrgbcolor } bd /SD { setdash } bd /W { setlinewidth } bd /SM { setmiterlimit } bd /SLC { setlinecap } bd /SLJ { setlinejoin } bd /SH { show } bd /FF { findfont } bd /MS { makefont setfont } bd /AR { arcto 4 {pop} repeat } bd /CURP { currentpoint } bd /FLAT { flattenpath strokepath clip newpath } bd /TGSM { tgiforigctm setmatrix } def /TGRM { savematrix setmatrix } def end %%EndProlog %%Page: 1 1 %%PageBoundingBox: 18 556 498 802 tgifdict begin /tgifsavedpage save def 1 SM 1 W 0 SG 72 0 MU 72 11.602 MU TR 72 128 DI 100.000 MU 100 DI DU NE SC GS /tgiforigctm matrix currentmatrix def % POLY/OPEN-SPLINE 0 SG GS NP 603 253 M 713 253 L 713 93 L 213 93 L 213 253 L 0 90 atan DU cos 22.000 MU 303 exch SU exch sin 22.000 MU 253 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 303 253 22.000 9.000 90 0 TGAT 1 SG CP F 0 SG NP 303 253 22.000 9.000 90 0 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 603 303 M 713 303 L 713 463 L 213 463 L 213 303 L 0 90 atan DU cos 22.000 MU 303 exch SU exch sin 22.000 MU 303 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 303 303 22.000 9.000 90 0 TGAT 1 SG CP F 0 SG NP 303 303 22.000 9.000 90 0 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 603 203 M 653 203 L 653 133 L 253 133 L 253 203 L 0 50 atan DU cos 22.000 MU 303 exch SU exch sin 22.000 MU 203 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 303 203 22.000 9.000 50 0 TGAT 1 SG CP F 0 SG NP 303 203 22.000 9.000 50 0 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 603 353 M 653 353 L 653 423 L 253 423 L 253 353 L 0 50 atan DU cos 22.000 MU 303 exch SU exch sin 22.000 MU 353 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 303 353 22.000 9.000 50 0 TGAT 1 SG CP F 0 SG NP 303 353 22.000 9.000 50 0 TGAT CP F GR % POLY/OPEN-SPLINE 0 SG GS NP 713 253 M 0 160 atan DU cos 22.000 MU 873 exch SU exch sin 22.000 MU 253 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 873 253 22.000 9.000 160 0 TGAT 1 SG CP F 0 SG NP 873 253 22.000 9.000 160 0 TGAT CP F GR % BOX 0 SG NP 310 160 M 610 160 L 610 400 L 310 400 L CP F GS 10 SM GS NP 310 160 M 610 160 L 610 400 L 310 400 L CP 2 W S GR GR % BOX 0 SG NP 300 150 M 600 150 L 600 390 L 300 390 L CP 1 SG F 0 SG GS 10 SM GS NP 300 150 M 600 150 L 600 390 L 300 390 L CP 2 W S GR GR % TEXT NP 0 SG GS 1 W 442 283 M GS 0 SG /Helvetica FF [34 0 0 -34 0 0] MS (A) SH GR GR % TEXT NP 0 SG GS 1 W 523 208 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (w\(k+s\(k\)\)) SH GR GR % TEXT NP 0 SG GS 1 W 523 258 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (q\(k+s\(k\)\)) SH GR GR % TEXT NP 0 SG GS 1 W 523 308 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (q\(k+s\(k\)\)) SH GR GR % TEXT NP 0 SG GS 1 W 523 358 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (n\(k+s\(k\)\)) SH GR GR % TEXT NP 0 SG GS 1 W 306 204 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (w\(k\)) SH GR GR % TEXT NP 0 SG GS 1 W 306 254 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (q\(k\)) SH GR GR % TEXT NP 0 SG GS 1 W 306 304 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (q\(k\)) SH GR GR % TEXT NP 0 SG GS 1 W 306 354 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (n\(k\)) SH GR GR % TEXT NP 0 SG GS 1 W 233 229 M GS 0 SG /Helvetica FF [17 0 0 -17 0 0] MS (+) SH GR GR % TEXT NP 0 SG GS 1 W 261 190 M GS 0 SG /Helvetica FF [17 0 0 -17 0 0] MS (+) SH GR GR % TEXT NP 0 SG NP 115 173 M 148 173 L 148 196 L 115 196 L CP 1 SG F 0 SG GS 1 W 116 191 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (u\(k\)) SH GR GR % TEXT NP 0 SG NP 779 222 M 812 222 L 812 245 L 779 245 L CP 1 SG F 0 SG GS 1 W 780 240 M GS 0 SG /Helvetica-Oblique FF [18 0 0 -18 0 0] MS (y\(k\)) SH GR GR % TEXT NP 0 SG NP 719 202 M 883 202 L 883 223 L 719 223 L CP 1 SG F 0 SG GS 1 W 720 219 M GS 0 SG /Helvetica FF [17 0 0 -17 0 0] MS (Current Queue Length) SH GR GR % TEXT NP 0 SG NP 34 101 M 202 101 L 202 168 L 34 168 L CP 1 SG F 0 SG GS 1 W 118 120 M GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (Window Size of) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (Window Size of) SH GR 0 22 RM GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (TCP Connections ) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (TCP Connections ) SH GR 0 22 RM GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (in Slow-Start Phase) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (in Slow-Start Phase) SH GR GR % POLY/OPEN-SPLINE 0.159 0.302 0.286 RG GS NP 600 251 M 710 251 L 710 91 L 210 91 L 210 251 L 0 90 atan DU cos 22.000 MU 300 exch SU exch sin 22.000 MU 251 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 300 251 22.000 9.000 90 0 TGAT 1 SG CP F 0.159 0.302 0.286 RG NP 300 251 22.000 9.000 90 0 TGAT CP F GR % POLY/OPEN-SPLINE 0.159 0.302 0.286 RG GS NP 600 301 M 710 301 L 710 461 L 210 461 L 210 301 L 0 90 atan DU cos 22.000 MU 300 exch SU exch sin 22.000 MU 301 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 300 301 22.000 9.000 90 0 TGAT 1 SG CP F 0.159 0.302 0.286 RG NP 300 301 22.000 9.000 90 0 TGAT CP F GR % POLY/OPEN-SPLINE 0.159 0.302 0.286 RG GS NP 600 201 M 650 201 L 650 131 L 250 131 L 250 201 L 0 50 atan DU cos 22.000 MU 300 exch SU exch sin 22.000 MU 201 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 300 201 22.000 9.000 50 0 TGAT 1 SG CP F 0.159 0.302 0.286 RG NP 300 201 22.000 9.000 50 0 TGAT CP F GR % POLY/OPEN-SPLINE 0.159 0.302 0.286 RG GS NP 600 351 M 650 351 L 650 421 L 250 421 L 250 351 L 0 50 atan DU cos 22.000 MU 300 exch SU exch sin 22.000 MU 351 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 300 351 22.000 9.000 50 0 TGAT 1 SG CP F 0.159 0.302 0.286 RG NP 300 351 22.000 9.000 50 0 TGAT CP F GR % POLY/OPEN-SPLINE 0.159 0.302 0.286 RG GS NP 710 251 M 0 160 atan DU cos 22.000 MU 870 exch SU exch sin 22.000 MU 251 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 870 251 22.000 9.000 160 0 TGAT 1 SG CP F 0.159 0.302 0.286 RG NP 870 251 22.000 9.000 160 0 TGAT CP F GR % POLY/OPEN-SPLINE 0.159 0.302 0.286 RG GS NP 65 202 M 0 190 atan DU cos 22.000 MU 255 exch SU exch sin 22.000 MU 202 exch SU L TGSM 7 W S 1 W GR GS TGSM NP 255 202 22.000 9.000 190 0 TGAT 1 SG CP F 0.159 0.302 0.286 RG NP 255 202 22.000 9.000 190 0 TGAT CP F GR % TEXT NP 0 SG NP 377 309 M 514 309 L 514 376 L 377 376 L CP 1 SG F 0 SG GS 1 W 446 328 M GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (State Transition ) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (State Transition ) SH GR 0 22 RM GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (Matrix) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (Matrix) SH GR 0 22 RM GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (of RED and TCP) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (of RED and TCP) SH GR GR % TEXT NP 0 SG NP 304 100 M 599 100 L 599 123 L 304 123 L CP 1 SG F 0 SG GS 1 W 452 119 M GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (Window Size of TCP Connections ) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (Window Size of TCP Connections ) SH GR GR % TEXT NP 0 SG NP 346 61 M 531 61 L 531 84 L 346 84 L CP 1 SG F 0 SG GS 1 W 439 80 M GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (Current Queue Length) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (Current Queue Length) SH GR GR % TEXT NP 0 SG NP 331 428 M 574 428 L 574 451 L 331 451 L CP 1 SG F 0 SG GS 1 W 453 447 M GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (# of Active TCP Connections) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (# of Active TCP Connections) SH GR GR % TEXT NP 0 SG GS 1 W 442 489 M GS GS 0 /Helvetica FF [18 0 0 -18 0 0] MS (Average Queue Length) TGSW AD GR 2 DI NE 0 RM 0 SG /Helvetica FF [18 0 0 -18 0 0] MS (Average Queue Length) SH GR GR % POLY/OPEN-SPLINE 0 SG GS NP 306 288 M 320 288 L TGSM 2 W S 1 W GR % POLY/OPEN-SPLINE 0 SG GS NP 524 291 M 537 291 L TGSM 2 W S 1 W GR GR tgifsavedpage restore end showpage %%Trailer %MatchingCreationDate: Sat Jun 8 07:29:15 2002 %%DocumentFonts: Helvetica-Oblique %%+ Helvetica %%EOF %%EndDocument @endspecial Fq 1987 2405 a(Figur) o(e) p 2245 2405 a(3:) p Fh 2338 2405 a(Cases) p 2534 2405 a(C3) p 2643 2405 a(and) p 2773 2405 a(C4) p 2882 2405 a(where) p 3086 2405 a(a) p 3141 2405 a(part) p 3279 2405 a(of) p 3363 2405 a(TCP) p 3522 2405 a(connections) p 3901 2405 a(in) 2331 2496 y(slo) n(w) p 2489 2496 a(start) p 2636 2496 a(phase.) p Fi 2715 2848 a(B) p Fm 2866 2848 a(=) p 3014 2848 a([) p 3058 2848 a(1) p 3120 2848 a(0) p 3182 2848 a(0) p 3244 2848 a(0) p 3307 2848 a(]) p Fn 3330 2814 a(T) p Fi 2714 2973 a(C) p Fm 2866 2973 a(=) p 3014 2973 a([) p 3058 2973 a(0) p 3120 2973 a(1) p 3182 2973 a(0) p 3244 2973 a(0) p 3307 2973 a(]) p Fr 1987 3242 a(In) p 2078 3242 a(this) p 2219 3242 a(paper) m(,) p 2443 3242 a(we) p 2562 3242 a(analyze) p 2837 3242 a(the) p 2960 3242 a(transient) p 3268 3242 a(beha) n(vior) p 3579 3242 a(of) p 3670 3242 a(the) p 3793 3242 a(RED) 1987 3342 y(gate) n(w) o(ay) p 2284 3342 a(for) p 2404 3342 a(v) n(arious) p 2671 3342 a(types) p 2870 3342 a(of) p 2963 3342 a(TCP) p 3139 3342 a(connection) p 3527 3342 a(v) n(ariations) p 3876 3342 a(by) 1987 3441 y(utilizing) p 2281 3441 a(the) p 2399 3441 a(transfer) p 2670 3441 a(function.) p 2992 3441 a(The) p 3138 3441 a(transfer) p 3409 3441 a(function) p 3703 3441 a(of) p 3790 3441 a(a) p 3844 3441 a(lin-) 1987 3541 y(ear) p 2111 3541 a(system) p 2364 3541 a(describes) p 2696 3541 a(the) p 2821 3541 a(relation) p 3097 3541 a(between) p 3397 3541 a(the) p 3521 3541 a(input) p 3715 3541 a(and) p 3858 3541 a(the) 1987 3640 y(output) p 2227 3640 a(in) p 2320 3640 a(frequenc) o(y) p 2680 3640 a(domain) p 2957 3640 a([12].) p 3165 3640 a(W) p 3236 3640 a(e) p 3303 3640 a(de\002ne) p Fo 3534 3640 a(z) p Fr 3577 3640 a(-transforms) 1987 3740 y(of) p 2076 3740 a(the) p 2197 3740 a(input) p Fo 2387 3740 a(u) p Fm(\() p Fo(k) p Fm 2513 3740 a(\)) p Fr 2565 3740 a(and) p 2705 3740 a(the) p 2826 3740 a(output) p Fo 3058 3740 a(y) p Fm 3102 3740 a(\() p Fo(k) p Fm 3180 3740 a(\)) p Fr 3232 3740 a(as) p Fo 3321 3740 a(U) p Fm 3387 3740 a(\() p Fo(z) p Fm 3462 3740 a(\)) p Fr 3513 3740 a(and) p Fo 3653 3740 a(Y) p Fm 3719 3740 a(\() p Fo(z) p Fm 3794 3740 a(\)) p Fr(,) p 3867 3740 a(re-) 1987 3840 y(specti) n(v) o(ely) p 2317 3840 a(.) p 2368 3840 a(The) p 2520 3840 a(transfer) p 2796 3840 a(function) p Fo 3096 3840 a(G) p Fm(\() p Fo(z) p Fm 3236 3840 a(\)) p Fr 3291 3840 a(of) p 3383 3840 a(a) p 3443 3840 a(system) p 3696 3840 a(satis\002es) 1987 3939 y(the) p 2109 3939 a(follo) n(wing) p 2450 3939 a(relation.) p Fo 2592 4126 a(Y) p Fm 2658 4126 a(\() p Fo(z) p Fm 2733 4126 a(\)) p 2848 4126 a(=) p Fo 2996 4126 a(G) p Fm(\() p Fo(z) p Fm 3136 4126 a(\)) p Fo 3182 4126 a(U) p Fm 3248 4126 a(\() p Fo(z) p Fm 3323 4126 a(\)) p Fr 3862 4126 a(\(7\)) 1987 4312 y(The) p 2142 4312 a(transfer) p 2422 4312 a(functions) p 2757 4312 a(of) p 2852 4312 a(the) p 2980 4312 a(system) p 3237 4312 a(described) p 3581 4312 a(by) p 3691 4312 a(Eqs.) p 3862 4312 a(\(5\)) 1987 4412 y(and) p 2127 4412 a(\(6\)) p 2245 4412 a(are) p 2367 4412 a(gi) n(v) o(en) p 2569 4412 a(by) p 2673 4412 a(the) p 2795 4412 a(follo) n(wing) p 3136 4412 a(equation) p 3443 4412 a([12].) p Fo 2486 4598 a(G) p Fm(\() p Fo(z) p Fm 2626 4598 a(\)) p 2741 4598 a(=) p Fi 2889 4598 a(C) p Fm(\() p Fo(z) p Fi 3046 4598 a(I) p Fs 3101 4598 a(\000) p Fi 3184 4598 a(A) p Fm(\)) p Fj 3288 4564 a(\000) p Fl(1) p Fi 3391 4598 a(B) p Fr 1987 4867 a(It) p 2060 4867 a(is) p 2138 4867 a(kno) n(wn) p 2384 4867 a(that) p 2531 4867 a(the) p 2655 4867 a(stability) p 2945 4867 a(and) p 3087 4867 a(the) p 3211 4867 a(transient) p 3519 4867 a(beha) n(vior) p 3831 4867 a(of) p 3922 4867 a(a) 1987 4967 y(closed-loop) p 2394 4967 a(system) p 2645 4967 a(are) p 2767 4967 a(determined) p 3161 4967 a(by) p 3264 4967 a(the) p 3386 4967 a(poles) p 3582 4967 a(of) p 3671 4967 a(its) p 3770 4967 a(trans-) 1987 5066 y(fer) p 2103 5066 a(function.) p 2437 5066 a(By) p 2558 5066 a(in) m(v) o(estigating) p 3006 5066 a(the) p 3132 5066 a(modulus) p 3443 5066 a(of) p 3536 5066 a(poles) p Fo 3736 5066 a(\025) p Fn 3784 5078 a(i) p Fr 3812 5066 a(,) p 3858 5066 a(the) 1987 5166 y(stability) p 2272 5166 a(and) p 2410 5166 a(the) p 2530 5166 a(transient) p 2834 5166 a(beha) n(vior) p 3140 5166 a(of) p 3228 5166 a(the) p 3347 5166 a(system) p 3596 5166 a(can) p 3729 5166 a(be) p 3825 5166 a(eas-) 1987 5266 y(ily) p 2090 5266 a(kno) n(wn.) p 2359 5266 a(In) p 2444 5266 a(our) p 2571 5266 a(transient) p 2872 5266 a(beha) n(vior) p 3177 5266 a(analysis,) p 3482 5266 a(the) p 3600 5266 a(input) p 3786 5266 a(is) p 3858 5266 a(the) p Fo 1987 5365 a(z) p Fr 2030 5365 a(-transform) p 2403 5365 a(of) p 2496 5365 a(either) p 2708 5365 a(the) p 2833 5365 a(dif) n(ference) p 3191 5365 a(in) p 3279 5365 a(the) p 3405 5365 a(numbers) p 3714 5365 a(of) p 3807 5365 a(TCP) 1987 5465 y(connections) p 2416 5465 a(\(C1) p 2573 5465 a(and) p 2726 5465 a(C2\)) p 2883 5465 a(or) p 2985 5465 a(the) p 3120 5465 a(dif) n(ference) p 3487 5465 a(in) p 3584 5465 a(the) p 3719 5465 a(sum) p 3890 5465 a(of) 1987 5565 y(windo) n(w) p 2272 5565 a(sizes) p 2453 5565 a(of) p 2541 5565 a(all) p 2644 5565 a(source) p 2880 5565 a(hosts) p 3070 5565 a(\(C3) p 3214 5565 a(and) p 3354 5565 a(C4\).) p 3524 5565 a(The) p 3673 5565 a(transient) 1987 5664 y(performance) p 2437 5664 a(of) p 2537 5664 a(the) p 2669 5664 a(RED) p 2865 5664 a(gate) n(w) o(ay) p 3169 5664 a(is) p 3255 5664 a(therefore) p 3586 5664 a(determined) 1987 5764 y(by) p 2092 5764 a(poles) p 2289 5764 a(of) p Fo 2381 5764 a(G) p Fm(\() p Fo(z) p Fm 2521 5764 a(\)) p Fs 2573 5764 a(\002) p Fo 2657 5764 a(U) p Fm 2723 5764 a(\() p Fo(z) p Fm 2798 5764 a(\)) p Fr(.) p 2880 5764 a(Ho) n(we) n(v) o(er) m(,) p 3219 5764 a(Eq.) p 3354 5764 a(\(7\)) p 3474 5764 a(al) o(w) o(ays) p 3725 5764 a(has) p 3858 5764 a(the) 3830 6013 y(p.) p 3918 6013 a(3) p 90 rotate dyy eop %%Page: 4 4 4 3 bop Fr -222 107 a(modulus) p 87 107 a(of) p 180 107 a(1.0) p 307 107 a(since) p 501 107 a(the) p 625 107 a(number) p 902 107 a(of) p 995 107 a(TCP) p 1170 107 a(connections) p Fo 1590 107 a(n) p Fm(\() p Fo(k) p Fm 1718 107 a(\)) p Fr -222 206 a(is) p -146 206 a(changed) p 152 206 a(only) p 321 206 a(by) p 425 206 a(the) p 547 206 a(input) p Fo 739 206 a(U) p Fm 805 206 a(\() p Fo(z) p Fm 880 206 a(\)) p Fr(.) p 959 206 a(It) p 1031 206 a(is) p 1107 206 a(therefore) p 1428 206 a(necessary) -222 306 y(to) p -135 306 a(e) o(xclude) p 144 306 a(the) p 268 306 a(modulus) p 576 306 a(of) p 668 306 a(1.0) p 794 306 a(when) p 996 306 a(analyzing) p 1341 306 a(the) p 1464 306 a(transient) -222 406 y(beha) n(vior) p 86 406 a(since) p 275 406 a(the) p 395 406 a(pole) p 557 406 a(corresponding) p 1050 406 a(to) p 1134 406 a(the) p 1254 406 a(modulus) p 1559 406 a(of) p 1647 406 a(1.0) -222 505 y(has) p -90 505 a(no) p 15 505 a(impact) p 263 505 a(on) p 367 505 a(the) p 491 505 a(transient) p 798 505 a(beha) n(vior) p 1109 505 a(of) p 1200 505 a(the) p 1323 505 a(queue) p 1543 505 a(length) -222 605 y(of) p -125 605 a(the) p 5 605 a(RED) p 200 605 a(gate) n(w) o(ay) p 470 605 a(.) p 537 605 a(Note) p 727 605 a(that) p 880 605 a(we) p 1005 605 a(ha) n(v) o(e) p 1187 605 a(linearly) p 1469 605 a(approxi-) -222 704 y(mated) p 0 704 a(the) p 121 704 a(system) p 371 704 a(around) p 621 704 a(its) p 719 704 a(equilibrium) p 1126 704 a(v) n(alues) p 1355 704 a(when) p 1554 704 a(deri) n(v-) -222 804 y(ing) p -92 804 a(Eq.) p 45 804 a(\(4\).) p 197 804 a(It) p 272 804 a(is) p 351 804 a(therefore) p 675 804 a(e) o(xpected) p 992 804 a(that) p 1141 804 a(the) p 1266 804 a(approximation) -222 904 y(error) p -34 904 a(becomes) p 282 904 a(lar) o(ge) p 473 904 a(when) p 679 904 a(the) p 807 904 a(v) n(alue) p 1011 904 a(of) p 1106 904 a(the) p 1234 904 a(windo) n(w) p 1526 904 a(size) p 1681 904 a(or) -222 1003 y(the) p -98 1003 a(queue) p 124 1003 a(length) p 354 1003 a(de) n(viates) p 647 1003 a(from) p 832 1003 a(their) p 1007 1003 a(equilibrium) p 1418 1003 a(v) n(alues.) p 1681 1003 a(In) -222 1103 y(Section) p 57 1103 a(4,) p 151 1103 a(we) p 278 1103 a(therefore) p 607 1103 a(v) n(alidate) p 898 1103 a(our) p 1038 1103 a(approximate) p 1483 1103 a(analysis) -222 1203 y(by) p -118 1203 a(comparing) p 258 1203 a(analytic) p 541 1203 a(results) p 779 1203 a(with) p 947 1203 a(simulation) p 1318 1203 a(ones.) -222 1385 y(First,) p -17 1385 a(we) p 109 1385 a(e) o(xplain) p 381 1385 a(e) o(xamples) p 723 1385 a(of) p 822 1385 a(the) p 953 1385 a(input) p Fo 1153 1385 a(U) p Fm 1219 1385 a(\() p Fo(z) p Fm 1294 1385 a(\)) p Fr 1355 1385 a(in) p 1449 1385 a(cases) p 1654 1385 a(C1) -222 1485 y(and) p -81 1485 a(C2,) p 58 1485 a(where) p 282 1485 a(all) p 387 1485 a(TCP) p 560 1485 a(connections) p 978 1485 a(will) p 1129 1485 a(operate) p 1394 1485 a(in) p 1480 1485 a(the) p 1603 1485 a(con-) -222 1585 y(gestion) p 39 1585 a(a) n(v) n(oidance) p 393 1585 a(phase.) -160 1820 y(1.) p -56 1820 a(Case) p 129 1820 a(of) p 221 1820 a(temporary) p 586 1820 a(change) p 845 1820 a(in) p 933 1820 a(the) p 1058 1820 a(number) p 1335 1820 a(of) p 1427 1820 a(TCP) p 1603 1820 a(con-) -56 1920 y(nections) -56 2049 y(A) p 20 2049 a(temporary) p 378 2049 a(change) p 630 2049 a(in) p 711 2049 a(the) p 829 2049 a(number) p 1099 2049 a(of) p 1185 2049 a(TCP) p 1354 2049 a(connections) -56 2149 y(can) p 84 2149 a(be) p 186 2149 a(formulated) p 575 2149 a(by) p 683 2149 a(an) p 785 2149 a(impulse.) p 1106 2149 a(F) o(or) p 1244 2149 a(e) o(xample,) p 1571 2149 a(when) -56 2249 y(the) p 75 2249 a(number) p 358 2249 a(of) p 457 2249 a(TCP) p 639 2249 a(connections) p 1065 2249 a(is) p 1150 2249 a(increased) p 1493 2249 a(by) p Fm 1605 2249 a(\001) p Fo(N) p Fr -56 2348 a(\(or) p 63 2348 a(decreased) p 412 2348 a(if) p Fm 485 2348 a(\001) p Fo(N) p Fr 652 2348 a(is) p 729 2348 a(ne) o(gati) n(v) o(e\)) p 1055 2348 a(at) p 1137 2348 a(sequence) p Fo 1463 2348 a(i) p Fr(,) p 1535 2348 a(the) p 1658 2348 a(in-) -56 2448 y(put) p Fo 71 2448 a(u) p Fm(\() p Fo(k) p Fm 197 2448 a(\)) p Fr 250 2448 a(and) p 390 2448 a(its) p Fo 489 2448 a(z) p Fr 532 2448 a(-transform) p Fo 903 2448 a(U) p Fm 969 2448 a(\() p Fo(z) p Fm 1044 2448 a(\)) p Fr 1096 2448 a(are) p 1218 2448 a(gi) n(v) o(en) p 1420 2448 a(by) p Fo 300 2664 a(u) p Fm(\() p Fo(k) p Fm 426 2664 a(\)) p 541 2664 a(=) p Fk 689 2547 a(\032) p Fm 793 2613 a(\001) p Fo(N) p Fr 1021 2613 a(if) p Fo 1092 2613 a(k) p Fm 1161 2613 a(=) p Fo 1249 2613 a(S) p Fn 1300 2625 a(i) p Fm 793 2713 a(0) p Fr 1021 2713 a(otherwise) p Fo 286 2849 a(U) p Fm 352 2849 a(\() p Fo(z) p Fm 427 2849 a(\)) p 541 2849 a(=) p 689 2849 a(\001) p Fo(N) p 848 2849 a(z) p Fj 891 2814 a(\000) p Fn(i) p Fr 1654 2849 a(\(8\)) -160 3045 y(2.) p -56 3045 a(Case) p 127 3045 a(of) p 217 3045 a(generic) p 483 3045 a(change) p 740 3045 a(in) p 826 3045 a(the) p 948 3045 a(number) p 1223 3045 a(of) p 1314 3045 a(TCP) p 1488 3045 a(connec-) -56 3144 y(tions) -56 3274 y(A) p 33 3274 a(generic) p 306 3274 a(change) p 569 3274 a(in) p 663 3274 a(the) p 793 3274 a(number) p 1075 3274 a(of) p 1173 3274 a(TCP) p 1354 3274 a(connections) -56 3373 y(can) p 83 3373 a(be) p 186 3373 a(gi) n(v) o(en) p 391 3373 a(by) p 499 3373 a(the) p 624 3373 a(con) m(v) n(olution) p 1040 3373 a(of) p 1133 3373 a(multiple) p 1434 3373 a(impulses.) -56 3473 y(F) o(or) p 82 3473 a(instance,) p 399 3473 a(when) p 603 3473 a(the) p 728 3473 a(number) p 1006 3473 a(of) p 1099 3473 a(TCP) p 1275 3473 a(connections) p 1695 3473 a(is) -56 3573 y(increased) p 288 3573 a(\(or) p 416 3573 a(decreased\)) p 802 3573 a(by) p Fm 916 3573 a(\001) p Fo(N) p Fn 1052 3585 a(i) p Fr 1111 3573 a(at) p 1202 3573 a(sequence) p Fo 1537 3573 a(t) p Fn 1567 3585 a(i) p Fr 1595 3573 a(,) p 1649 3573 a(the) p Fo -56 3672 a(z) p Fr -13 3672 a(-transform) p 357 3672 a(of) p 447 3672 a(the) p 570 3672 a(input,) p Fo 782 3672 a(U) p Fm 848 3672 a(\() p Fo(z) p Fm 923 3672 a(\)) p Fr(,) p 996 3672 a(is) p 1072 3672 a(gi) n(v) o(en) p 1274 3672 a(by) p Fo 422 3855 a(U) p Fm 488 3855 a(\() p Fo(z) p Fm 563 3855 a(\)) p 678 3855 a(=) p Fk 825 3776 a(X) p Fn 874 3953 a(i) p Fm 959 3855 a(\001) p Fo(N) p Fn 1095 3867 a(i) p Fo 1123 3855 a(z) p Fj 1166 3821 a(\000) p Fn(t) p Fg 1243 3829 a(i) p Fr 1654 3855 a(\(9\)) -160 4123 y(3.) p -56 4123 a(Case) p 126 4123 a(of) p 216 4123 a(continuous) p 602 4123 a(change) p 857 4123 a(in) p 943 4123 a(the) p 1065 4123 a(number) p 1340 4123 a(of) p 1430 4123 a(TCP) p 1603 4123 a(con-) -56 4222 y(nections) -56 4352 y(A) p 34 4352 a(continuous) p 429 4352 a(change) p 695 4352 a(in) p 790 4352 a(the) p 921 4352 a(number) p 1205 4352 a(of) p 1305 4352 a(TCP) p 1488 4352 a(connec-) -56 4451 y(tions) p 132 4451 a(can) p 273 4451 a(be) p 378 4451 a(formulated) p 768 4451 a(by) p 878 4451 a(the) p 1005 4451 a(step) p 1166 4451 a(function.) p 1505 4451 a(F) o(or) p 1646 4451 a(e) o(x-) -56 4551 y(ample,) p 206 4551 a(when) p 421 4551 a(the) p 557 4551 a(number) p 845 4551 a(of) p 949 4551 a(TCP) p 1137 4551 a(connections) p 1568 4551 a(is) p 1658 4551 a(in-) -56 4651 y(creased) p 223 4651 a(\(or) p 349 4651 a(decreased\)) p 734 4651 a(by) p Fm 846 4651 a(\001) p Fo(N) p Fr 1021 4651 a(at) p 1110 4651 a(each) p 1292 4651 a(sequence,) p 1649 4651 a(the) p Fo -56 4750 a(z) p Fr -13 4750 a(-transform) p 357 4750 a(of) p 447 4750 a(the) p 570 4750 a(input,) p Fo 782 4750 a(U) p Fm 848 4750 a(\() p Fo(z) p Fm 923 4750 a(\)) p Fr(,) p 996 4750 a(is) p 1072 4750 a(gi) n(v) o(en) p 1274 4750 a(by) p Fo 535 4959 a(U) p Fm 601 4959 a(\() p Fo(z) p Fm 676 4959 a(\)) p 791 4959 a(=) 948 4902 y(\001) p Fo(N) p 1107 4902 a(z) p 948 4939 202 4 v 956 5016 a(z) p Fs 1017 5016 a(\000) p Fm 1100 5016 a(1) p Fr -222 5229 a(Second,) p 64 5229 a(we) p 181 5229 a(e) o(xplain) p 444 5229 a(e) o(xamples) p 777 5229 a(of) p 867 5229 a(the) p 989 5229 a(input) p Fo 1180 5229 a(U) p Fm 1246 5229 a(\() p Fo(z) p Fm 1321 5229 a(\)) p Fr 1373 5229 a(in) p 1458 5229 a(cases) p 1654 5229 a(C3) -222 5329 y(and) p -83 5329 a(C4,) p 54 5329 a(where) p 275 5329 a(a) p 331 5329 a(part) p 479 5329 a(of) p 567 5329 a(TCP) p 739 5329 a(connections) p 1154 5329 a(will) p 1302 5329 a(operate) p 1565 5329 a(in) p 1649 5329 a(the) -222 5428 y(slo) n(w) p -47 5428 a(start) p 117 5428 a(phase.) -160 5664 y(1.) p -56 5664 a(Case) p 125 5664 a(of) p 213 5664 a(temporary) p 574 5664 a(increase) p 865 5664 a(in) p 949 5664 a(the) p 1070 5664 a(number) p 1343 5664 a(of) p 1431 5664 a(TCP) p 1603 5664 a(con-) -56 5764 y(nections) 2153 107 y(When) p 2383 107 a(a) p 2451 107 a(part) p 2612 107 a(of) p 2713 107 a(TCP) p 2896 107 a(connections) p 3325 107 a(will) p 3485 107 a(operate) p 3761 107 a(in) p 3858 107 a(the) 2153 206 y(slo) n(w) p 2341 206 a(start) p 2517 206 a(phase,) p 2763 206 a(windo) n(w) p 3062 206 a(sizes) p 3256 206 a(of) p 3359 206 a(these) p 3562 206 a(connections) 2153 306 y(are) p 2284 306 a(doubled) p 2582 306 a(e) n(v) o(ery) p 2793 306 a(round-trip) p 3160 306 a(time.) p 3382 306 a(Hence,) p 3648 306 a(when) p 3858 306 a(the) 2153 406 y(number) p 2431 406 a(of) p 2526 406 a(TCP) p 2703 406 a(connections) p 3125 406 a(in) p 3215 406 a(the) p 3341 406 a(slo) n(w) p 3521 406 a(start) p 3689 406 a(phase) p 3904 406 a(is) 2153 505 y(increased) p 2499 505 a(by) p Fm 2615 505 a(\001) p Fo(N) p Fr 2793 505 a(at) p 2886 505 a(sequence) p Fo 3223 505 a(i) p Fr(,) p Fo 3308 505 a(u) p Fm(\() p Fo(k) p Fm 3434 505 a(\)) p Fr 3499 505 a(and) p Fo 3652 505 a(U) p Fm 3718 505 a(\() p Fo(z) p Fm 3793 505 a(\)) p Fr 3858 505 a(are) 2153 605 y(approximately) p 2653 605 a(gi) n(v) o(en) p 2855 605 a(by) p Fo 2227 818 a(u) p Fm(\() p Fo(k) p Fm 2353 818 a(\)) p Fs 2468 818 a(') p Fk 2615 701 a(\032) p Fl 2737 730 a(\001) p Fn(N) p 2729 744 130 4 v 2729 792 a(n) p Fl(\() p Fn(k) p Fl 2832 792 a(\)) p Fs 2887 763 a(\002) p Fm 2970 763 a(2) p 3012 698 32 4 v Fn 3012 733 a(s) p Fl(\() p Fn(k) p Fl 3105 733 a(\)\() p Fn(k) p Fj 3193 733 a(\000) p Fn(S) p Fg 3286 741 a(i) p Fj 3313 733 a(\000) p Fl(1\)) p Fr 3511 763 a(if) p Fo 3583 763 a(k) p 3652 763 a(>) p 3739 763 a(S) p Fn 3790 775 a(i) p Fm 2719 876 a(0) p Fr 3511 876 a(otherwise) p Fo 2212 1070 a(U) p Fm 2278 1070 a(\() p Fo(z) p Fm 2353 1070 a(\)) p Fs 2468 1070 a(') p Fm 2625 1014 a(2) p 2667 948 V Fn 2667 983 a(s) p Ff 2698 958 a(\003) p Fl 2733 983 a(\() p Fj(\000) p Fn(S) p Fg 2852 991 a(i) p Fj 2878 983 a(\000) p Fl(1\)) p Fm 3007 1014 a(\001) p Fo(N) p 3166 1014 a(z) p 2625 1051 583 4 v 2734 1127 a(n) p Fj 2784 1103 a(\003) p Fm 2850 1127 a(\() p Fo(z) p Fs 2943 1127 a(\000) p Fm 3026 1127 a(2\)) p Fr 3821 1070 a(\(10\)) 2153 1276 y(In) p 2256 1276 a(the) p 2393 1276 a(abo) o(v) o(e) p 2623 1276 a(equation,) p 2968 1276 a(we) p 3099 1276 a(approximate) p Fo 3549 1276 a(n) p Fj 3599 1246 a(\003) p Fs 3685 1276 a(\021) p Fo 3799 1276 a(n) p Fm(\() p Fo(k) p Fm 3927 1276 a(\)) p Fr 2153 1376 a(since) p 2344 1376 a(the) p 2467 1376 a(number) p Fo 2741 1376 a(n) p Fm(\() p Fo(k) p Fm 2869 1376 a(\)) p Fr 2923 1376 a(of) p 3013 1376 a(TCP) p 3186 1376 a(connections) p 3604 1376 a(in) p 3689 1376 a(the) p 3812 1376 a(con-) 2153 1475 y(gestion) p 2423 1475 a(a) n(v) n(oidance) p 2786 1475 a(phase) p 3006 1475 a(does) p 3188 1475 a(not) p 3324 1475 a(change.) p 3635 1475 a(Similarly) p 3940 1475 a(,) 2153 1575 y(we) p 2275 1575 a(approximate) p 2716 1529 39 4 v Fo 2716 1575 a(s) p Fj 2755 1543 a(\003) p Fs 2825 1575 a(\021) p 2922 1529 V Fo 2922 1575 a(s) p Fm(\() p Fo(k) p Fm 3039 1575 a(\)) p Fr(.) p 3132 1575 a(Note) p 3319 1575 a(that) p 3469 1575 a(in) p 3560 1575 a(Eq.) p 3698 1575 a(\(10\)) p 3862 1575 a(we) 2153 1675 y(assume) p 2428 1675 a(that) p Fm 2584 1675 a(\001) p Fo(N) p Fr 2760 1675 a(TCP) p 2943 1675 a(connections) p 3371 1675 a(established) p 3771 1675 a(at) p 3862 1675 a(se-) 2153 1774 y(quence) p Fo 2413 1774 a(i) p Fr 2467 1774 a(will) p 2622 1774 a(not) p 2754 1774 a(operate) p 3024 1774 a(in) p 3114 1774 a(the) p 3241 1774 a(congestion) p 3626 1774 a(a) n(v) n(oidance) 2153 1874 y(phase) p 2362 1874 a(at) p 2443 1874 a(slot) p Fo 2584 1874 a(k) p Fr 2650 1874 a(\() p Fo(k) p 2747 1874 a(>) p 2835 1874 a(S) p Fn 2886 1886 a(i) p Fr 2913 1874 a(\).) 2049 2030 y(2.) p 2153 2030 a(Case) p 2331 2030 a(of) p 2418 2030 a(generic) p 2679 2030 a(increase) p 2969 2030 a(in) p 3051 2030 a(the) p 3169 2030 a(number) p 3440 2030 a(of) p 3527 2030 a(TCP) p 3696 2030 a(connec-) 2153 2130 y(tions) 2153 2258 y(A) p 2237 2258 a(generic) p 2505 2258 a(increase) p 2801 2258 a(in) p 2890 2258 a(the) p 3015 2258 a(number) p 3293 2258 a(of) p 3386 2258 a(TCP) p 3562 2258 a(connections) 2153 2357 y(can) p 2291 2357 a(be) p 2392 2357 a(formulated) p 2780 2357 a(by) p 2886 2357 a(the) p 3010 2357 a(con) m(v) n(olution) p 3425 2357 a(of) p 3517 2357 a(Eq.) p 3653 2357 a(\(10\).) p 3845 2357 a(F) o(or) 2153 2457 y(instance,) p 2473 2457 a(when) p 2680 2457 a(the) p 2808 2457 a(number) p 3088 2457 a(of) p 3184 2457 a(TCP) p 3362 2457 a(connections) p 3786 2457 a(oper) n(-) 2153 2556 y(ating) p 2350 2556 a(in) p 2446 2556 a(the) p 2578 2556 a(slo) n(w) p 2764 2556 a(start) p 2939 2556 a(phase) p 3159 2556 a(is) p 3245 2556 a(increased) p 3590 2556 a(by) p Fm 3704 2556 a(\001) p Fo(N) p Fn 3840 2568 a(i) p Fr 3899 2556 a(at) 2153 2656 y(sequence) p Fo 2478 2656 a(t) p Fn 2508 2668 a(i) p Fr 2535 2656 a(,) p Fo 2577 2656 a(z) p Fr 2620 2656 a(-transform) p Fo 2990 2656 a(U) p Fm 3056 2656 a(\() p Fo(z) p Fm 3131 2656 a(\)) p Fr 3184 2656 a(is) p 3260 2656 a(gi) n(v) o(en) p 3462 2656 a(by) p Fo 2381 2874 a(U) p Fm 2447 2874 a(\() p Fo(z) p Fm 2522 2874 a(\)) p 2637 2874 a(=) p Fk 2784 2795 a(X) p Fn 2833 2972 a(i) p Fm 2928 2818 a(\001) p Fo(N) p Fn 3064 2830 a(i) p Fm 3105 2818 a(2) p 3147 2753 32 4 v Fn 3147 2788 a(s) p Ff 3178 2763 a(\003) p Fl 3213 2788 a(\() p Fj(\000) p Fn(S) p Fg 3332 2796 a(i) p Fj 3358 2788 a(\000) p Fl(1\)) p Fo 3487 2818 a(z) p Fj 3530 2788 a(\000) p Fn(t) p Fg 3607 2796 a(i) p Fl 3632 2788 a(+1) p 2928 2855 793 4 v Fo 3142 2931 a(n) p Fj 3192 2907 a(\003) p Fm 3257 2931 a(\() p Fo 3290 2931 a(z) p Fs 3350 2931 a(\000) p Fm 3433 2931 a(2\)) p Fq 2271 3277 a(4) p 2354 3277 a(Numerical) p 2748 3277 a(Examples) p 3115 3277 a(and) p 3269 3277 a(Discussions) p Fr 1987 3489 a(In) p 2084 3489 a(this) p 2233 3489 a(section,) p 2519 3489 a(by) p 2631 3489 a(presenting) p 3005 3489 a(se) n(v) o(eral) p 3265 3489 a(numerical) p 3626 3489 a(e) o(xamples,) 1987 3589 y(we) p 2107 3589 a(discuss) p 2370 3589 a(the) p 2495 3589 a(relation) p 2772 3589 a(between) p 3072 3589 a(a) p 3133 3589 a(choice) p 3373 3589 a(of) p 3465 3589 a(control) p 3724 3589 a(param-) 1987 3688 y(eters) p 2175 3688 a(of) p 2275 3688 a(the) p 2408 3688 a(RED) p 2605 3688 a(gate) n(w) o(ay) p 2910 3688 a(and) p 3061 3688 a(its) p 3171 3688 a(transient) p 3488 3688 a(beha) n(vior) p 3774 3688 a(.) p 3850 3688 a(W) p 3921 3688 a(e) 1987 3788 y(also) p 2149 3788 a(v) n(alidate) p 2439 3788 a(our) p 2579 3788 a(approximate) p 3023 3788 a(analysis) p 3320 3788 a(by) p 3432 3788 a(comparing) p 3816 3788 a(ana-) 1987 3888 y(lytic) p 2150 3888 a(results) p 2383 3888 a(with) p 2547 3888 a(simulation) p 2914 3888 a(ones.) p 3111 3888 a(In) p 3196 3888 a(all) p 3295 3888 a(analytic) p 3574 3888 a(and) p 3710 3888 a(simula-) 1987 3987 y(tion) p 2140 3987 a(results,) p 2402 3987 a(without) p 2679 3987 a(e) o(xplicitly) p 3015 3987 a(stated,) p 3254 3987 a(the) p 3379 3987 a(follo) n(wing) p 3724 3987 a(param-) 1987 4087 y(eters) p 2174 4087 a(are) p 2306 4087 a(used:) p 2526 4087 a(the) p 2658 4087 a(number) p 2942 4087 a(of) p 3042 4087 a(TCP) p 3225 4087 a(connections) p 3652 4087 a(in) p 3747 4087 a(steady) 1987 4186 y(state) p Fo 2171 4186 a(n) p Fj 2221 4156 a(\003) p Fm 2303 4186 a(=) p 2412 4186 a(5) p Fr(,) p 2510 4186 a(the) p 2644 4186 a(processing) p 3031 4186 a(speed) p 3252 4186 a(of) p 3354 4186 a(the) p 3487 4186 a(RED) p 3686 4186 a(gate) n(w) o(ay) p Fo 1987 4286 a(B) p Fm 2091 4286 a(=) p 2193 4286 a(0) p Fo(:) p Fm(2) p Fr 2327 4286 a([pack) o(et/ms],) p 2769 4286 a(the) p 2899 4286 a(propagation) p 3324 4286 a(delay) p Fo 3532 4286 a(\034) p Fm 3615 4286 a(=) p 3716 4286 a(1) p Fr 3786 4286 a([ms].) 1987 4386 y(F) o(our) p 2161 4386 a(control) p 2415 4386 a(parameters) p 2798 4386 a(of) p 2886 4386 a(the) p 3007 4386 a(RED) p 3192 4386 a(gate) n(w) o(ay) p 3484 4386 a(are) p 3604 4386 a(con\002gured) 1987 4485 y(according) p 2342 4485 a(to) p 2434 4485 a(the) p 2563 4485 a(recommendation) p 3149 4485 a(in) p 3242 4485 a([2],) p 3389 4485 a(i.e.,) p Fo 3541 4485 a(min) p Fn 3693 4497 a(th) p Fm 3796 4485 a(=) p 3897 4485 a(5) p Fr(,) p Fo 1987 4585 a(max) p Fn 2151 4597 a(th) p Fm 2242 4585 a(=) p 2330 4585 a(15) p Fr(,) p Fo 2454 4585 a(max) p Fn 2618 4597 a(p) p Fm 2680 4585 a(=) p 2767 4585 a(0) p Fo(:) p Fm(1) p Fr 2894 4585 a(and) p Fo 3035 4585 a(q) p Fn 3072 4597 a(w) p Fm 3149 4585 a(=) p 3236 4585 a(0) p Fo(:) p Fm(002) p Fr(.) 1987 4768 y(Figure) p 2221 4768 a(4) p 2279 4768 a(sho) n(ws) p 2502 4768 a(the) p 2621 4768 a(stability) p 2906 4768 a(re) o(gion) p 3134 4768 a(when) p 3331 4768 a(the) p 3450 4768 a(number) p 3720 4768 a(of) p 3807 4768 a(TCP) 1987 4867 y(connections,) p 2421 4867 a(operating) p 2751 4867 a(in) p 2833 4867 a(the) p 2951 4867 a(congestion) p 3327 4867 a(a) n(v) n(oidance) p 3677 4867 a(phase,) p 3904 4867 a(is) 1987 4967 y(incremented) p 2418 4967 a(by) p 2523 4967 a(one.) p 2691 4967 a(This) p 2861 4967 a(\002gure) p 3076 4967 a(sho) n(ws) p 3303 4967 a(the) p 3426 4967 a(maximum) p 3784 4967 a(mod-) 1987 5066 y(ulus) p 2144 5066 a(of) p 2231 5066 a(poles) p 2425 5066 a(of) p Fo 2513 5066 a(U) p Fm 2579 5066 a(\() p Fo(z) p Fm 2654 5066 a(\)) p Fs 2696 5066 a(\002) p Fo 2771 5066 a(G) p Fm(\() p Fo(z) p Fm 2911 5066 a(\)) p Fr 2961 5066 a(\(Eq.) p 3120 5066 a(\(7\)\)) p 3263 5066 a(in) p 3346 5066 a(the) p Fo 3466 5066 a(min) p Fn 3618 5078 a(th) p Fr 3685 5066 a(\226) p Fo(max) p Fn 3891 5078 a(th) p Fr 1987 5166 a(plane) p 2191 5166 a(when) p 2396 5166 a(the) p 2522 5166 a(input) p Fo 2718 5166 a(U) p Fm 2784 5166 a(\() p Fo(z) p Fm 2859 5166 a(\)) p Fr 2916 5166 a(is) p 2996 5166 a(gi) n(v) o(en) p 3202 5166 a(by) p 3310 5166 a(Eq.) p 3448 5166 a(\(8\)) p 3570 5166 a(with) p Fo 3742 5166 a(i) p Fm 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2760 5664 a(poles) p 2962 5664 a(is,) p 3067 5664 a(the) p 3195 5664 a(better) p 3412 5664 a(the) p 3540 5664 a(transient) p 3853 5664 a(be-) 1987 5764 y(ha) n(vior) p 2214 5764 a(of) p 2300 5764 a(the) p 2418 5764 a(RED) p 2601 5764 a(gate) n(w) o(ay) p 2892 5764 a(becomes.) p 3227 5764 a(One) p 3383 5764 a(can) p 3515 5764 a(\002nd) p 3661 5764 a(from) p 3839 5764 a(this) 3830 6013 y(p.) p 3918 6013 a(4) p 90 rotate dyy eop %%Page: 5 5 5 4 bop -177 885 a @beginspecial 33 @llx 180 @lly 562 @urx 594 @ury 2257 @rwi 1033 @rhi @setspecial %%BeginDocument: figure/minthmaxth30.eps %!PS-Adobe-2.0 %%Creator: MATLAB, The Mathworks, Inc. %%Title: C:\matlab_sv12\work\fromohsaki\minthmaxth30.ps %%CreationDate: 12/19/2001 04:43:01 %%DocumentNeededFonts: GothicBBB-Medium-83pv-RKSJ-H %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: (atend) %%BoundingBox: (atend) %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def 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dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill 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157 0 899 4614 23 MP stroke gr 1700 5135 mt (Minimum Threshold [packet]) s 413 4020 mt -90 rotate (Maximum Threshold [packet]) s 90 rotate end eplot %%EndObject 396 18 moveto epage end showpage %%Trailer %%BoundingBox: 33 180 562 594 %%Pages: 001 %%EOF %%EndDocument @endspecial Fq -222 1067 a(Figur) o(e) p 32 1067 a(4:) p Fh 121 1067 a(The) p 255 1067 a(maximum) p 576 1067 a(modulus) p 851 1067 a(of) p 932 1067 a(poles) p 1107 1067 a(in) p 1184 1067 a(the) p Fe 1293 1067 a(min) p Fd 1433 1076 a(th) p Fh 1497 1067 a(\226) p Fe(max) p Fd 1687 1076 a(th) p Fh 122 1159 a(plane.) -177 2248 y @beginspecial 44 @llx 180 @lly 562 @urx 594 @ury 2257 @rwi 1033 @rhi @setspecial %%BeginDocument: figure/b-tau30.eps %!PS-Adobe-2.0 %%Creator: MATLAB, The Mathworks, Inc. %%Title: C:\matlab_sv12\work\fromohsaki\b-tau30.ps %%CreationDate: 12/19/2001 08:24:21 %%DocumentNeededFonts: GothicBBB-Medium-83pv-RKSJ-H %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: (atend) %%BoundingBox: (atend) %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef /rc {rectclip} bdef /rf {rectfill} bdef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont} bdef /ISOLatin1Encoding where {pop /WindowsLatin1Encoding 256 array bdef ISOLatin1Encoding WindowsLatin1Encoding copy pop /.notdef/.notdef/quotesinglbase/florin/quotedblbase/ellipsis/dagger /daggerdbl/circumflex/perthousand/Scaron/guilsinglleft/OE/.notdef/.notdef /.notdef/.notdef/quoteleft/quoteright/quotedblleft/quotedblright/bullet /endash/emdash/tilde/trademark/scaron/guilsinglright/oe/.notdef/.notdef /Ydieresis WindowsLatin1Encoding 128 32 getinterval astore pop} {/WindowsLatin1Encoding StandardEncoding bdef} ifelse /reencode {exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop} bdef /isroman {findfont /CharStrings get /Agrave known} bdef /FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS} bdef /csm {1 dpi2point div -1 dpi2point div scale neg translate dup landscapeMode eq {pop -90 rotate} {rotateMode eq {90 rotate} if} ifelse} bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L {lineto stroke} bdef /MP {3 1 roll moveto 1 sub {rlineto} repeat} bdef /AP {{rlineto} repeat} bdef /PDlw -1 def /W {/PDlw currentlinewidth def setlinewidth} def /PP {closepath eofill} bdef /DP {closepath stroke} bdef /MR {4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath} bdef /FR {MR stroke} bdef /PR {MR fill} bdef /L1i {{currentfile picstr readhexstring pop} image} bdef /tMatrix matrix def /MakeOval {newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix} bdef /FO {MakeOval stroke} bdef /PO {MakeOval fill} bdef /PD {currentlinecap 1 cap 3 1 roll 2 copy mt lineto stroke cap PDlw -1 eq not {PDlw w /PDlw -1 def} if} def /FA {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke} bdef /PA {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill} bdef /FAn {newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke} bdef /PAn {newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill} bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR {/vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath} bdef /FRR {MRR stroke } bdef /PRR {MRR fill } bdef /MlrRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath} bdef /FlrRR {MlrRR stroke } bdef /PlrRR {MlrRR fill } bdef /MtbRR {/lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath} bdef /FtbRR {MtbRR stroke } bdef /PtbRR {MtbRR fill } bdef /stri 6 array def /dtri 6 array def /smat 6 array def /dmat 6 array def /tmat1 6 array def /tmat2 6 array def /dif 3 array def /asub {/ind2 exch def /ind1 exch def dup dup ind1 get exch ind2 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a(\001) p Fo(N) p Fl 752 5477 a(1) p Fm 844 5465 a(=) p 963 5465 a(1) p Fr 1042 5465 a(are) p 1181 5465 a(used) p 1371 5465 a(for) p 1506 5465 a(analyz-) -222 5565 y(ing) p -88 5565 a(the) p 41 5565 a(case) p 211 5565 a(that) p 363 5565 a(the) p 492 5565 a(number) p 773 5565 a(of) p 870 5565 a(TCP) p 1050 5565 a(connections) p 1474 5565 a(is) p 1557 5565 a(incre-) -222 5664 y(mented) p 57 5664 a(by) p 174 5664 a(one.) p 381 5664 a(In) p 484 5664 a(Fig.) p 650 5664 a(7,) p Fm 750 5664 a(\() p Fo(t) p Fl 812 5676 a(1) p Fo 849 5664 a(;) p 886 5664 a(t) p Fl 916 5676 a(2) p Fo 953 5664 a(;) p 990 5664 a(t) p Fl 1020 5676 a(3) p Fm 1057 5664 a(\)) p 1138 5664 a(=) p 1250 5664 a(\(5) p Fo(;) p Fm 1361 5664 a(10) p Fo(;) p Fm 1482 5664 a(15\)) p Fr 1631 5664 a(and) p Fm -222 5764 a(\(\001) p Fo(N) p Fl -54 5776 a(1) p Fo -17 5764 a(;) p Fm 20 5764 a(\001) p Fo(N) p Fl 156 5776 a(2) p Fo 193 5764 a(;) p Fm 230 5764 a(\001) p Fo(N) p Fl 366 5776 a(3) p Fm 403 5764 a(\)) p 472 5764 a(=) p 573 5764 a(\(1) p Fo(;) p Fm 684 5764 a(1) p Fo(;) p Fm 763 5764 a(1\)) p Fr 864 5764 a(are) p 993 5764 a(used) p 1173 5764 a(for) p 1298 5764 a(analyzing) p 1649 5764 a(the) 2032 1287 y @beginspecial 43 @llx 184 @lly 552 @urx 592 @ury 2257 @rwi 1515 @rhi @setspecial %%BeginDocument: figure/transient-f1g.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: transient-f1g.eps %%CreationDate: 12/17/ 1 13:35:10 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 43 184 552 592 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 43 184 552 592 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def 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2384 mt (25) s 6259 2171 mt 6259 2117 L 6259 389 mt 6259 443 L 6153 2384 mt (30) s 899 1874 mt 953 1874 L 6259 1874 mt 6205 1874 L 758 1945 mt (7) s 899 1280 mt 953 1280 L 6259 1280 mt 6205 1280 L 758 1351 mt (8) s 899 686 mt 953 686 L 6259 686 mt 6205 686 L 758 757 mt (9) s 899 2171 mt 6259 2171 L 899 389 mt 6259 389 L 899 2171 mt 899 389 L 6259 2171 mt 6259 389 L gs 899 389 5361 1783 MR c np 143 0 0 0 179 0 0 0 179 0 0 0 178 0 0 1 179 0 0 0 179 0 0 0 178 0 0 1 179 0 0 1 179 0 0 0 178 0 0 1 179 0 0 2 179 0 0 1 178 0 0 2 179 0 0 3 179 0 0 3 178 0 0 4 179 0 0 4 179 0 0 6 178 0 0 8 179 0 0 9 179 0 0 12 178 0 0 15 179 0 0 18 179 0 0 24 178 0 0 29 179 0 0 37 179 0 0 47 178 0 0 64 179 0 0 -389 179 0 0 0 178 0 0 0 179 0 0 0 179 0 0 0 178 0 0 0 179 0 899 1901 70 MP stroke gr 2782 2580 mt (Sequence Number) s 703 2247 mt -90 rotate (Queue Length [packet]) s 90 rotate 1 sg 0 1782 5360 0 0 -1782 899 4613 4 MP PP -5360 0 0 1782 5360 0 0 -1782 899 4613 5 MP stroke 4 w DO SO 6 w 0 sg 899 4613 mt 6259 4613 L 899 2831 mt 6259 2831 L 899 4613 mt 899 2831 L 6259 4613 mt 6259 2831 L 899 4613 mt 6259 4613 L 899 4613 mt 899 2831 L 899 4613 mt 899 4586 L 899 2831 mt 899 2858 L 899 4613 mt 899 4559 L 899 2831 mt 899 2885 L 720 4886 mt (10) s %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 128 FMSR 933 4767 mt (-3) s 1388 4613 mt 1388 4586 L 1388 2831 mt 1388 2858 L 1674 4613 mt 1674 4586 L 1674 2831 mt 1674 2858 L 1877 4613 mt 1877 4586 L 1877 2831 mt 1877 2858 L 2034 4613 mt 2034 4586 L 2034 2831 mt 2034 2858 L 2163 4613 mt 2163 4586 L 2163 2831 mt 2163 2858 L 2271 4613 mt 2271 4586 L 2271 2831 mt 2271 2858 L 2365 4613 mt 2365 4586 L 2365 2831 mt 2365 2858 L 2448 4613 mt 2448 4586 L 2448 2831 mt 2448 2858 L 2523 4613 mt 2523 4586 L 2523 2831 mt 2523 2858 L 2523 4613 mt 2523 4559 L 2523 2831 mt 2523 2885 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 192 FMSR 2344 4886 mt (10) s %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 128 FMSR 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2858 L 5613 4613 mt 5613 4586 L 5613 2831 mt 5613 2858 L 5696 4613 mt 5696 4586 L 5696 2831 mt 5696 2858 L 5770 4613 mt 5770 4586 L 5770 2831 mt 5770 2858 L 5770 4613 mt 5770 4559 L 5770 2831 mt 5770 2885 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 192 FMSR 5628 4886 mt (10) s %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 128 FMSR 5841 4767 mt (0) s 6259 4613 mt 6259 4586 L 6259 2831 mt 6259 2858 L 899 4257 mt 953 4257 L 6259 4257 mt 6205 4257 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 192 FMSR 544 4328 mt (100) s 899 3900 mt 953 3900 L 6259 3900 mt 6205 3900 L 544 3971 mt (200) s 899 3544 mt 953 3544 L 6259 3544 mt 6205 3544 L 544 3615 mt (300) s 899 3187 mt 953 3187 L 6259 3187 mt 6205 3187 L 544 3258 mt (400) s 899 2831 mt 953 2831 L 6259 2831 mt 6205 2831 L 544 2902 mt (500) s 899 4613 mt 6259 4613 L 899 2831 mt 6259 2831 L 899 4613 mt 899 2831 L 6259 4613 mt 6259 2831 L gs 899 2831 5361 1783 MR c np 48 0 49 0 49 0 49 0 0 0 49 0 49 0 49 0 49 0 0 0 48 0 49 0 99 1 196 0 196 1 195 1 196 1 196 1 196 1 196 1 195 1 196 2 196 1 196 1 196 3 195 3 196 4 196 6 196 8 196 11 196 15 195 20 196 27 196 35 196 46 196 61 195 80 196 107 196 140 899 4034 40 MP stroke gr gs 826 3961 5825 725 MR c np 874 4009 mt 924 4059 L 924 4009 mt 874 4059 L 1070 4149 mt 1120 4199 L 1120 4149 mt 1070 4199 L 1266 4256 mt 1316 4306 L 1316 4256 mt 1266 4306 L 1461 4336 mt 1511 4386 L 1511 4336 mt 1461 4386 L 1657 4397 mt 1707 4447 L 1707 4397 mt 1657 4447 L 1853 4443 mt 1903 4493 L 1903 4443 mt 1853 4493 L 2049 4478 mt 2099 4528 L 2099 4478 mt 2049 4528 L 2245 4505 mt 2295 4555 L 2295 4505 mt 2245 4555 L 2440 4525 mt 2490 4575 L 2490 4525 mt 2440 4575 L 2636 4540 mt 2686 4590 L 2686 4540 mt 2636 4590 L 2832 4551 mt 2882 4601 L 2882 4551 mt 2832 4601 L 3028 4559 mt 3078 4609 L 3078 4559 mt 3028 4609 L 3224 4565 mt 3274 4615 L 3274 4565 mt 3224 4615 L 3420 4569 mt 3470 4619 L 3470 4569 mt 3420 4619 L 3615 4572 mt 3665 4622 L 3665 4572 mt 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%%EndObject epage end showpage %%Trailer %%EOF %%EndDocument @endspecial Fq 1987 1469 a(Figur) o(e) p 2251 1469 a(6:) p Fh 2351 1469 a(Impulse) p 2620 1469 a(response) p 2909 1469 a(and) p 3044 1469 a(gain) p 3200 1469 a(characteristic) p 3626 1469 a(of) p Fe 3716 1469 a(U) p Fc 3776 1469 a(\() p Fe(z) p Fc 3845 1469 a(\)) p Fb 3899 1469 a(\002) p Fe 2331 1561 a(G) p Fc(\() p Fe(z) p Fc 2460 1561 a(\)) p Fh 2508 1561 a(for) p Fc 2614 1561 a(\001) p Fe(N) p Fa 2739 1569 a(1) p Fc 2796 1561 a(=) p 2877 1561 a(1) p Fh(.) 2032 3044 y @beginspecial 43 @llx 184 @lly 552 @urx 592 @ury 2257 @rwi 1515 @rhi @setspecial %%BeginDocument: figure/transient-f2g.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: transient-f2g.eps %%CreationDate: 12/17/ 1 13:35:29 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 43 184 552 592 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup %%PageBoundingBox: 43 184 552 592 MathWorks begin bpage %%EndPageSetup %%BeginObject: obj1 bplot /dpi2point 12 def portraitMode 0216 7344 csm 306 232 6109 4895 MR c np 93 dict begin %Colortable dictionary /c0 { 0 0 0 sr} bdef /c1 { 1 1 1 sr} bdef /c2 { 1 0 0 sr} bdef /c3 { 0 1 0 sr} bdef /c4 { 0 0 1 sr} bdef /c5 { 1 1 0 sr} bdef /c6 { 1 0 1 sr} bdef /c7 { 0 1 1 sr} bdef c0 1 j 1 sg 0 0 6918 5185 PR 6 w 0 1782 5360 0 0 -1782 899 2171 4 MP PP -5360 0 0 1782 5360 0 0 -1782 899 2171 5 MP stroke 4 w DO SO 6 w 0 sg 899 2171 mt 6259 2171 L 899 389 mt 6259 389 L 899 2171 mt 899 389 L 6259 2171 mt 6259 389 L 899 2171 mt 6259 2171 L 899 2171 mt 899 389 L 899 2171 mt 899 2117 L 899 389 mt 899 443 L %%IncludeResource: font Helvetica /Helvetica 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62 179 0 0 82 179 0 0 -365 178 0 0 29 179 0 0 37 179 0 0 47 178 0 0 64 179 0 0 -389 179 0 0 0 178 0 0 0 179 0 0 0 179 0 0 0 178 0 0 0 179 0 899 1901 70 MP stroke gr 2782 2580 mt (Sequence Number) s 703 2247 mt -90 rotate (Queue Length [packet]) s 90 rotate 1 sg 0 1782 5360 0 0 -1782 899 4613 4 MP PP -5360 0 0 1782 5360 0 0 -1782 899 4613 5 MP stroke 4 w DO SO 6 w 0 sg 899 4613 mt 6259 4613 L 899 2831 mt 6259 2831 L 899 4613 mt 899 2831 L 6259 4613 mt 6259 2831 L 899 4613 mt 6259 4613 L 899 4613 mt 899 2831 L 899 4613 mt 899 4586 L 899 2831 mt 899 2858 L 899 4613 mt 899 4559 L 899 2831 mt 899 2885 L 720 4886 mt (10) s %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 128 FMSR 933 4767 mt (-3) s 1388 4613 mt 1388 4586 L 1388 2831 mt 1388 2858 L 1674 4613 mt 1674 4586 L 1674 2831 mt 1674 2858 L 1877 4613 mt 1877 4586 L 1877 2831 mt 1877 2858 L 2034 4613 mt 2034 4586 L 2034 2831 mt 2034 2858 L 2163 4613 mt 2163 4586 L 2163 2831 mt 2163 2858 L 2271 4613 mt 2271 4586 L 2271 2831 mt 2271 2858 L 2365 4613 mt 2365 4586 L 2365 2831 mt 2365 2858 L 2448 4613 mt 2448 4586 L 2448 2831 mt 2448 2858 L 2523 4613 mt 2523 4586 L 2523 2831 mt 2523 2858 L 2523 4613 mt 2523 4559 L 2523 2831 mt 2523 2885 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 192 FMSR 2344 4886 mt (10) s %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 128 FMSR 2557 4767 mt (-2) s 3012 4613 mt 3012 4586 L 3012 2831 mt 3012 2858 L 3297 4613 mt 3297 4586 L 3297 2831 mt 3297 2858 L 3500 4613 mt 3500 4586 L 3500 2831 mt 3500 2858 L 3658 4613 mt 3658 4586 L 3658 2831 mt 3658 2858 L 3786 4613 mt 3786 4586 L 3786 2831 mt 3786 2858 L 3895 4613 mt 3895 4586 L 3895 2831 mt 3895 2858 L 3989 4613 mt 3989 4586 L 3989 2831 mt 3989 2858 L 4072 4613 mt 4072 4586 L 4072 2831 mt 4072 2858 L 4146 4613 mt 4146 4586 L 4146 2831 mt 4146 2858 L 4146 4613 mt 4146 4559 L 4146 2831 mt 4146 2885 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 192 FMSR 3967 4886 mt (10) s 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3900 mt 6205 3900 L 544 3971 mt (200) s 899 3544 mt 953 3544 L 6259 3544 mt 6205 3544 L 544 3615 mt (300) s 899 3187 mt 953 3187 L 6259 3187 mt 6205 3187 L 544 3258 mt (400) s 899 2831 mt 953 2831 L 6259 2831 mt 6205 2831 L 544 2902 mt (500) s 899 4613 mt 6259 4613 L 899 2831 mt 6259 2831 L 899 4613 mt 899 2831 L 6259 4613 mt 6259 2831 L gs 899 2831 5361 1783 MR c np 21 0 12 -1 9 0 6 0 0 0 7 0 8 0 12 1 16 1 6 0 15 1 30 1 4 0 6 0 40 -1 3 0 26 -1 22 -1 1 0 15 0 11 -1 9 0 6 0 7 0 1 0 8 0 11 1 16 0 14 0 7 0 30 0 12 0 9 0 16 -1 12 0 8 0 3 0 4 0 6 0 9 0 12 1 15 0 3 0 19 1 29 1 40 2 54 1 42 0 73 -1 53 -1 40 -1 29 -1 22 -1 16 -1 12 0 8 0 7 0 6 0 9 0 11 0 16 1 22 0 29 1 40 1 54 0 42 1 72 -1 54 0 40 -1 29 -1 22 0 16 -1 11 0 9 0 6 0 7 0 8 0 12 0 16 1 22 1 29 0 40 2 53 2 73 2 99 4 134 5 157 5 157 4 157 4 157 4 157 4 156 5 157 7 157 8 157 11 157 14 157 18 157 23 157 29 2624 4460 100 MP stroke 156 37 157 47 157 58 157 72 157 92 157 113 157 143 156 177 157 223 157 277 157 347 899 2874 12 MP stroke gr gs 826 2801 5825 1886 MR c np 874 2849 mt 924 2899 L 924 2849 mt 874 2899 L 1031 3196 mt 1081 3246 L 1081 3196 mt 1031 3246 L 1188 3473 mt 1238 3523 L 1238 3473 mt 1188 3523 L 1345 3696 mt 1395 3746 L 1395 3696 mt 1345 3746 L 1501 3873 mt 1551 3923 L 1551 3873 mt 1501 3923 L 1658 4016 mt 1708 4066 L 1708 4016 mt 1658 4066 L 1815 4129 mt 1865 4179 L 1865 4129 mt 1815 4179 L 1972 4221 mt 2022 4271 L 2022 4221 mt 1972 4271 L 2129 4293 mt 2179 4343 L 2179 4293 mt 2129 4343 L 2286 4351 mt 2336 4401 L 2336 4351 mt 2286 4401 L 2443 4398 mt 2493 4448 L 2493 4398 mt 2443 4448 L 2599 4435 mt 2649 4485 L 2649 4435 mt 2599 4485 L 2756 4464 mt 2806 4514 L 2806 4464 mt 2756 4514 L 2913 4487 mt 2963 4537 L 2963 4487 mt 2913 4537 L 3070 4505 mt 3120 4555 L 3120 4505 mt 3070 4555 L 3227 4519 mt 3277 4569 L 3277 4519 mt 3227 4569 L 3384 4530 mt 3434 4580 L 3434 4530 mt 3384 4580 L 3541 4538 mt 3591 4588 L 3591 4538 mt 3541 4588 L 3698 4545 mt 3748 4595 L 3748 4545 mt 3698 4595 L 3854 4550 mt 3904 4600 L 3904 4550 mt 3854 4600 L 4011 4554 mt 4061 4604 L 4061 4554 mt 4011 4604 L 4168 4558 mt 4218 4608 L 4218 4558 mt 4168 4608 L 4325 4562 mt 4375 4612 L 4375 4562 mt 4325 4612 L 4482 4566 mt 4532 4616 L 4532 4566 mt 4482 4616 L 4639 4571 mt 4689 4621 L 4689 4571 mt 4639 4621 L 4773 4576 mt 4823 4626 L 4823 4576 mt 4773 4626 L 4872 4580 mt 4922 4630 L 4922 4580 mt 4872 4630 L 4945 4582 mt 4995 4632 L 4995 4582 mt 4945 4632 L 4998 4584 mt 5048 4634 L 5048 4584 mt 4998 4634 L 5038 4586 mt 5088 4636 L 5088 4586 mt 5038 4636 L 5067 4586 mt 5117 4636 L 5117 4586 mt 5067 4636 L 5089 4587 mt 5139 4637 L 5139 4587 mt 5089 4637 L 5105 4588 mt 5155 4638 L 5155 4588 mt 5105 4638 L 5117 4588 mt 5167 4638 L 5167 4588 mt 5117 4638 L 5125 4588 mt 5175 4638 L 5175 4588 mt 5125 4638 L 5132 4588 mt 5182 4638 L 5182 4588 mt 5132 4638 L 5138 4588 mt 5188 4638 L 5188 4588 mt 5138 4638 L 5147 4588 mt 5197 4638 L 5197 4588 mt 5147 4638 L 5158 4588 mt 5208 4638 L 5208 4588 mt 5158 4638 L 5174 4587 mt 5224 4637 L 5224 4587 mt 5174 4637 L 5196 4587 mt 5246 4637 L 5246 4587 mt 5196 4637 L 5225 4586 mt 5275 4636 L 5275 4586 mt 5225 4636 L 5265 4585 mt 5315 4635 L 5315 4585 mt 5265 4635 L 5319 4585 mt 5369 4635 L 5369 4585 mt 5319 4635 L 5391 4584 mt 5441 4634 L 5441 4584 mt 5391 4634 L 5433 4585 mt 5483 4635 L 5483 4585 mt 5433 4635 L 5487 4585 mt 5537 4635 L 5537 4585 mt 5487 4635 L 5527 4586 mt 5577 4636 L 5577 4586 mt 5527 4636 L 5556 4587 mt 5606 4637 L 5606 4587 mt 5556 4637 L 5578 4587 mt 5628 4637 L 5628 4587 mt 5578 4637 L 5594 4588 mt 5644 4638 L 5644 4588 mt 5594 4638 L 5605 4588 mt 5655 4638 L 5655 4588 mt 5605 4638 L 5614 4588 mt 5664 4638 L 5664 4588 mt 5614 4638 L 5620 4588 mt 5670 4638 L 5670 4588 mt 5620 4638 L 5627 4588 mt 5677 4638 L 5677 4588 mt 5627 4638 L 5635 4588 mt 5685 4638 L 5685 4588 mt 5635 4638 L 5647 4588 mt 5697 4638 L 5697 4588 mt 5647 4638 L 5663 4587 mt 5713 4637 L 5713 4587 mt 5663 4637 L 5685 4586 mt 5735 4636 L 5735 4586 mt 5685 4636 L 5714 4585 mt 5764 4635 L 5764 4585 mt 5714 4635 L 5754 4584 mt 5804 4634 L 5804 4584 mt 5754 4634 L 5807 4583 mt 5857 4633 L 5857 4583 mt 5807 4633 L 5880 4582 mt 5930 4632 L 5930 4582 mt 5880 4632 L 5922 4582 mt 5972 4632 L 5972 4582 mt 5922 4632 L 5976 4583 mt 6026 4633 L 6026 4583 mt 5976 4633 L 6016 4585 mt 6066 4635 L 6066 4585 mt 6016 4635 L 6045 4586 mt 6095 4636 L 6095 4586 mt 6045 4636 L 6064 4587 mt 6114 4637 L 6114 4587 mt 6064 4637 L 6067 4587 mt 6117 4637 L 6117 4587 mt 6067 4637 L 6082 4587 mt 6132 4637 L 6132 4587 mt 6082 4637 L 6094 4588 mt 6144 4638 L 6144 4588 mt 6094 4638 L 6103 4588 mt 6153 4638 L 6153 4588 mt 6103 4638 L 6109 4588 mt 6159 4638 L 6159 4588 mt 6109 4638 L 6113 4588 mt 6163 4638 L 6163 4588 mt 6113 4638 L 6116 4588 mt 6166 4638 L 6166 4588 mt 6116 4638 L 6124 4588 mt 6174 4638 L 6174 4588 mt 6124 4638 L 6136 4588 mt 6186 4638 L 6186 4588 mt 6136 4638 L 6152 4587 mt 6202 4637 L 6202 4587 mt 6152 4637 L 6161 4587 mt 6211 4637 L 6211 4587 mt 6161 4637 L 6173 4587 mt 6223 4637 L 6223 4587 mt 6173 4637 L 6203 4587 mt 6253 4637 L 6253 4587 mt 6203 4637 L 6210 4587 mt 6260 4637 L 6260 4587 mt 6210 4637 L 6224 4587 mt 6274 4637 L 6274 4587 mt 6224 4637 L gs 899 2831 5361 1783 MR c np gr gr 2469 5082 mt (Frequency [rad/sequence]) s 489 4147 mt -90 rotate (Amplitude) s 90 rotate end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument @endspecial Fq 1987 3227 a(Figur) o(e) p 2251 3227 a(7:) p Fh 2351 3227 a(Impulse) p 2620 3227 a(response) p 2909 3227 a(and) p 3044 3227 a(gain) p 3200 3227 a(characteristic) p 3626 3227 a(of) p Fe 3716 3227 a(U) p Fc 3776 3227 a(\() p Fe(z) p Fc 3845 3227 a(\)) p Fb 3899 3227 a(\002) p Fe 2331 3318 a(G) p Fc(\() p Fe(z) p Fc 2460 3318 a(\)) p Fh 2508 3318 a(for) p Fc 2614 3318 a(\(\001) p Fe(N) p Fa 2769 3326 a(1) p Fe 2804 3318 a(;) p Fc 2838 3318 a(\001) p Fe(N) p Fa 2963 3326 a(2) p Fe 2998 3318 a(;) p Fc 3032 3318 a(\001) p Fe(N) p Fa 3157 3326 a(3) p Fc 3192 3318 a(\)) p 3244 3318 a(=) p 3325 3318 a(\(1) p Fe(;) p Fc 3427 3318 a(1) p Fe(;) p Fc 3500 3318 a(1\)) p Fh(.) p Fr 1987 3688 a(case) p 2163 3688 a(that) p 2321 3688 a(the) p 2455 3688 a(number) p 2742 3688 a(of) p 2845 3688 a(TCP) p 3030 3688 a(connections) p 3460 3688 a(is) p 3549 3688 a(incremented) 1987 3788 y(by) p 2100 3788 a(three.) p 2341 3788 a(Finally) p 2572 3788 a(,) p 2625 3788 a(in) p 2720 3788 a(Fig.) p 2882 3788 a(8,) p Fm 2977 3788 a(\() p Fo(t) p Fl 3039 3800 a(1) p Fo 3076 3788 a(;) p 3113 3788 a(t) p Fl 3143 3800 a(2) p Fo 3180 3788 a(;) p 3217 3788 a(t) p Fl 3247 3800 a(3) p Fm 3284 3788 a(\)) p 3357 3788 a(=) p 3463 3788 a(\(5) p Fo(;) p Fm 3574 3788 a(10) p Fo(;) p Fm 3695 3788 a(15\)) p Fr 3839 3788 a(and) p Fm 1987 3888 a(\(\001) p Fo(N) p Fl 2155 3900 a(1) p Fo 2192 3888 a(;) p Fm 2229 3888 a(\001) p Fo(N) p Fl 2365 3900 a(2) p Fo 2402 3888 a(;) p Fm 2439 3888 a(\001) p Fo(N) p Fl 2575 3900 a(3) p Fm 2612 3888 a(\)) p 2678 3888 a(=) p 2776 3888 a(\(1) p Fo(;) p Fm 2887 3888 a(2) p Fo(;) p Fm 2966 3888 a(1\)) p Fr 3065 3888 a(for) p 3188 3888 a(analyzing) p 3537 3888 a(the) p 3665 3888 a(case) p 3835 3888 a(that) 1987 3987 y(the) p 2109 3987 a(number) p 2383 3987 a(of) p 2473 3987 a(TCP) p 2646 3987 a(connections) p 3063 3987 a(is) p 3140 3987 a(incremented) p 3571 3987 a(by) p 3675 3987 a(four) p 3810 3987 a(.) 1987 4170 y(In) p 2087 4170 a(each) p 2270 4170 a(\002gure,) p 2518 4170 a(the) p 2651 4170 a(impulse) p 2945 4170 a(response) p 3266 4170 a(of) p 3367 4170 a(the) p 3499 4170 a(transfer) p 3784 4170 a(func-) 1987 4269 y(tion) p Fo 2152 4269 a(U) p Fm 2218 4269 a(\() p Fo(z) p Fm 2293 4269 a(\)) p Fs 2355 4269 a(\002) p Fo 2449 4269 a(G) p Fm(\() p Fo(z) p Fm 2589 4269 a(\)) p Fr 2658 4269 a(\(upper\)) p 2938 4269 a(and) p 3094 4269 a(the) p 3232 4269 a(gain) p 3411 4269 a(characteristic) p 3890 4269 a(of) p Fo 1987 4369 a(U) p Fm 2053 4369 a(\() p Fo(z) p Fm 2128 4369 a(\)) p Fs 2180 4369 a(\002) p Fo 2265 4369 a(G) p Fm(\() p Fo(z) p Fm 2405 4369 a(\)) p Fr 2461 4369 a(\(lo) n(wer\).) p 2758 4369 a(The) p 2911 4369 a(impulse) p 3197 4369 a(response) p 3511 4369 a(illustrates) p 3858 4369 a(the) 1987 4469 y(e) n(v) n(olution) p 2315 4469 a(of) p 2402 4469 a(the) p 2522 4469 a(queue) p 2738 4469 a(length) p 2964 4469 a(of) p 3052 4469 a(the) p 3171 4469 a(RED) p 3356 4469 a(gate) n(w) o(ay) p 3626 4469 a(.) p 3669 4469 a(The) p 3817 4469 a(gain) 1987 4568 y(characteristic) p 2454 4568 a(illustrates) p 2802 4568 a(the) p 2928 4568 a(amplitude) p 3285 4568 a(of) p 3379 4568 a(the) p 3505 4568 a(transfer) p 3784 4568 a(func-) 1987 4668 y(tion) p Fo 2141 4668 a(U) p Fm 2207 4668 a(\() p Fo(z) p Fm 2282 4668 a(\)) p Fs 2335 4668 a(\002) p Fo 2421 4668 a(G) p Fm(\() p Fo(z) p Fm 2561 4668 a(\)) p Fr 2618 4668 a(at) p 2703 4668 a(dif) n(ferent) p 3011 4668 a(frequencies.) p 3453 4668 a(Note) p 3639 4668 a(that) p 3788 4668 a(these) 1987 4768 y(impulse) p 2279 4768 a(responses) p 2632 4768 a(are) p 2764 4768 a(obtained) p 3079 4768 a(not) p 3215 4768 a(from) p 3407 4768 a(iterati) n(v) o(e) p 3705 4768 a(compu-) 1987 4867 y(tation) p 2206 4867 a(using) p 2416 4867 a(Eq.) p 2559 4867 a(\(4\),) p 2709 4867 a(b) n(ut) p 2843 4867 a(from) p 3034 4867 a(direct) p 3253 4867 a(calculation) p 3648 4867 a(using) p 3858 4867 a(the) 1987 4967 y(transfer) p 2268 4967 a(function) p 2573 4967 a(and) p 2722 4967 a(the) p 2851 4967 a(MA) p 2976 4967 a(TLAB) p 3221 4967 a(language.) p 3590 4967 a(By) p 3715 4967 a(analyz-) 1987 5066 y(ing) p 2125 5066 a(these) p 2329 5066 a(impulse) p 2624 5066 a(responses,) p 3003 5066 a(we) p 3133 5066 a(can) p 3281 5066 a(in) m(v) o(estigate) p 3668 5066 a(the) p 3802 5066 a(tran-) 1987 5166 y(sient) p 2162 5166 a(beha) n(vior) p 2468 5166 a(of) p 2556 5166 a(the) p 2675 5166 a(RED) p 2859 5166 a(gate) n(w) o(ay) p 3151 5166 a(for) p 3266 5166 a(v) n(arious) p 3526 5166 a(types) p 3720 5166 a(of) p 3807 5166 a(TCP) 1987 5266 y(connection) p 2378 5266 a(v) n(ariations.) p 2768 5266 a(F) o(or) p 2909 5266 a(e) o(xample,) p 3239 5266 a(comparing) p 3621 5266 a(gain) p 3790 5266 a(char) n(-) 1987 5365 y(acteristics) p 2341 5365 a(of) p 2432 5365 a(Figs.) p 2617 5365 a(7) p 2681 5365 a(and) p 2823 5365 a(8) p 2886 5365 a(tells) p 3047 5365 a(us) p 3142 5365 a(that) p 3289 5365 a(the) p 3412 5365 a(amplitude) p 3766 5365 a(of) p 3858 5365 a(the) 1987 5465 y(queue) p 2202 5465 a(length) p 2426 5465 a(of) p 2513 5465 a(the) p 2631 5465 a(RED) p 2814 5465 a(gate) n(w) o(ay) p 3104 5465 a(in) p 3186 5465 a(Fig.) p 3335 5465 a(8) p 3393 5465 a(is) p 3465 5465 a(lar) o(ger) p 3675 5465 a(than) p 3835 5465 a(that) 1987 5565 y(in) p 2070 5565 a(Fig.) p 2219 5565 a(7.) p 2307 5565 a(In) p 2394 5565 a(other) p 2583 5565 a(w) o(ords,) p 2825 5565 a(using) p 3023 5565 a(the) p 3143 5565 a(transfer) p 3415 5565 a(function) p 3710 5565 a(enables) 1987 5664 y(us) p 2079 5664 a(to) p 2163 5664 a(analyze) p 2435 5664 a(the) p 2555 5664 a(transient) p 2860 5664 a(beha) n(vior) p 3168 5664 a(of) p 3256 5664 a(the) p 3376 5664 a(RED) p 3561 5664 a(gate) n(w) o(ay) p 3853 5664 a(not) 1987 5764 y(in) p 2072 5764 a(time) p 2240 5764 a(domain) p 2510 5764 a(b) n(ut) p 2635 5764 a(in) p 2721 5764 a(frequenc) o(y) p 3072 5764 a(domain.) 3830 6013 y(p.) p 3918 6013 a(5) p 90 rotate dyy eop %%Page: 6 6 6 5 bop -177 1287 a @beginspecial 43 @llx 184 @lly 552 @urx 592 @ury 2257 @rwi 1515 @rhi @setspecial %%BeginDocument: figure/transient-f3g.eps %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: transient-f3g.eps %%CreationDate: 12/17/ 1 13:35:47 %%DocumentNeededFonts: Helvetica %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 43 184 552 592 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 160 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /sg /setgray ldef /w /setlinewidth ldef /j /setlinejoin ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup where {pop load} {pop StandardEncoding} ifelse exch dup 3 1 roll findfont dup length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall /Encoding exch def currentdict end definefont pop } bdef /isroman { findfont /CharStrings get /Agrave known } bdef /FMSR { 3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse exch FMS } bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if } bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath eofill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { currentlinecap 1 setlinecap 3 1 roll 2 copy moveto lineto stroke setlinecap } bdef /FA { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arc tMatrix setmatrix stroke } bdef /PA { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arc closepath tMatrix setmatrix fill } bdef /FAn { newpath tMatrix currentmatrix pop translate scale 0 0 1 5 -2 roll arcn tMatrix setmatrix stroke } bdef /PAn { newpath tMatrix currentmatrix pop translate 0 0 moveto scale 0 0 1 5 -2 roll arcn closepath tMatrix setmatrix fill } bdef /vradius 0 def /hradius 0 def /lry 0 def /lrx 0 def /uly 0 def /ulx 0 def /rad 0 def /MRR { /vradius xdef /hradius xdef /lry xdef /lrx xdef /uly xdef /ulx xdef newpath tMatrix currentmatrix pop ulx hradius add uly vradius add translate hradius vradius scale 0 0 1 180 270 arc tMatrix setmatrix lrx hradius sub uly vradius add translate hradius vradius scale 0 0 1 270 360 arc tMatrix setmatrix lrx hradius sub lry vradius sub translate hradius vradius scale 0 0 1 0 90 arc tMatrix setmatrix ulx hradius add lry vradius sub translate hradius vradius scale 0 0 1 90 180 arc tMatrix setmatrix closepath } bdef /FRR { MRR stroke } bdef /PRR { MRR fill } bdef /MlrRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lry uly sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 90 270 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 270 90 arc tMatrix setmatrix closepath } bdef /FlrRR { MlrRR stroke } bdef /PlrRR { MlrRR fill } bdef /MtbRR { /lry xdef /lrx xdef /uly xdef /ulx xdef /rad lrx ulx sub 2 div def newpath tMatrix currentmatrix pop ulx rad add uly rad add translate rad rad scale 0 0 1 180 360 arc tMatrix setmatrix lrx rad sub lry rad sub translate rad rad scale 0 0 1 0 180 arc tMatrix setmatrix closepath } bdef /FtbRR { MtbRR stroke } bdef /PtbRR { MtbRR fill } bdef currentdict end def %%EndProlog %%BeginSetup MathWorks begin 0 cap end %%EndSetup %%Page: 1 1 %%BeginPageSetup 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mt 4472 2117 L 4472 389 mt 4472 443 L 4366 2384 mt (20) s 5366 2171 mt 5366 2117 L 5366 389 mt 5366 443 L 5260 2384 mt (25) s 6259 2171 mt 6259 2117 L 6259 389 mt 6259 443 L 6153 2384 mt (30) s 899 1874 mt 953 1874 L 6259 1874 mt 6205 1874 L 758 1945 mt (7) s 899 1280 mt 953 1280 L 6259 1280 mt 6205 1280 L 758 1351 mt (8) s 899 686 mt 953 686 L 6259 686 mt 6205 686 L 758 757 mt (9) s 899 2171 mt 6259 2171 L 899 389 mt 6259 389 L 899 2171 mt 899 389 L 6259 2171 mt 6259 389 L gs 899 389 5361 1783 MR c np 143 0 0 2 179 0 0 3 179 0 0 3 178 0 0 5 179 0 0 5 179 0 0 7 178 0 0 8 179 0 0 11 179 0 0 13 178 0 0 17 179 0 0 20 179 0 0 26 178 0 0 33 179 0 0 41 179 0 0 51 178 0 0 64 179 0 0 82 179 0 0 107 178 0 0 -335 179 0 0 67 179 0 0 86 178 0 0 109 179 0 0 146 179 0 0 -754 178 0 0 29 179 0 0 37 179 0 0 47 178 0 0 64 179 0 0 -389 179 0 0 0 178 0 0 0 179 0 0 0 179 0 0 0 178 0 0 0 179 0 899 1901 70 MP stroke gr 2782 2580 mt (Sequence Number) s 703 2247 mt -90 rotate (Queue Length [packet]) s 90 rotate 1 sg 0 1782 5360 0 0 -1782 899 4613 4 MP PP -5360 0 0 1782 5360 0 0 -1782 899 4613 5 MP stroke 4 w DO SO 6 w 0 sg 899 4613 mt 6259 4613 L 899 2831 mt 6259 2831 L 899 4613 mt 899 2831 L 6259 4613 mt 6259 2831 L 899 4613 mt 6259 4613 L 899 4613 mt 899 2831 L 899 4613 mt 899 4586 L 899 2831 mt 899 2858 L 899 4613 mt 899 4559 L 899 2831 mt 899 2885 L 720 4886 mt (10) s %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 128 FMSR 933 4767 mt (-3) s 1388 4613 mt 1388 4586 L 1388 2831 mt 1388 2858 L 1674 4613 mt 1674 4586 L 1674 2831 mt 1674 2858 L 1877 4613 mt 1877 4586 L 1877 2831 mt 1877 2858 L 2034 4613 mt 2034 4586 L 2034 2831 mt 2034 2858 L 2163 4613 mt 2163 4586 L 2163 2831 mt 2163 2858 L 2271 4613 mt 2271 4586 L 2271 2831 mt 2271 2858 L 2365 4613 mt 2365 4586 L 2365 2831 mt 2365 2858 L 2448 4613 mt 2448 4586 L 2448 2831 mt 2448 2858 L 2523 4613 mt 2523 4586 L 2523 2831 mt 2523 2858 L 2523 4613 mt 2523 4559 L 2523 2831 mt 2523 2885 L %%IncludeResource: font Helvetica 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5281 4586 L 5281 2831 mt 5281 2858 L 5410 4613 mt 5410 4586 L 5410 2831 mt 5410 2858 L 5519 4613 mt 5519 4586 L 5519 2831 mt 5519 2858 L 5613 4613 mt 5613 4586 L 5613 2831 mt 5613 2858 L 5696 4613 mt 5696 4586 L 5696 2831 mt 5696 2858 L 5770 4613 mt 5770 4586 L 5770 2831 mt 5770 2858 L 5770 4613 mt 5770 4559 L 5770 2831 mt 5770 2885 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 192 FMSR 5628 4886 mt (10) s %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 128 FMSR 5841 4767 mt (0) s 6259 4613 mt 6259 4586 L 6259 2831 mt 6259 2858 L 899 4257 mt 953 4257 L 6259 4257 mt 6205 4257 L %%IncludeResource: font Helvetica /Helvetica /ISOLatin1Encoding 192 FMSR 544 4328 mt (100) s 899 3900 mt 953 3900 L 6259 3900 mt 6205 3900 L 544 3971 mt (200) s 899 3544 mt 953 3544 L 6259 3544 mt 6205 3544 L 544 3615 mt (300) s 899 3187 mt 953 3187 L 6259 3187 mt 6205 3187 L 544 3258 mt (400) s 899 2831 mt 953 2831 L 6259 2831 mt 6205 2831 L 544 2902 mt (500) s 899 4613 mt 6259 4613 L 899 2831 mt 6259 2831 L 899 4613 mt 899 2831 L 6259 4613 mt 6259 2831 L gs 899 2831 5361 1783 MR c np 1 0 5 0 9 0 11 0 16 1 6 0 16 1 29 1 4 0 3 1 46 1 27 0 22 0 32 -1 17 -1 22 -1 27 -1 3 0 21 -1 16 0 9 0 3 0 8 0 7 0 6 0 9 0 12 0 4 0 11 0 22 1 15 0 14 1 35 1 5 0 54 3 73 2 22 0 0 0 134 -1 99 -3 73 -2 53 -1 40 -1 29 0 22 0 16 0 11 0 9 0 6 0 7 0 9 0 11 0 16 0 22 0 29 0 40 1 53 1 73 2 99 4 134 5 162 7 162 6 162 6 162 6 163 5 162 5 162 6 162 8 162 9 162 13 162 18 162 22 162 29 162 37 162 46 162 60 162 75 162 95 162 119 162 151 162 190 162 238 162 301 162 378 162 476 899 2294 86 MP stroke gr gs 826 2221 5825 2466 MR c np 1198 3123 mt 1248 3173 L 1248 3123 mt 1198 3173 L 1360 3424 mt 1410 3474 L 1410 3424 mt 1360 3474 L 1522 3662 mt 1572 3712 L 1572 3662 mt 1522 3712 L 1684 3852 mt 1734 3902 L 1734 3852 mt 1684 3902 L 1846 4003 mt 1896 4053 L 1896 4003 mt 1846 4053 L 2008 4122 mt 2058 4172 L 2058 4122 mt 2008 4172 L 2170 4217 mt 2220 4267 L 2220 4217 mt 2170 4267 L 2332 4292 mt 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5334 4637 L 5334 4587 mt 5284 4637 L 5324 4588 mt 5374 4638 L 5374 4588 mt 5324 4638 L 5353 4588 mt 5403 4638 L 5403 4588 mt 5353 4638 L 5375 4588 mt 5425 4638 L 5425 4588 mt 5375 4638 L 5391 4588 mt 5441 4638 L 5441 4588 mt 5391 4638 L 5402 4588 mt 5452 4638 L 5452 4588 mt 5402 4638 L 5411 4588 mt 5461 4638 L 5461 4588 mt 5411 4638 L 5418 4588 mt 5468 4638 L 5468 4588 mt 5418 4638 L 5424 4588 mt 5474 4638 L 5474 4588 mt 5424 4638 L 5433 4588 mt 5483 4638 L 5483 4588 mt 5433 4638 L 5444 4588 mt 5494 4638 L 5494 4588 mt 5444 4638 L 5460 4588 mt 5510 4638 L 5510 4588 mt 5460 4638 L 5482 4588 mt 5532 4638 L 5532 4588 mt 5482 4638 L 5511 4588 mt 5561 4638 L 5561 4588 mt 5511 4638 L 5551 4587 mt 5601 4637 L 5601 4587 mt 5551 4637 L 5604 4586 mt 5654 4636 L 5654 4586 mt 5604 4636 L 5677 4584 mt 5727 4634 L 5727 4584 mt 5677 4634 L 5776 4581 mt 5826 4631 L 5826 4581 mt 5776 4631 L 5910 4580 mt 5960 4630 L 5960 4580 mt 5910 4630 L 5910 4580 mt 5960 4630 L 5960 4580 mt 5910 4630 L 5932 4580 mt 5982 4630 L 5982 4580 mt 5932 4630 L 6005 4582 mt 6055 4632 L 6055 4582 mt 6005 4632 L 6059 4585 mt 6109 4635 L 6109 4585 mt 6059 4635 L 6064 4585 mt 6114 4635 L 6114 4585 mt 6064 4635 L 6099 4586 mt 6149 4636 L 6149 4586 mt 6099 4636 L 6113 4587 mt 6163 4637 L 6163 4587 mt 6113 4637 L 6128 4587 mt 6178 4637 L 6178 4587 mt 6128 4637 L 6150 4588 mt 6200 4638 L 6200 4588 mt 6150 4638 L 6161 4588 mt 6211 4638 L 6211 4588 mt 6161 4638 L 6165 4588 mt 6215 4638 L 6215 4588 mt 6165 4638 L 6177 4588 mt 6227 4638 L 6227 4588 mt 6177 4638 L 6186 4588 mt 6236 4638 L 6236 4588 mt 6186 4638 L 6192 4588 mt 6242 4638 L 6242 4588 mt 6192 4638 L 6199 4588 mt 6249 4638 L 6249 4588 mt 6199 4638 L 6207 4588 mt 6257 4638 L 6257 4588 mt 6207 4638 L 6210 4588 mt 6260 4638 L 6260 4588 mt 6210 4638 L 6219 4588 mt 6269 4638 L 6269 4588 mt 6219 4638 L 6235 4588 mt 6285 4638 L 6285 4588 mt 6235 4638 L gs 899 2831 5361 1783 MR c np gr gr 2469 5082 mt (Frequency [rad/sequence]) s 489 4147 mt -90 rotate (Amplitude) s 90 rotate end eplot %%EndObject epage end showpage %%Trailer %%EOF %%EndDocument @endspecial Fq -222 1469 a(Figur) o(e) p 42 1469 a(8:) p Fh 142 1469 a(Impulse) p 411 1469 a(response) p 700 1469 a(and) p 836 1469 a(gain) p 992 1469 a(characteristic) p 1418 1469 a(of) p Fe 1508 1469 a(U) p Fc 1568 1469 a(\() p Fe(z) p Fc 1637 1469 a(\)) p Fb 1691 1469 a(\002) p Fe 122 1561 a(G) p Fc(\() p Fe(z) p Fc 251 1561 a(\)) p Fh 300 1561 a(for) p Fc 406 1561 a(\(\001) p Fe(N) p Fa 561 1569 a(1) p Fe 595 1561 a(;) p Fc 630 1561 a(\001) p Fe(N) p Fa 755 1569 a(2) p Fe 790 1561 a(;) p Fc 824 1561 a(\001) p Fe(N) p Fa 949 1569 a(3) p Fc 984 1561 a(\)) p 1035 1561 a(=) p 1116 1561 a(\(1) p Fe(;) p Fc 1218 1561 a(2) p Fe(;) p Fc 1291 1561 a(1\)) p Fh(.) -177 2639 y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2257 @rwi 1033 @rhi @setspecial %%BeginDocument: figure/n1default.eps %!PS-Adobe-2.0 EPSF-2.0 %%Creator: gnuplot 3.7 patchlevel 1 %%CreationDate: Wed Dec 19 03:00:30 2001 %%DocumentFonts: (atend) %%BoundingBox: 50 50 410 302 %%Orientation: Portrait %%EndComments /gnudict 256 dict def gnudict begin /Color false def /Solid false def /gnulinewidth 5.000 def /userlinewidth gnulinewidth def /vshift -80 def /dl {10 mul} def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} 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 Solid {pop []} if 0 setdash} ifelse } def /BL { stroke userlinewidth 2 mul setlinewidth } def /AL { stroke userlinewidth 2 div setlinewidth } def /UL { dup gnulinewidth mul /userlinewidth exch def 10 mul /udl exch def } def /PL { stroke userlinewidth setlinewidth } 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 [] 1 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 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] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 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 /MFshow {{dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch rmoveto dup dup 5 get exch 4 get {show} {stringwidth pop 0 rmoveto}ifelse dup 3 get {2 get neg 0 exch rmoveto pop} {pop aload pop moveto}ifelse} forall} bind def /MFwidth {0 exch {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 5 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 240 scalefont setfont 1.000 UL LTb 936 720 M 63 0 V 5793 0 R -63 0 V stroke 792 720 M [ [(Helvetica) 240.0 0.0 true true (0)] ] -80.0 MRshow 936 1526 M 63 0 V 5793 0 R -63 0 V stroke 792 1526 M [ [(Helvetica) 240.0 0.0 true true (5)] ] -80.0 MRshow 936 2333 M 63 0 V 5793 0 R -63 0 V stroke 792 2333 M [ [(Helvetica) 240.0 0.0 true true (10)] ] -80.0 MRshow 936 3139 M 63 0 V 5793 0 R -63 0 V stroke 792 3139 M [ [(Helvetica) 240.0 0.0 true true (15)] ] -80.0 MRshow 936 3946 M 63 0 V 5793 0 R -63 0 V stroke 792 3946 M [ [(Helvetica) 240.0 0.0 true true (20)] ] -80.0 MRshow 936 4752 M 63 0 V 5793 0 R -63 0 V stroke 792 4752 M [ [(Helvetica) 240.0 0.0 true true (25)] ] -80.0 MRshow 936 720 M 0 63 V 0 3969 R 0 -63 V stroke 936 480 M [ [(Helvetica) 240.0 0.0 true true (8)] ] -80.0 MCshow 1668 720 M 0 63 V 0 3969 R 0 -63 V stroke 1668 480 M [ [(Helvetica) 240.0 0.0 true true (9)] ] -80.0 MCshow 2400 720 M 0 63 V 0 3969 R 0 -63 V stroke 2400 480 M [ [(Helvetica) 240.0 0.0 true true (10)] ] -80.0 MCshow 3132 720 M 0 63 V 0 3969 R 0 -63 V stroke 3132 480 M [ [(Helvetica) 240.0 0.0 true true (11)] ] -80.0 MCshow 3864 720 M 0 63 V 0 3969 R 0 -63 V stroke 3864 480 M [ [(Helvetica) 240.0 0.0 true true (12)] ] -80.0 MCshow 4596 720 M 0 63 V 0 3969 R 0 -63 V stroke 4596 480 M [ [(Helvetica) 240.0 0.0 true true (13)] ] -80.0 MCshow 5328 720 M 0 63 V 0 3969 R 0 -63 V stroke 5328 480 M [ [(Helvetica) 240.0 0.0 true true (14)] ] -80.0 MCshow 6060 720 M 0 63 V 0 3969 R 0 -63 V stroke 6060 480 M [ [(Helvetica) 240.0 0.0 true true (15)] ] -80.0 MCshow 6792 720 M 0 63 V 0 3969 R 0 -63 V stroke 6792 480 M [ [(Helvetica) 240.0 0.0 true true (16)] ] -80.0 MCshow 1.000 UL LTb 936 720 M 5856 0 V 0 4032 V -5856 0 V 936 720 L stroke 240 2736 M currentpoint gsave translate 90 rotate 0 0 moveto [ [(Helvetica) 240.0 0.0 true true (Queue Length \(packet\))] ] -80.0 MCshow grestore 3864 120 M [ [(Helvetica) 240.0 0.0 true true (Time \(s\))] ] -80.0 MCshow 1.000 UL LT0 5721 4569 M [ [(Helvetica) 240.0 0.0 true true (Queue Length \(Analysis\))] ] -80.0 MRshow 5865 4569 M 639 0 V 936 2139 M 1464 0 V 49 0 V 25 842 V 66 -134 V 64 -341 V 81 -300 V 115 -139 V 136 18 V 135 97 V 123 97 V 110 52 V 104 3 V 102 -27 V 105 -31 V 109 -18 V 112 -4 V 112 7 V 111 9 V 110 7 V 109 2 V 109 -2 V 109 -3 V 110 -2 V 109 -1 V 110 1 V 110 1 V 110 0 V 110 1 V 109 0 V 110 -1 V 109 0 V 110 0 V 110 0 V 109 0 V 110 0 V 110 0 V 109 0 V 110 0 V 110 0 V 109 0 V 110 0 V 110 0 V 102 0 V 1.000 UL LT1 5721 4329 M [ [(Helvetica) 240.0 0.0 true true (Queue Length \(Simulation\))] ] -80.0 MRshow 5865 4329 M 639 0 V 936 1423 M 26 103 V 26 162 V 32 161 V 33 161 V 41 162 V 40 161 V 29 -161 V 19 161 V 29 -323 V 18 -645 V 40 161 V 26 162 V 33 161 V 33 161 V 40 162 V 22 -162 V 18 162 V 26 -323 V 15 -484 V 40 161 V 26 162 V 32 161 V 33 161 V 26 -161 V 15 161 V 25 -322 V 15 -484 V 33 161 V 22 161 V 29 162 V 29 161 V 37 161 V 37 162 V 33 -162 V 10 162 V 33 -323 V 15 -484 V 40 161 V 26 162 V 33 161 V 33 161 V 40 162 V 40 161 V 48 161 V 7 -161 V 41 161 V 10 -322 V 19 -646 V 47 162 V 30 161 V 14 161 V 22 162 V 11 161 V 0 161 V 0 161 V 0 162 V 0 161 V 0 161 V 0 161 V 0 162 V 0 161 V 30 161 V 18 -161 V 14 161 V 48 162 V 18 -323 V 15 -484 V 48 161 V 47 -161 V 22 161 V 7 162 V 41 -323 V 18 -645 V 11 161 V 55 162 V 4 -162 V 25 162 V 33 -323 V 22 161 V 15 -161 V 33 -161 V 7 161 V 44 -322 V 7 -162 V 0 162 V 18 -162 V 22 162 V 30 161 V 14 161 V 15 -161 V 15 161 V 18 161 V 18 -322 V 8 -161 V 29 161 V 44 161 V 7 161 V 18 -161 V 22 161 V 11 162 V 22 -323 V 15 -484 V 22 162 V 36 -162 V 4 162 V 11 161 V 29 -323 V 8 -161 V 7 161 V 40 162 V 41 161 V 22 -161 V 25 161 V 11 -161 V 0 161 V 33 161 V 29 -161 V 22 161 V 4 161 V 26 -322 V 14 -484 V 11 161 V 40 162 V 11 -162 V 4 162 V 26 161 V 14 -323 V 8 -161 V 22 161 V 44 162 V 7 161 V 4 -161 V 29 161 V 18 -323 V 7 -161 V 22 161 V 37 162 V 4 -162 V 3 162 V 41 161 V 18 -323 V 7 -161 V 22 161 V 37 162 V 7 161 V 33 -161 V 4 161 V 7 161 V 37 -322 V 14 161 V 15 -323 V 29 162 V 18 161 V 11 -161 V 11 161 V 22 161 V 15 -322 V 7 -162 V 44 162 V 26 161 V 15 161 V 21 -161 V 8 161 V 22 161 V 29 162 V 15 -323 V 11 -322 V 18 -162 V 11 162 V 33 -323 V 7 -161 V 8 161 V 32 161 V 19 162 V 22 161 V 18 -161 V 0 161 V 26 161 V 22 -322 V 29 161 V 44 161 V 3 -161 V 8 161 V 40 -161 V 7 161 V 11 -161 V 11 -323 V 19 -161 V 11 161 V 29 -322 V 11 161 V 33 161 V 18 162 V 40 161 V 30 -323 V 7 -161 V 11 161 V 37 162 V 18 161 V 22 161 V 7 -161 V 15 161 V 58 -322 V 8 -162 V 11 162 V 40 161 V 22 161 V 3 -161 V 22 161 V 30 -322 V 18 161 V 22 -161 V 22 161 V 22 -161 V 26 161 V 29 -161 V 14 161 V 33 -323 V 19 -645 V 40 161 V 15 162 V 11 161 V 14 161 V 19 -161 V 3 161 V 37 -322 V 11 -323 V 0 161 V 25 162 V 19 161 V 14 161 V 19 162 V 62 -162 V 0 162 V 25 -162 V 15 162 V 44 161 V 18 161 V 19 -161 V 7 161 V 22 161 V 22 -322 V 11 -323 V 22 162 V 40 161 V 11 161 V 26 -161 V 7 161 V 15 161 V 29 -322 V 7 -161 V 19 161 V 43 161 V 8 -161 V 11 161 V 36 -161 V 11 161 V 11 -161 V 11 -323 V 30 162 V 25 -162 V 15 162 V 3 161 V 26 -323 V 7 -161 V 11 161 V 41 162 V 7 -162 V 7 162 V 26 161 V 7 -161 V 8 161 V 14 -161 V 8 -162 V 25 162 V 40 161 V 8 161 V 7 -161 V 33 161 V 7 155 V 1.000 UL LT2 5721 4089 M [ [(Helvetica) 240.0 0.0 true true (Average Queue Length \(Simulation\))] ] -80.0 MRshow 5865 4089 M 639 0 V 936 1881 M 4 -1 V 4 -1 V 3 -1 V 4 -1 V 4 -2 V 3 -1 V 4 -1 V 4 -1 V 3 -1 V 4 0 V 4 -1 V 3 -1 V 4 0 V 4 -1 V 3 -1 V 4 0 V 4 -1 V 3 0 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 1 V 4 0 V 3 0 V 4 1 V 4 0 V 3 0 V 4 0 V 4 1 V 3 0 V 4 0 V 4 1 V 3 1 V 4 0 V 4 1 V 3 1 V 4 0 V 4 1 V 3 0 V 4 1 V 4 1 V 3 0 V 4 1 V 0 1 V 4 1 V 3 0 V 4 1 V 4 1 V 3 1 V 4 1 V 4 1 V 3 1 V 4 0 V 4 1 V 3 0 V 4 1 V 4 0 V 0 1 V 3 1 V 4 1 V 3 1 V 4 1 V 4 1 V 11 0 V 18 -1 V 4 -1 V 3 -1 V 4 -1 V 4 -1 V 3 -1 V 4 -1 V 4 -1 V 3 -1 V 4 -1 V 4 -1 V 3 -1 V 0 -1 V 4 -1 V 4 -1 V 3 0 V 4 -1 V 4 -1 V 3 0 V 4 -1 V 4 -1 V 3 0 V 4 -1 V 4 0 V 3 0 V 4 -1 V 4 0 V 3 0 V 4 -1 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 1 V 4 0 V 3 0 V 4 1 V 4 0 V 3 0 V 4 0 V 4 1 V 3 0 V 4 0 V 0 1 V 4 0 V 3 1 V 4 1 V 4 0 V 3 1 V 4 0 V 4 0 V 3 1 V 4 0 V 4 0 V 3 0 V 0 1 V 4 1 V 4 0 V 3 1 V 4 0 V 11 0 V 15 -1 V 3 -1 V 4 -1 V 4 -1 V 3 -1 V 4 -1 V 4 -1 V 3 -1 V 4 -1 V 4 -1 V 3 -1 V 4 -1 V 0 -1 V 4 0 V 3 -1 V 4 -1 V 4 0 V 3 -1 V 4 -1 V 4 0 V 0 -1 V 3 0 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 1 V 4 0 V 3 0 V 4 0 V 4 1 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 1 V 4 0 V 4 0 V 3 0 V 11 0 V 15 -1 V 4 -2 V 3 -1 V 4 -1 V 4 -1 V 3 -2 V 4 -1 V 4 -1 V 3 -2 V 4 -1 V 0 -1 V 4 -1 V 3 -1 V 4 -1 V 3 -1 V 4 -1 V 4 -1 V 3 -1 V 4 -1 V 4 0 V 3 -1 V 4 0 V 4 -1 V 3 -1 V 4 0 V 0 -1 V 4 0 V 3 0 V 4 -1 V 4 0 V 3 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 0 1 V 4 0 V 3 0 V 4 1 V 4 0 V 3 0 V 4 1 V 4 0 V 3 0 V 4 1 V 4 0 V 0 1 V 3 0 V 4 1 V 4 1 V 3 0 V 4 1 V 4 1 V 3 0 V 4 1 V 4 0 V 3 1 V 4 0 V 3 0 V 0 1 V 4 1 V 4 0 V 3 1 V 4 1 V 4 0 V 3 1 V 11 0 V 15 -1 V 4 -1 V 3 -1 V 4 -1 V 4 -1 V 3 -1 V 4 -1 V 4 -1 V 3 -1 V 4 -1 V 4 -1 V 3 -1 V 4 -1 V 4 0 V 3 -1 V 4 -1 V 4 0 V 3 -1 V 4 0 V 0 -1 V 4 0 V 3 0 V 4 -1 V 4 0 V 3 0 V 4 -1 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 3 1 V 4 0 V 4 0 V 3 1 V 4 0 V 4 0 V 3 1 V 4 0 V 4 1 V 3 0 V 4 0 V 0 1 V 4 1 V 3 0 V 4 1 V 4 1 V 3 0 V 4 1 V 4 1 V 3 0 V 4 1 V 4 1 V 3 0 V 0 1 V 4 1 V 4 1 V 3 1 V 4 1 V 4 1 V 3 1 V 4 1 V 4 1 V 3 1 V 4 1 V 4 1 V 3 1 V 4 1 V 0 1 V 4 1 V 3 1 V 4 1 V 4 1 V 3 1 V 4 1 V 4 1 V 3 1 V 4 1 V 4 1 V 3 1 V 4 1 V 4 1 V 0 1 V 10 0 V 19 0 V 3 -1 V 4 -1 V 4 0 V 3 -1 V 4 -1 V 4 0 V 3 -1 V 4 -1 V 4 0 V 3 -1 V 4 -1 V 4 -1 V 3 0 V 0 -1 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 1 V 4 0 V 3 0 V 4 0 V 4 1 V 3 0 V currentpoint stroke M 0 1 V 4 0 V 4 1 V 3 0 V 0 1 V 0 2 V 0 1 V 0 2 V 0 2 V 0 3 V 0 3 V 0 3 V 0 3 V 4 4 V 4 3 V 3 4 V 4 3 V 4 4 V 3 3 V 4 4 V 4 3 V 0 4 V 3 3 V 4 4 V 3 4 V 4 4 V 4 3 V 3 3 V 4 4 V 4 3 V 3 4 V 0 3 V 4 4 V 4 4 V 3 3 V 4 4 V 4 3 V 3 4 V 4 4 V 4 3 V 3 4 V 4 4 V 4 3 V 3 4 V 4 3 V 0 4 V 4 4 V 3 4 V 11 3 V 15 2 V 4 3 V 3 2 V 4 2 V 4 2 V 3 3 V 4 2 V 4 2 V 3 2 V 4 2 V 4 3 V 3 2 V 4 2 V 4 2 V 0 3 V 3 2 V 4 3 V 4 2 V 3 3 V 4 2 V 4 3 V 3 2 V 4 3 V 3 2 V 4 3 V 4 2 V 3 3 V 4 2 V 4 2 V 3 2 V 4 2 V 4 2 V 3 2 V 4 2 V 0 3 V 4 2 V 3 3 V 0 2 V 4 3 V 4 3 V 3 2 V 4 3 V 4 3 V 3 3 V 4 2 V 4 3 V 11 2 V 18 1 V 4 0 V 3 1 V 4 1 V 0 1 V 4 1 V 3 1 V 4 1 V 4 1 V 3 1 V 4 1 V 4 1 V 3 1 V 4 1 V 4 1 V 3 1 V 4 1 V 4 1 V 3 2 V 4 1 V 0 1 V 4 1 V 3 1 V 4 1 V 3 1 V 4 1 V 4 1 V 3 1 V 4 1 V 0 1 V 4 2 V 3 1 V 4 1 V 4 2 V 3 1 V 4 1 V 11 1 V 4 1 V 3 0 V 4 1 V 4 0 V 3 1 V 4 1 V 0 1 V 4 1 V 3 1 V 8 0 V 3 1 V 4 1 V 4 0 V 3 1 V 4 1 V 4 0 V 3 1 V 4 1 V 4 0 V 3 0 V 4 0 V 0 1 V 4 1 V 3 0 V 4 1 V 4 1 V 3 0 V 4 1 V 4 0 V 3 1 V 4 1 V 11 0 V 7 -1 V 4 0 V 3 0 V 4 0 V 7 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 1 V 4 0 V 3 0 V 0 1 V 4 0 V 4 1 V 3 1 V 4 0 V 4 0 V 3 1 V 4 0 V 4 0 V 0 1 V 3 0 V 4 1 V 4 1 V 3 0 V 4 1 V 0 1 V 4 1 V 3 1 V 11 0 V 8 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 3 0 V 4 0 V 4 1 V 3 0 V 4 0 V 4 0 V 3 1 V 4 0 V 4 0 V 3 1 V 4 0 V 4 0 V 0 1 V 3 0 V 4 1 V 0 1 V 4 1 V 3 1 V 4 1 V 4 0 V 3 1 V 4 1 V 4 0 V 3 1 V 4 0 V 4 1 V 3 1 V 4 1 V 4 1 V 3 1 V 0 1 V 4 2 V 4 1 V 3 1 V 11 0 V 15 0 V 4 0 V 3 -1 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 1 V 4 0 V 3 0 V 11 0 V 8 -1 V 3 -1 V 4 0 V 0 -1 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 1 V 4 0 V 4 0 V 3 0 V 8 0 V 3 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 7 0 V 4 1 V 3 0 V 4 0 V 4 0 V 3 1 V 4 0 V 4 0 V 3 0 V 4 1 V 4 1 V 3 0 V 4 1 V 4 1 V 3 0 V 4 1 V 4 0 V 3 1 V 4 0 V 4 0 V 3 0 V 4 0 V 4 1 V 3 0 V 0 1 V 4 0 V 0 1 V 4 1 V 3 1 V 4 1 V 4 0 V 11 1 V 14 -1 V 4 -1 V 4 -1 V 3 0 V 0 -1 V 4 0 V 4 -1 V 3 0 V 4 0 V 3 -1 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 0 V 4 -1 V 4 0 V 3 0 V 4 0 V 4 0 V 3 1 V 11 -1 V 8 0 V 3 -1 V 4 -1 V 4 -1 V 3 0 V 4 -1 V 4 -1 V 3 -1 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 0 V currentpoint stroke M 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 1 V 11 -1 V 7 -1 V 4 0 V 4 -1 V 3 -1 V 4 0 V 4 -1 V 3 -1 V 4 0 V 4 -1 V 3 0 V 4 -1 V 4 0 V 3 0 V 4 -1 V 4 0 V 3 0 V 4 -1 V 4 0 V 3 0 V 0 -1 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 1 V 4 0 V 11 0 V 7 -1 V 4 -1 V 4 0 V 3 -1 V 4 -1 V 3 -1 V 4 0 V 0 -1 V 4 0 V 3 0 V 4 -1 V 4 0 V 3 0 V 4 -1 V 4 0 V 3 0 V 4 -1 V 4 0 V 3 0 V 4 0 V 4 1 V 3 0 V 4 0 V 4 0 V 3 1 V 4 0 V 4 0 V 3 1 V 4 0 V 4 0 V 3 0 V 4 0 V 0 1 V 4 1 V 3 0 V 4 1 V 4 1 V 3 0 V 4 1 V 4 0 V 11 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 1 V 11 -1 V 4 0 V 3 0 V 4 -1 V 4 0 V 3 0 V 4 -1 V 3 0 V 4 0 V 0 -1 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 0 1 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 1 V 4 0 V 3 0 V 4 0 V 4 1 V 3 0 V 0 1 V 4 0 V 11 0 V 7 0 V 4 0 V 4 -1 V 3 0 V 4 -1 V 4 0 V 3 0 V 4 -1 V 4 0 V 3 0 V 4 -1 V 4 0 V 3 0 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 0 V 4 0 V 0 1 V 4 0 V 3 0 V 4 1 V 4 0 V 3 1 V 4 1 V 3 0 V 4 1 V 4 0 V 3 1 V 4 0 V 4 0 V 0 1 V 3 1 V 4 0 V 4 1 V 3 0 V 4 1 V 4 1 V 3 1 V 4 1 V 4 1 V 3 1 V 4 1 V 4 1 V 3 1 V 4 1 V 0 1 V 4 1 V 11 1 V 11 0 V 3 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 11 0 V 7 -1 V 4 -1 V 4 -1 V 0 -1 V 3 -1 V 4 -1 V 3 0 V 4 -1 V 4 -1 V 3 0 V 4 -1 V 4 -1 V 3 0 V 0 -1 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 1 V 4 0 V 4 0 V 3 0 V 4 0 V 0 1 V 4 0 V 3 0 V 4 1 V 4 0 V 3 0 V 4 0 V 4 1 V 3 1 V 4 0 V 4 1 V 11 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 1 V 4 0 V 3 0 V 4 0 V 3 1 V 4 0 V 4 0 V 3 0 V 4 1 V 4 0 V 0 1 V 3 0 V 4 0 V 4 0 V 0 1 V 3 1 V 4 0 V 4 1 V 3 0 V 4 1 V 4 0 V 3 1 V 4 1 V 4 0 V 7 0 V 4 1 V 3 0 V 4 1 V 7 0 V 11 0 V 4 -1 V 4 0 V 3 0 V 4 -1 V 4 0 V 3 -1 V 4 -1 V 4 -1 V 3 0 V 4 -1 V 4 0 V 3 -1 V 4 0 V 11 -1 V 4 -1 V 3 -1 V 4 -1 V 0 -1 V 4 0 V 3 -1 V 4 -1 V 3 -1 V 4 0 V 4 -1 V 3 -1 V 4 0 V 4 -1 V 3 -1 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 -1 V 4 0 V 3 0 V 0 1 V 4 0 V 4 0 V 3 1 V 4 0 V 4 0 V 11 0 V 7 -1 V 4 -1 V 3 0 V 4 -1 V 4 -1 V 3 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 -1 V 3 0 V 4 -1 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 3 1 V 4 0 V 4 0 V 3 0 V 4 1 V 4 0 V 0 1 V 3 0 V 4 1 V 4 0 V 3 0 V 4 0 V 4 1 V 3 1 V 4 1 V 4 0 V 3 1 V 4 0 V 4 1 V 3 1 V 4 0 V 4 1 V 3 0 V 4 1 V 4 1 V 3 0 V 11 0 V 8 0 V 3 -1 V 4 0 V 4 0 V 3 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 1 V 3 0 V 4 0 V 4 0 V 3 1 V 4 0 V 0 1 V 3 0 V 4 0 V 4 0 V 3 1 V 4 0 V 4 0 V 3 0 V 0 1 V 4 1 V 4 0 V 3 1 V currentpoint stroke M 4 0 V 4 1 V 11 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 1 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 1 V 4 0 V 7 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 -1 V 0 1 V 3 0 V 4 0 V 4 0 V 3 1 V 4 0 V 3 0 V 4 1 V 4 -1 V 3 0 V 4 0 V 4 0 V 3 0 V 4 1 V 4 0 V 3 0 V 4 0 V 4 1 V 3 0 V 11 0 V 19 -2 V 3 -2 V 4 -2 V 4 -1 V 3 -2 V 4 -2 V 4 -1 V 3 -2 V 4 -2 V 4 -1 V 3 -2 V 4 -1 V 0 -2 V 4 -1 V 3 -1 V 4 -2 V 4 -1 V 0 -1 V 3 -1 V 4 -1 V 4 -1 V 0 -1 V 3 0 V 4 -1 V 4 -1 V 3 0 V 0 -1 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 -1 V 3 0 V 0 -1 V 4 0 V 3 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 -1 V 11 -1 V 11 -1 V 0 -2 V 3 -1 V 4 -1 V 4 -1 V 3 -2 V 4 -1 V 4 -1 V 3 -1 V 0 -1 V 4 -1 V 4 -1 V 3 -1 V 4 -1 V 4 -1 V 0 -1 V 3 0 V 4 -1 V 4 0 V 3 -1 V 4 -1 V 4 0 V 3 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 1 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 7 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 7 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 1 V 4 0 V 4 0 V 3 1 V 4 0 V 4 0 V 3 1 V 4 1 V 4 1 V 3 1 V 4 0 V 4 1 V 3 0 V 4 0 V 0 1 V 4 1 V 3 0 V 4 1 V 4 1 V 3 0 V 4 1 V 0 1 V 4 1 V 3 1 V 4 1 V 11 0 V 11 0 V 3 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 1 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 1 V 4 0 V 0 1 V 4 0 V 3 1 V 4 1 V 4 0 V 3 1 V 4 1 V 4 0 V 3 0 V 4 1 V 4 1 V 3 1 V 4 0 V 4 1 V 0 1 V 3 1 V 4 1 V 4 1 V 3 1 V 4 1 V 11 0 V 7 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 1 V 4 0 V 3 0 V 4 0 V 4 1 V 3 0 V 4 0 V 4 1 V 3 0 V 4 0 V 4 1 V 3 0 V 0 1 V 4 0 V 4 1 V 3 0 V 4 0 V 4 0 V 0 1 V 3 1 V 4 0 V 4 1 V 3 1 V 4 0 V 4 1 V 3 0 V 4 1 V 7 0 V 4 1 V 4 0 V 3 0 V 0 1 V 4 0 V 7 1 V 11 -1 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 -1 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 3 -1 V 4 0 V 4 -1 V 3 0 V 0 1 V 4 0 V 4 0 V 3 1 V 4 0 V 11 0 V 7 -1 V 4 -1 V 4 -1 V 3 0 V 0 -1 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 0 V 4 -1 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 7 0 V 4 0 V 4 0 V 3 0 V 4 1 V 7 0 V 8 -1 V 3 0 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 -1 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 0 V 4 0 V 3 0 V 4 1 V 4 0 V 3 1 V 4 0 V 4 1 V 3 0 V 4 0 V 4 1 V 3 0 V 4 0 V 4 1 V 3 0 V 4 0 V 0 1 V 4 0 V 3 1 V stroke grestore end showpage %%Trailer %%DocumentFonts: Helvetica %%EndDocument @endspecial Fq -222 2822 a(Figur) o(e) p 32 2822 a(9:) p Fh 122 2822 a(Comparison) p 506 2822 a(between) p 774 2822 a(analytic) p 1029 2822 a(and) p 1156 2822 a(simulation) p 1490 2822 a(results.) p Fr -222 3187 a(Finally) p 9 3187 a(,) p 48 3187 a(in) p 131 3187 a(Fig.) p 281 3187 a(9,) p 363 3187 a(we) p 478 3187 a(sho) n(w) p 670 3187 a(a) p 725 3187 a(simulation) p 1095 3187 a(result) p 1298 3187 a(when) p 1496 3187 a(all) p 1598 3187 a(TCP) -222 3287 y(connections) p 194 3287 a(operate) p 457 3287 a(in) p 541 3287 a(the) p 661 3287 a(congestion) p 1040 3287 a(a) n(v) n(oidance) p 1392 3287 a(phase) p 1601 3287 a(\(i.e.,) -222 3387 y(case) p -43 3387 a(C2\).) p 173 3387 a(This) p 356 3387 a(\002gure) p 586 3387 a(sho) n(ws) p 827 3387 a(the) p 964 3387 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4782 a(\)) p Fr 1097 4782 a(or) p Fo 1186 4782 a(q) p Fm 1226 4782 a(\() p Fo(k) p Fm 1304 4782 a(\)) p Fr(.) p 1383 4782 a(As) p 1495 4782 a(a) p 1552 4782 a(future) -222 4881 y(w) o(ork,) p -7 4881 a(more) p 187 4881 a(in) m(v) o(estigation) p 635 4881 a(for) p 755 4881 a(minimizing) p 1161 4881 a(the) p 1286 4881 a(dif) n(ference) p 1644 4881 a(be-) -222 4981 y(tween) p -4 4981 a(analytic) p 279 4981 a(and) p 419 4981 a(simulation) p 790 4981 a(results) p 1026 4981 a(w) o(ould) p 1253 4981 a(be) p 1352 4981 a(appropriate.) p Fq 204 5342 a(5) p 287 5342 a(Conclusion) p 705 5342 a(and) p 859 5342 a(Futur) o(e) p 1123 5342 a(W) p 1200 5342 a(ork) p Fr -222 5565 a(In) p -121 5565 a(this) p 31 5565 a(paper) m(,) p 268 5565 a(we) p 396 5565 a(ha) n(v) o(e) p 582 5565 a(analyzed) p 909 5565 a(the) p 1043 5565 a(transient) p 1360 5565 a(beha) n(vior) p 1681 5565 a(of) -222 5664 y(the) p -101 5664 a(RED) p 85 5664 a(gate) n(w) o(ay) p 378 5664 a(for) p 494 5664 a(v) n(arious) p 756 5664 a(types) p 951 5664 a(of) p 1040 5664 a(TCP) p 1212 5664 a(connection) p 1596 5664 a(v) n(ari-) -222 5764 y(ations) p 6 5764 a(such) p 188 5764 a(as) p 287 5764 a(intermittent) p 704 5764 a(arri) n(v) n(al) p 946 5764 a(or) p 1045 5764 a(continuous) p 1439 5764 a(arri) n(v) n(al) p 1681 5764 a(of) 1987 107 y(multiple) p 2294 107 a(TCP) p 2477 107 a(connections.) p 2949 107 a(W) p 3020 107 a(e) p 3088 107 a(ha) n(v) o(e) p 3273 107 a(used) p 3455 107 a(a) p 3523 107 a(control) p 3788 107 a(theo-) 1987 206 y(retic) p 2160 206 a(approach,) p 2512 206 a(which) p 2740 206 a(is) p 2821 206 a(based) p 3036 206 a(on) p 3144 206 a(the) p 3272 206 a(transfer) p 3551 206 a(function) p 3853 206 a(de-) 1987 306 y(scribing) p 2282 306 a(the) p 2412 306 a(relation) p 2693 306 a(between) p 2998 306 a(input) p 3197 306 a(and) p 3344 306 a(output) p 3585 306 a(not) p 3719 306 a(in) p 3811 306 a(time) 1987 406 y(domain) p 2262 406 a(b) n(ut) p 2392 406 a(in) p 2483 406 a(frequenc) o(y) p 2840 406 a(domain.) p 3152 406 a(Using) p 3377 406 a(the) p 3504 406 a(transfer) p 3784 406 a(func-) 1987 505 y(tion,) p 2157 505 a(v) n(arious) p 2420 505 a(characteristics) p 2915 505 a(of) p 3004 505 a(a) p 3062 505 a(feedback) p 3382 505 a(system) p 3633 505 a(can) p 3768 505 a(be) p 3867 505 a(in-) 1987 605 y(v) o(estigated.) p 2369 605 a(W) p 2440 605 a(e) p 2498 605 a(are) p 2621 605 a(currently) p 2941 605 a(w) o(orking) p 3238 605 a(to) p 3324 605 a(e) o(xtend) p 3565 605 a(our) p 3696 605 a(analytic) 1987 704 y(approach) p 2312 704 a(for) p 2429 704 a(other) p 2621 704 a(A) p 2676 704 a(QM) p 2830 704 a(mechanisms.) p Fq 2780 1047 a(Refer) o(ences) p Fr 1992 1176 a([1]) p 2199 1176 a(B.) p 2300 1176 a(Braden) p 2565 1176 a(et) p 2650 1176 a(al.,) p 2777 1176 a(\223Recommendations) p 3457 1176 a(on) p 3565 1176 a(queue) p 3788 1176 a(man-) 1987 1275 y(agement) p 2288 1275 a(and) p 2428 1275 a(congestion) p 2807 1275 a(a) n(v) n(oidance) p 3160 1275 a(in) p 3245 1275 a(the) p 3366 1275 a(Internet,) p 3641 1275 a(\224) p Fp 3696 1275 a(Request) 1987 1375 y(for) p 2104 1375 a(Comments) p 2476 1375 a(\(RFC\)) p 2708 1375 a(2309) p Fr(,) p 2916 1375 a(Apr) p 3041 1375 a(.) p 3082 1375 a(1998.) 1992 1508 y([2]) p 2199 1508 a(S.) p 2294 1508 a(Flo) o(yd) p 2515 1508 a(and) p 2662 1508 a(V) p 2711 1508 a(.) p 2760 1508 a(Jacobson,) p 3115 1508 a(\223Random) p 3461 1508 a(early) p 3655 1508 a(detection) 1987 1607 y(gate) n(w) o(ays) p 2323 1607 a(for) p 2450 1607 a(congestion) p 2841 1607 a(a) n(v) n(oidance,) p 3191 1607 a(\224) p Fp 3259 1607 a(IEEE/A) n(CM) p 3665 1607 a(T) p 3706 1607 a(r) o(ansac-) 1987 1707 y(tions) p 2169 1707 a(on) p 2273 1707 a(Networking) p Fr(,) p 2702 1707 a(v) n(ol.) p 2848 1707 a(1,) p 2931 1707 a(pp.) p 3055 1707 a(397\226413,) p 3387 1707 a(Aug.) p 3572 1707 a(1993.) 1992 1840 y([3]) p 2199 1840 a(M.) p 2321 1840 a(Christiansen,) p 2785 1840 a(K.) p 2892 1840 a(Jef) n(f) o(ay) p 3088 1840 a(,) p 3136 1840 a(D.) p 3243 1840 a(Ott,) p 3399 1840 a(and) p 3545 1840 a(F) p 3584 1840 a(.) p 3632 1840 a(D.) p 3740 1840 a(Smith,) 1987 1939 y(\223T) l(uning) p 2280 1939 a(RED) p 2466 1939 a(for) p 2583 1939 a(web) p 2741 1939 a(traf) n(\002c,) p 2953 1939 a(\224) p 3009 1939 a(in) p Fp 3094 1939 a(Pr) l(oceedings) p 3525 1939 a(of) p 3610 1939 a(A) n(CM) p 3802 1939 a(SIG-) 1987 2039 y(COMM) p 2261 2039 a(2000) p Fr(,) p 2469 2039 a(pp.) p 2593 2039 a(139\226150,) p 2925 2039 a(Aug.) p 3110 2039 a(2000.) 1992 2172 y([4]) p 2199 2172 a(C.) p 2296 2172 a(Hollot,) p 2549 2172 a(V) p 2598 2172 a(.) p 2640 2172 a(Misra,) p 2874 2172 a(D.) p 2976 2172 a(T) p 3020 2172 a(o) n(wsle) o(y) p 3248 2172 a(,) p 3287 2172 a(and) p 3428 2172 a(W) p 3498 2172 a(.-B.) p 3643 2172 a(Gong,) p 3869 2172 a(\223) p 3899 2172 a(A) 1987 2272 y(control) p 2251 2272 a(theoretic) p 2571 2272 a(analysis) p 2868 2272 a(of) p 2967 2272 a(RED,) p 3148 2272 a(\224) p 3214 2272 a(T) p 3259 2272 a(ech.) p 3425 2272 a(Rep.) p 3609 2272 a(TR) p 3745 2272 a(00-41,) 1987 2371 y(CMPSCI,) p 2333 2371 a(July) p 2492 2371 a(2000.) 1992 2504 y([5]) p 2199 2504 a(V) p 2248 2504 a(.) p 2299 2504 a(Firoiu) p 2533 2504 a(and) p 2683 2504 a(M.) p 2808 2504 a(Borden,) p 3106 2504 a(\223) p 3136 2504 a(A) p 3226 2504 a(study) p 3436 2504 a(of) p 3536 2504 a(acti) n(v) o(e) p 3761 2504 a(queue) 1987 2604 y(management) p 2454 2604 a(for) p 2594 2604 a(congestion) p 2997 2604 a(control,) p 3249 2604 a(\224) p 3332 2604 a(in) p Fp 3440 2604 a(Pr) l(oceedings) p 3894 2604 a(of) 1987 2703 y(IEEE) p 2187 2703 a(INFOCOM) p 2586 2703 a(2000) p Fr(,) p 2794 2703 a(Mar) p 2928 2703 a(.) p 2969 2703 a(2000.) 1992 2836 y([6]) p 2199 2836 a(M.) p 2315 2836 a(May) p 2463 2836 a(,) p 2504 2836 a(T) p 2549 2836 a(.) p 2591 2836 a(Bonald,) p 2872 2836 a(and) p 3014 2836 a(J.-C.) p 3192 2836 a(Bolot,) p 3418 2836 a(\223) p 3448 2836 a(Analytic) p 3756 2836 a(e) n(v) n(alu-) 1987 2936 y(ation) p 2172 2936 a(of) p 2261 2936 a(RED) p 2447 2936 a(performance,) p 2885 2936 a(\224) p 2938 2936 a(in) p Fp 3023 2936 a(Pr) l(oceedings) p 3454 2936 a(of) p 3538 2936 a(IEEE) p 3738 2936 a(INFO-) 1987 3035 y(COM) p 2192 3035 a(2000) p Fr(,) p 2399 3035 a(Mar) p 2533 3035 a(.) p 2575 3035 a(2000.) 1992 3168 y([7]) p 2199 3168 a(H.) p 2329 3168 a(M.) p 2473 3168 a(Alazemi,) p 2831 3168 a(A.) p 2961 3168 a(Mokhtar) m(,) p 3321 3168 a(and) p 3490 3168 a(M.) p 3634 3168 a(Azizoglu,) 1987 3268 y(\223Stochastic) p 2391 3268 a(approach) p 2721 3268 a(for) p 2844 3268 a(modeling) p 3183 3268 a(random) p 3463 3268 a(early) p 3655 3268 a(detection) 1987 3367 y(gate) n(w) o(ays) p 2314 3367 a(in) p 2401 3367 a(TCP/IP) p 2672 3367 a(netw) o(orks,) p 2992 3367 a(\224) p 3050 3367 a(in) p Fp 3136 3367 a(Pr) l(oceedings) p 3570 3367 a(IEEE) p 3772 3367 a(Inter) n(-) 1987 3467 y(national) p 2284 3467 a(Confer) m(ence) p 2685 3467 a(on) p 2788 3467 a(Communications) p 3372 3467 a(2001) p Fr(,) p 3579 3467 a(June) p 3752 3467 a(2001.) 1992 3600 y([8]) p 2199 3600 a(H.) p 2316 3600 a(Ohsaki,) p 2612 3600 a(M.) p 2743 3600 a(Murata,) p 3044 3600 a(and) p 3200 3600 a(H.) p 3317 3600 a(Miyahara,) p 3696 3600 a(\223Steady) 1987 3700 y(state) p 2184 3700 a(analysis) p 2496 3700 a(of) p 2611 3700 a(the) p 2757 3700 a(RED) p 2968 3700 a(gate) n(w) o(ay:) p 3339 3700 a(stability) p 3602 3700 a(,) p 3673 3700 a(transient) 1987 3799 y(beha) n(vior) m(,) p 2332 3799 a(and) p 2487 3799 a(parameter) p 2854 3799 a(setting,) p 3091 3799 a(\224) p Fp 3166 3799 a(IEICE) p 3413 3799 a(T) p 3454 3799 a(r) o(ansactions) p 3876 3799 a(on) 1987 3899 y(Communications) p Fr(,) p 2591 3899 a(v) n(ol.) p 2737 3899 a(E85-B,) p 2995 3899 a(pp.) p 3120 3899 a(107\226115,) p 3452 3899 a(Jan.) p 3604 3899 a(2002.) 1992 4032 y([9]) p 2199 4032 a(V) p 2248 4032 a(.) p 2291 4032 a(Misra,) p 2528 4032 a(W) p 2598 4032 a(.-B.) p 2745 4032 a(Gong,) p 2972 4032 a(and) p 3114 4032 a(D.) p 3217 4032 a(T) p 3261 4032 a(o) n(wsle) o(y) p 3489 4032 a(,) p 3530 4032 a(\223Fluid-based) 1987 4131 y(analysis) p 2271 4131 a(of) p 2357 4131 a(a) p 2411 4131 a(netw) o(ork) p 2700 4131 a(of) p 2786 4131 a(A) p 2841 4131 a(QM) p 2992 4131 a(routers) p 3240 4131 a(supporting) p 3612 4131 a(TCP) p 3781 4131 a(\003o) n(ws) 1987 4231 y(with) p 2159 4231 a(an) p 2263 4231 a(application) p 2657 4231 a(to) p 2746 4231 a(RED,) p 2927 4231 a(\224) p 2989 4231 a(in) p Fp 3079 4231 a(Pr) l(oceedings) p 3515 4231 a(of) p 3605 4231 a(A) n(CM) p 3802 4231 a(SIG-) 1987 4330 y(COMM) p 2261 4330 a(2000) p Fr(,) p 2469 4330 a(Aug.) p 2653 4330 a(2000.) 1992 4463 y([10]) p 2199 4463 a(P) p 2236 4463 a(.) p 2279 4463 a(K) o(uusela,) p 2593 4463 a(P) p 2630 4463 a(.) p 2673 4463 a(Lassila,) p 2952 4463 a(J.) p 3027 4463 a(V) p 3082 4463 a(irtamo,) p 3343 4463 a(and) p 3485 4463 a(P) p 3522 4463 a(.) p 3565 4463 a(K) n(e) o(y) p 3696 4463 a(,) p 3738 4463 a(\223Mod-) 1987 4563 y(eling) p 2177 4563 a(RED) p 2368 4563 a(with) p 2541 4563 a(idealized) p 2865 4563 a(TCP) p 3042 4563 a(sources,) p 3307 4563 a(\224) p 3369 4563 a(in) p Fp 3458 4563 a(Pr) l(oceedings) p 3894 4563 a(of) 1987 4663 y(9th) p 2115 4663 a(IFIP) p 2294 4663 a(Confer) m(ence) p 2696 4663 a(on) p 2801 4663 a(P) p 2845 4663 a(erformance) p 3250 4663 a(Modeling) p 3591 4663 a(and) p 3738 4663 a(Evalu-) 1987 4762 y(ation) p 2178 4762 a(of) p 2263 4762 a(A) m(TM) p 2447 4762 a(&) p 2532 4762 a(IP) p 2632 4762 a(Networks) p Fr(,) p 2987 4762 a(pp.) p 3111 4762 a(155\226166,) p 3443 4762 a(June) p 3616 4762 a(2001.) 1992 4895 y([11]) p 2199 4895 a(M.) p 2315 4895 a(Kisimoto,) p 2666 4895 a(H.) p 2768 4895 a(Ohsaki,) p 3045 4895 a(and) p 3186 4895 a(M.) p 3301 4895 a(Murata,) p 3583 4895 a(\223) p 3613 4895 a(Analyzing) 1987 4995 y(the) p 2106 4995 a(impact) p 2349 4995 a(of) p 2436 4995 a(TCP) p 2606 4995 a(connections) p 3020 4995 a(v) n(ariation) p 3331 4995 a(on) p 3431 4995 a(transient) p 3735 4995 a(beha) n(v-) 1987 5094 y(ior) p 2108 5094 a(of) p 2206 5094 a(RED) p 2401 5094 a(gate) n(w) o(ay) p 2671 5094 a(,) p 2686 5094 a(\224) p 2752 5094 a(in) p Fp 2846 5094 a(Pr) l(oceedings) p 3286 5094 a(of) p 3380 5094 a(the) p 3510 5094 a(16th) p 3687 5094 a(Interna-) 1987 5194 y(tional) p 2204 5194 a(Confer) m(ence) p 2608 5194 a(on) p 2715 5194 a(Information) p 3135 5194 a(Networking) p 3546 5194 a(\(ICOIN-16\)) p Fr(,) 1987 5294 y(pp.) p 2111 5294 a(10A2.1\22610A2.12,) p 2729 5294 a(Jan.) p 2881 5294 a(2002.) 1992 5426 y([12]) p 2199 5426 a(R.) p 2297 5426 a(Isermann,) p Fp 2649 5426 a(Digital) p 2907 5426 a(contr) l(ol) p 3165 5426 a(systems,) p 3461 5426 a(V) p 3503 5426 a(olume) p 3728 5426 a(1:) p 3825 5426 a(fun-) 1987 5526 y(damentails,) p 2406 5526 a(deterministic) p 2871 5526 a(contr) l(ol) p Fr(.) p 3192 5526 a(Springer) n(-V) p 3557 5526 a(erlag) p 3752 5526 a(Berlin) 1987 5626 y(Heidelber) o(g,) p 2395 5626 a(1989.) 3830 6013 y(p.) p 3918 6013 a(6) p 90 rotate dyy eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF