%!PS-Adobe-2.0 %%Creator: dvi2ps %%Title: paper.dvi %%Pages: (atend) %%BoundingBox: 0 0 595 842 %%DocumentPaperSizes: A4 %%Orientation: Portrait %%EndComments %%BeginFile: /usr/local/tex/lib/dvi2ps/dvi2.ps % /TeXDict 300 dict def TeXDict begin /inch { 72 mul } bind def /largepaperarray [ /letter /legal /11x17 /b4 /b5 /a5 /a4 /a3 ] def /smallpaperarray [ /note dup where { pop }{ pop /lettersmall dup where { pop }{ pop /letter } ifelse } ifelse /legal /11x17 /b4 /b5 /a5 /a4small dup where { pop }{ pop /note dup where { pop }{ pop /a4 } ifelse } ifelse /a3 ] def /setpaper { papertray { dup where { exch get exec }{ pop } ifelse }{ pop } ifelse } bind def /trayarray [ /lettertray /legaltray /11x17tray /b4tray /b5tray /a5tray /a4tray /a3tray ] def /settray { dup statusdict exch known manualfeed not and { mark exch statusdict begin load { exec } stopped { $error /newerror get { $error /errorname get /rangecheck eq { (Tray not found, using default tray.\n) print flush TeXDict /papertray false put }{ handleerror } ifelse $error /newerror false put } if } if end cleartomark }{ pop } ifelse } bind def /papertray true def /widtharray [ 8.5 inch 8.5 inch 11 inch 9.84 inch 6.93 inch 5.83 inch 8.27 inch 11.69 inch ] def /heightarray [ 11 inch 14 inch 17 inch 13.9 inch 9.84 inch 8.27 inch 11.69 inch 16.54 inch ] def /xoffset 0 def /yoffset 0 def /leftm 72 def /topm 72 def /landscape false def /manualfeed false def /pagesetup { dup widtharray exch get /paperwidth exch def dup heightarray exch get /paperheight exch def dup trayarray exch get settray large {largepaperarray}{smallpaperarray} ifelse exch get setpaper } bind def /@letter {0 pagesetup} def /@legal {1 pagesetup} def /@tabloid {2 pagesetup} def /@b4 {3 pagesetup} def /@b5 {4 pagesetup} def /@a5 {5 pagesetup} def /@a4 {6 pagesetup} def /@a3 {7 pagesetup} def /@landscape {/landscape true def} bind def /@manualfeed { /manualfeed true def statusdict /manualfeed known { statusdict /manualfeed true put statusdict /manualfeedtimeout 120 put } if } bind def /@large { /large true def } bind def /@small { /large false def } bind def /@envelope { /xoffset 4.28 inch def /yoffset 1.5 inch def @letter } bind def /COPIES { /#copies exch def } bind def /NF { /newname exch def /fsize exch def /corr exch def newname 7 dict def newname load begin /FontType 3 def /FontMatrix [corr 0 0 corr neg 0 0] def /FontBBox [0 0 1 1] def /BitMaps fsize array def /BuildChar /CharBuilder load def /Encoding 256 array def 0 1 255 {Encoding exch /.notdef put} for end newname newname load definefont pop } bind def /ch-image {ch-data 0 get} bind def /ch-width {ch-data 1 get} bind def /ch-height {ch-data 2 get} bind def /ch-xoff {ch-data 3 get} bind def /ch-yoff {ch-data 4 get} bind def /ch-tfmw {ch-data 5 get} bind def /CharBuilder { /ch-code exch def /font-dict exch def /ch-data font-dict /BitMaps get ch-code get def ch-data null eq not { ch-tfmw 0 ch-xoff neg ch-yoff neg ch-width ch-xoff sub ch-height ch-yoff sub setcachedevice ch-width ch-height true [1 0 0 1 ch-xoff ch-yoff] {ch-image} imagemask } if } bind def /BFT { /bf-v exch def /bf-h exch def findfont [bf-h 0 0 bf-v 0 0] makefont def } bind def /BFE /BFT load def /BFF { /bf-v exch def /bf-h exch def /savecurfont currentfont def findfont dup setfont exch /bf-stand exch def [ bf-stand stringwidth pop dup bf-h exch div exch bf-v exch div 0 0 3 -1 roll 0 0 ] makefont def savecurfont setfont } bind def /SF /setfont load def /s3 3 string def /D { /ch-code exch def /ch-data exch def currentfont /BitMaps get ch-code ch-data put currentfont /Encoding get ch-code dup s3 cvs cvn put } bind def /BP { userdict /bop-hook known { bop-hook } if /SaveImage save def xoffset yoffset translate leftm topm landscape { exch translate 90 rotate }{ paperheight exch sub translate } ifelse 72 Resolution div dup neg scale 0 0 moveto } bind def /EP { showpage SaveImage restore userdict /eop-hook known { eop-hook } if } bind def /START { userdict /start-hook known { start-hook } if /Resolution exch def } bind def /END /end load def /l /lineto load def /p /moveto load def /r { 0 rmoveto } def /s /show load def /ru { /dy exch neg def /dx exch def /x currentpoint /y exch def def newpath x y moveto dx 0 rlineto 0 dy rlineto dx neg 0 rlineto closepath fill x y moveto } bind def /TeXscale { 65781.76 div } def /DocumentInitState [ matrix currentmatrix currentlinewidth currentlinecap currentlinejoin currentdash currentgray currentmiterlimit ] cvx def /startTexFig { /SavedState save def userdict maxlength dict begin currentpoint transform DocumentInitState setmiterlimit setgray setdash setlinejoin setlinecap setlinewidth setmatrix itransform moveto /ury exch TeXscale def /urx exch TeXscale def /lly exch TeXscale def /llx exch TeXscale def /y exch TeXscale def /x exch TeXscale def currentpoint /cy exch def /cx exch def /sx x urx llx sub div def /sy y ury lly sub div def sx sy scale cx sx div llx sub cy sy div ury sub translate /DefFigCTM matrix currentmatrix def /initmatrix { DefFigCTM setmatrix } def /defaultmatrix { DefFigCTM exch copy } def /initgraphics { DocumentInitState setmiterlimit setgray setdash setlinejoin setlinecap setlinewidth setmatrix DefFigCTM setmatrix } def /showpage {} def /erasepage {} def /copypage {} def } def /clipFig { currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll exch lineto exch lineto exch lineto closepath clip newpath moveto } def /doclip { llx lly urx ury clipFig } def /endTexFig { end SavedState restore } def /@SpecialDefaults { /hsi paperwidth inch def /vsi paperheight inch def /hof 0 def /vof 0 def /hsc 1 def /vsc 1 def /rotat 0 def /CLIP false def /BBOX false def /EPSF false def /ECL false def } bind def /@ecl {/ECL true def} bind def /@clip {/CLIP true def} bind def /@hsize {/hsi exch def @clip} bind def /@vsize {/vsi exch def @clip} bind def /@hoffset {/hof exch def} bind def /@voffset {/vof exch def} bind def /@scaleunit 1 def /@hscale {@scaleunit div /hsc exch def} bind def /@vscale {@scaleunit div /vsc exch def} bind def /@rotation {/rotat exch def} bind def /@angle /@rotation load def /@rwi {10 div /hsi exch def} bind def /@rhi {10 div /vsi exch def} bind def /@llx {/llx exch def /BBOX true def /hsi 0 def /vsi 0 def} bind def /@lly {/lly exch def} bind def /@urx {/urx exch def} bind def /@ury {/ury exch def} bind def /@bbox {{@clip}if @ury @urx @lly @llx} bind def /@setclipper { CLIP { newpath 0 0 moveto hsi 0 rlineto 0 vsi rlineto hsi neg 0 rlineto closepath clip } if } bind def /@beginspecial { /SpecialSave save def /dict_count countdictstack def /op_count count 2 sub def currentpoint transform initgraphics itransform translate dup scale landscape {90 rotate} if @SpecialDefaults @MacSetUp } bind def /@setspecial { hof vof translate rotat rotate BBOX { hsi 0 eq { vsi 0 eq { hsc vsc }{ vsi ury lly sub div dup }ifelse }{ vsi 0 eq { hsi urx llx sub div dup }{ hsi urx llx sub div vsi ury lly sub div } ifelse } ifelse scale llx neg ECL{ury}{lly}ifelse neg translate CLIP { newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip } if newpath }{ @setclipper hsc vsc scale rotat rotate } ifelse /CTM matrix currentmatrix def end /letter {} def /note {} def /legal {} def /11x17 {} def /b4 {} def /b5 {} def /a5 {} def /a4 {} def /a4small {} def /a3 {} def /showpage {} def /copypage {} def /erasepage {} def /initmatrix {TeXDict /CTM get setmatrix} bind def /defaultmatrix {TeXDict /CTM get exch copy} bind def /initclip { TeXDict begin currentmatrix CTM setmatrix newpath BBOX { llx lly moveto urx lly lineto urx ury lineto llx ury lineto }{ 0 0 moveto hsi 0 rlineto 0 vsi rlineto hsi neg 0 rlineto } ifelse closepath clip setmatrix end } bind def /initgraphics { initmatrix newpath initclip 1 setlinewidth 0 setlinecap 0 setlinejoin [] 0 setdash 0 setgray 10 setmiterlimit } bind def /languagelevel where { pop languagelevel 1 ne { false setstrokeadjust false setoverprint } if } if } bind def /@MacSetUp { userdict /md known { userdict /md get type /dicttype eq { md /txpose known { md /txpose {pxs pys neg scale} put } if md /cp known { md /cp {pop pop pm restore} put } if } if } if } bind def /@push { gsave currentpoint translate dup scale newpath } bind def /@pop { grestore } bind def /@pt { moveto currentpoint currentlinewidth 2 div 0 360 arc fill } bind def /@ln { moveto lineto stroke } bind def /@ar { matrix currentmatrix 7 -2 roll moveto currentpoint translate newpath 5 -2 roll scale 0 0 1 6 -2 roll arc setmatrix } bind def /@RGB /setrgbcolor load def /@HSB /sethsbcolor load def /@CMYK /setcmykcolor dup where { pop load }{ pop { 1 sub 4 1 roll 3 { 3 index add neg dup 0 lt {pop 0} if 3 1 roll } repeat setrgbcolor pop } bind } ifelse def /normalscale { Resolution 72 div Resolution 72 div neg scale 0 setgray } def end /@endspecial { TeXDict begin count op_count sub {pop} repeat countdictstack dict_count sub {end} repeat SpecialSave restore } bind def /SDict TeXDict def %%EndFile %%BeginFile: /usr/local/tex/lib/dvi2ps/fonts/ascfix-c.ps % This file is included in this dvi2ps (j-version) kit by the courtesy of % Matsushita Electric Industrial Co., Ltd. You are free to distribute this % file as a part of this dvi2ps kit, but if you use this file as a part of % your own program and want to re-distribute the program, you should contact % miyabe@sy6.isl.mei.co.jp, kakiuchi@sy6.isl.mei.co.jp % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Following procedures are used to define new japanese font which has %%% correct metrics. %%% Added by T.Kakiuchi (kakiuchi@sy6.isl.mei.co.JP) 89/5/19 %%% Copyright (c) Matsushita Electric Industrial Co.,Ltd. 1990 %%% % If the packed-array facility is available, this program sets the % array-packing mode. %systemdict /setpacking known { % /savepacking currentpacking def % true setpacking %} if TeXDict begin % Procedure to make a new font which has new metrics. /Set-New-Metrics % [New-FNam][FNam][Metrics-array] {/Set-Metrics exch def % [New-FNam][FNam] Set-Metrix=[Metrix-Array] findfont % [New-FNam][FDic] /OrigCompFont exch def % [New-FNam] OrigCompFont=[FDic] /NewCompFontName exch def % NewCompFontName=[New-FNam] % Create new composite font. OrigCompFont dup % [FDic][FDic] length dict % [FDic][dict] /NewCompFont exch def % [FDic] NewCompFont=[dict] {1 index % [FDic][key][value][key] /FID ne % [FDic][key][value][T/F] 2 index /UniqueID ne and % [FDic][key][value][T/F] {NewCompFont 3 1 roll put} % if TRUE NewCompFont <- {key,value} {pop pop} ifelse } forall OrigCompFont /FDepVector get % [FDepVector] dup length array % [FDepVector][array] copy % [array] (=[FDepVector]) /NewFDepVector exch def % NewFDepVector=[arrray] NewCompFont /FDepVector NewFDepVector put % [NewCompFont] <- {/FDepVector, NewFDepVector} NewCompFont /FontName NewCompFontName put % [NewCompFont] <- {/FontName, NewCompFontName} Set-Metrics % [code,NewBaseFontName,Metrics-Array] {dup 0 get /Code exch def % set Code dup 1 get /NewBaseFontName exch def % set NewBaseFontName 2 get /Metric-Array exch def % set Metrics-Array % Extract base font and its index to FDepVector. /Index OrigCompFont /Encoding get Code get def /OrigBaseFont NewFDepVector Index get def % Set Metric-Dictionary Metric-Array length dict /Metric-Dict exch def Metric-Dict begin Metric-Array {exec def} forall end % Create new base font. OrigBaseFont dup % [OrgFont][OrgFont] length 2 add % [OrgFont][2+current size] dict % [OrgFont][dict] /NewBaseFont exch def % [OrgFont] /NewBaseFont=[dict] {1 index % [OrgFont][key][value][key] /FID ne % [OrgFont][key][value][T/F] 2 index /UniqueID ne and % [OrgFont][key][value][T/F] {NewBaseFont % [OrgFont][key][value][NewBaseFont] 3 1 roll % [OrgFont][NewBaseFont][key][value] put} % [OrgFont] {pop pop} ifelse } forall NewBaseFont /Kusumi-Metrics Metric-Dict put NewBaseFont % [OrgFont][NewBaseFont] /CDevProc {currentfont /Kusumi-Metrics get exch 2 copy known {get % w0x w0y llx lly urx ury w1x w1y vx vy new-llx dup % w0x w0y llx lly urx ury w1x w1y vx vy new-llx new-llx 8 -1 roll % w0x w0y llx lly ury w1x w1y vx vy new-llx new-llx urx 10 -1 roll % w0x w0y lly ury w1x w1y vx vy new-llx new-llx urx llx sub add % w0x w0y lly ury w1x w1y vx vy new-llx new-urx 7 1 roll % w0x w0y lly new-urx ury w1x w1y vx vy new-llx 8 1 roll % w0x w0y new-llx lly new-urx ury w1x w1y vx vy } {pop pop} ifelse } bind put % Regist to FDepVector NewFDepVector Index NewBaseFontName NewBaseFont definefont put } forall NewCompFontName NewCompFont definefont pop % Define [NewCompFont] as [NewCompFontName] } bind def % Definition of new metrics for /Ryumin-Light-H /Ryumin-Metrics [ [33/Ryumin-Light-H-33[ {/c2B 56.3327 } {/c78 36.5515 } {/c22 127.507 } {/c54 52.5065 } {/c4B 137.007 } {/c39 35.7169 } {/c27 105.323 } {/c42 79.8026 } {/c30 106.905 } {/c6B 129.961 } {/c50 192.016 } {/c47 101.333 } {/c59 104.456 } {/c35 124.507 } {/c3E 51.8327 } {/c2C 81.7527 } {/c23 102.007 } {/c4E 132.007 } {/c2A 111.833 } {/c43 153.333 } {/c55 52.5065 } {/c4A 137.007 } {/c26 106.333 } {/c51 192.017 } {/c2D 73.195 } {/c46 101.833 } {/c58 104.457 } {/c6A 53.6868 } {/c71 162.717 } {/c68 12.747 } {/c56 87.0065 } {/c4D 120.007 } {/c29 50.4616 } {/c52 99.5065 } {/c5B 122.007 } {/c37 145.717 } {/c6D 73.5612 } {/c49 95.824 } {/c2E 73.1949 } {/c72 45.6719 } {/c25 106.833 } {/c69 33.1968 } {/c70 147.722 } {/c57 87.0065 } {/c33 123.507 } {/c53 99.5065 } {/c28 101.333 } {/c4C 120.007 } {/c2F 86.4865 } {/c48 95.6039 } {/c5A 122.007 } {/c6C 154.132 } {/c36 154.717 } {/c24 103.833 } {/c4F 131.507 } ]] [36/Ryumin-Light-H-36[ {/c30 154.133 } {/c27 97.2168 } {/c39 76.6303 } {/c23 76.1769 } {/c67 149.762 } {/c43 67.7751 } {/c6E 77.4092 } {/c31 105.385 } {/c63 75.9087 } {/c26 241.525 } {/c6A 273.126 } {/c29 82.2642 } {/c32 65.1122 } {/c25 184.155 } {/c21 83.9483 } {/c65 90.2671 } {/c3A 51.3751 } {/c2F 295.128 } ]] [37/Ryumin-Light-H-37[ {/c22 140.608 } {/c6F 163.078 } {/c30 99.7332 } {/c27 57.7171 } {/c42 59.748 } {/c47 67.1082 } {/c35 83.0882 } {/c3E 72.1387 } {/c23 138.672 } {/c67 152.293 } {/c4E 197.608 } {/c2A 134.608 } {/c43 117.717 } {/c6E 126.697 } {/c31 115.108 } {/c55 168.068 } {/c63 80.217 } {/c4A 116.233 } {/c26 162.618 } {/c75 124.712 } {/c3F 192.108 } {/c46 123.608 } {/c6A 239.098 } {/c5F 258.608 } {/c44 162.608 } {/c56 84.1834 } {/c29 108.717 } {/c76 83.6869 } {/c32 61.9606 } {/c64 109.108 } {/c49 202.688 } {/c25 122.757 } {/c72 193.323 } {/c40 110.209 } {/c69 178.108 } {/c45 91.8148 } {/c57 89.1683 } {/c21 107.237 } {/c65 49.507 } {/c2F 187.108 } {/c41 97.8211 } {/c48 277.108 } {/c36 51.291 } {/c61 191.608 } {/c24 186.108 } {/c3D 164.236 } ]] ] def % Definition of new metrics for /GothicBBB-Medium-H /Gothic-Metrics [ [33/GothicBBB-Medium-H-33[ {/c2B 62.8327 } {/c78 11.5265 } {/c22 129.507 } {/c54 58.5065 } {/c4B 136.007 } {/c39 14.7171 } {/c27 104.333 } {/c42 76.8826 } {/c30 110.507 } {/c6B 138.987 } {/c50 178.072 } {/c47 104.833 } {/c59 107.036 } {/c35 67.0065 } {/c3E -13.1673 } {/c2C 78.8429 } {/c23 98.9866 } {/c4E 132.507 } {/c2A 132.288 } {/c43 149.333 } {/c55 58.5065 } {/c4A 136.007 } {/c26 102.833 } {/c51 177.982 } {/c2D 55.8326 } {/c46 104.333 } {/c58 107.037 } {/c6A 43.6568 } {/c71 130.717 } {/c68 5.70184 } {/c56 93.5065 } {/c4D 120.007 } {/c29 81.9568 } {/c52 97.5065 } {/c5B 121.007 } {/c37 148.717 } {/c6D 75.5065 } {/c49 56.9765 } {/c2E 55.8327 } {/c72 101.717 } {/c25 102.833 } {/c69 20.1768 } {/c70 109.182 } {/c57 94.0065 } {/c33 76.5065 } {/c53 97.5065 } {/c28 104.333 } {/c4C 120.007 } {/c2F 102.506 } {/c48 56.0265 } {/c5A 121.007 } {/c6C 157.007 } {/c36 133.717 } {/c24 105.833 } {/c4F 132.507 } ]] [36/GothicBBB-Medium-H-36[ {/c30 154.608 } {/c27 97.2418 } {/c39 93.5732 } {/c23 58.2168 } {/c67 106.287 } {/c43 51.2172 } {/c6E 71.752 } {/c31 128.098 } {/c63 52.2169 } {/c26 207.583 } {/c6A 211.098 } {/c29 51.7468 } {/c32 69.0981 } {/c25 155.272 } {/c21 86.707 } {/c65 84.167 } {/c3A 70.6131 } {/c2F 256.108 } ]] [37/GothicBBB-Medium-H-37[ {/c22 82.6082 } {/c6F 135.608 } {/c30 91.1081 } {/c27 74.2168 } {/c42 55.1081 } {/c47 49.6081 } {/c35 87.1181 } {/c3E 83.6081 } {/c23 102.766 } {/c67 113.717 } {/c4E 163.334 } {/c2A 111.608 } {/c43 84.5454 } {/c6E 96.2168 } {/c31 77.6081 } {/c55 140.608 } {/c63 67.7169 } {/c4A 75.6082 } {/c26 149.118 } {/c75 110.257 } {/c3F 144.608 } {/c46 96.6082 } {/c6A 225.578 } {/c5F 215.108 } {/c44 117.481 } {/c56 91.1081 } {/c29 72.2168 } {/c76 63.2168 } {/c32 48.6081 } {/c64 96.6081 } {/c49 209.108 } {/c25 104.207 } {/c72 165.608 } {/c40 76.6081 } {/c69 129.108 } {/c45 72.1081 } {/c57 64.6481 } {/c21 47.2171 } {/c65 41.7168 } {/c2F 135.608 } {/c41 97.6082 } {/c48 262.608 } {/c36 52.1181 } {/c61 188.976 } {/c24 148.446 } {/c3D 123.059 } ]] ] def end % TeXDict %systemdict /setpacking known { % savepacking setpacking %} if %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%EndFile %%EndProlog %%BeginSetup %%PaperSize: A4 %%Feature: *ManualFeed False %%Feature: *Resolution 600 TeXDict begin @large @a4 1.000 121 /f0 NF f0 SF [ 40 29 -4 0 43.010] 65 D [ 40 28 -4 0 43.045] 66 D [<003FC0000001FFF8000007E01E00000F800700001E0001C0003C0000E0003C0000600078000030007800001800F800001800 F800001800F800000000F800000000F800000000F8000000007C000000007C000000007C000000003E000000003E00000300 1F000003000F00000300078000030003C000078001E000078000F8000F80003E001F80001FC071C00007FFE0C000007F8040> 40 30 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(again)s 29 r (increased)s 29 r (to)s 30 r (utilize)s 29 r (network)s -188 3447 p (resources.)s -105 3557 p (In)s 24 r (A)s -8 r (TM)s 24 r (networks,)s 26 r (such)s 25 r (a)s 26 r (mechanism)s 25 r (can)s 25 r (be)s 25 r (realized)s 25 r (as)s -188 3656 p (follows.)s 26 r (First,)s 20 r (each)s 19 r (SES)s 20 r (is)s 19 r (informed)s 20 r (of)s 19 r (congestion)s 20 r (from)s 19 r (the)s -188 3756 p (network)s 17 r (by)s 18 r (using)s 18 r (a)s 17 r (congestion)s 18 r (indicator)s 18 r (\(CI\))s 18 r (bit)s 18 r (in)s 18 r (RM)s 17 r (\(Re-)s -188 3856 p (source)s 16 r (Management\))s 16 r (cells,)s 17 r (which)s 17 r (are)s 17 r (returned)s 16 r (from)s 17 r (destina-)s -188 3955 p (tion)s 15 r (end)s 16 r (system)s 15 r (\(DES\))s 16 r (or)s 16 r (the)s 16 r (congested)s 16 r (switch)s 15 r (\(if)s 16 r (it)s 16 r (has)s 16 r (such)s -188 4055 p (an)s 19 r (ability\).)s 27 r (Next,)s 21 r (a)s 20 r (simplest)s 20 r (solution)s 20 r (to)s 20 r (detect)s 20 r (network)s 20 r (con-)s 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(simulation)s 19 r (stud-)s -188 4862 p (ies)s 30 r (have)s 32 r (been)s 31 r (contributed)s 31 r (by)s 31 r (researchers)s 32 r (to)s 31 r (A)s -8 r (TM)s 30 r (Forum,)s -188 4962 p (our)s 20 r (main)s 21 r (purpose)s 21 r (in)s 20 r (the)s 21 r (current)s 21 r (paper)s 21 r (is)s 21 r (to)s 21 r (give)s 21 r (analytic)s 20 r (re-)s -188 5061 p (sults)s 13 r (for)s 15 r (the)s 14 r (standard)s 14 r (mechanism.)s 26 r (Regarding)s 14 r (the)s 14 r (analytic)s 15 r (ap-)s -188 5161 p (proaches)s 19 r (for)s 19 r (rate-based)s 20 r (control)s 20 r (schemes,)s 19 r (Blot)s 20 r (et)s 20 r (al.)s 27 r (showed)s -188 5260 p (the)s 18 r (dynamical)s 19 r (behavior)s 19 r (by)s 19 r (utilizing)s 19 r (\256rst-order)s 18 r (\257uid)s 19 r (approx-)s -188 5360 p (imations)s 29 r (in)s 30 r ([4].)s 57 r (In)s 30 r (their)s 30 r (model,)s 33 r (the)s 30 r (switch)s 30 r (is)s 30 r (assumed)s 31 r (to)s -188 5460 p (recognize)s 25 r (congestion)s 26 r (when)s 25 r (an)s 26 r (arrival)s 26 r (rate)s 26 r (of)s 26 r (cells)s 26 r (exceeds)s -188 5559 p (its)s 21 r (service)s 23 r (rate,)s 22 r (i.e.,)s 23 r (the)s 22 r (link)s 23 r (bandwidth.)s 32 r (On)s 22 r (the)s 23 r (other)s 22 r (hand,)s -188 5659 p (we)s 22 r (deal)s 23 r (with)s 23 r (a)s 23 r (more)s 23 r (realistic)s 22 r (situation)s 23 r (in)s 23 r (which)s 23 r (congestion)s -188 5759 p (of)s 23 r (the)s 24 r (switch)s 24 r (is)s 24 r (detected)s 24 r (by)s 24 r (its)s 24 r (queue)s 24 r (length,)s 25 r (i.e.,)s 25 r (the)s 24 r (num-)s -188 5858 p (ber)s 27 r (of)s 28 r (cells)s 28 r (queued)s 28 r (at)s 28 r (the)s 29 r (switch)s 28 r (buf)s -1 r (fer)s -4 r (.)s 48 r (The)s 28 r (same)s 28 r (model)s -188 5958 p (has)s 30 r (been)s 32 r (treated)s 31 r (in)s 31 r ([1])s 31 r (and)s 32 r (analyzed)s 31 r (using)s 31 r (a)s 31 r (similar)s 32 r (ana-)s 1972 17 p (lytic)s 34 r (technique.)s 66 r (In)s 34 r (their)s 33 r (paper)s -2 r (,)s 36 r (however)s -3 r (,)s 36 r (the)s 34 r (method)s 33 r (for)s 1972 117 p (notifying)s 26 r (congestion)s 25 r (from)s 26 r (the)s 25 r (switch)s 26 r (to)s 25 r (SES)s 25 r (is)s 26 r (not)s 25 r (explic-)s 1972 217 p (itly)s 22 r (modelled.)s 32 r (That)s 22 r (is,)s 22 r (the)s 22 r (rate)s 22 r (is)s 22 r (increased)s 22 r (linearly)s 22 r (and)s 22 r (de-)s 1972 316 p (creased)s 31 r (exponentially)s -5 r (,)s 32 r (and)s 31 r (the)s 30 r (time)s 31 r (interval)s 30 r (to)s 31 r (update)s 30 r (the)s 1972 416 p (increase/decrease)s 19 r (rate)s 18 r (is)s 18 r (assumed)s 18 r (to)s 18 r (be)s 18 r (\256xed.)s 27 r (However)s -2 r (,)s 17 r (this)s 1972 515 p (scheme)s 27 r (has)s 27 r (recently)s 26 r (been)s 27 r (found)s 27 r (to)s 26 r (be)s 27 r (of)s 26 r (problem)s 27 r (in)s 27 r (some)s 1972 615 p (situations)s 21 r ([5].)s 2055 722 p (Hence,)s 41 r (an)s 36 r (improved)s 37 r (rate)s 36 r (control)s 37 r (algorithm)s 36 r (called)s 37 r (En-)s 1972 822 p (hanced)s 32 r (Proportional)s 32 r (Rate)s 32 r (Control)s 32 r (Algorithm)s 32 r (\(EPRCA\))s 33 r (is)s 1972 921 p (recently)s 36 r (proposed)s 36 r (in)s 35 r ([6],)s 39 r (which)s 36 r (is)s 35 r (adopted)s 36 r (by)s 36 r (A)s -9 r (TM)s 35 r (Fo-)s 1972 1021 p (rum)s 18 r (as)s 18 r (a)s 18 r (standard)s 18 r (draft)s 17 r (for)s 18 r (the)s 18 r (rate-based)s 18 r (congestion)s 18 r (control)s 1972 1121 p (mechanism)s 21 r (for)s 21 r (A)s -8 r (TM)s 20 r (networks.)s 28 r (In)s 21 r ([6],)s 20 r (they)s 21 r (suggested)s 21 r (three)s 1972 1220 p (types)s 29 r (of)s 29 r (switches,)s 31 r (EFCI)s 29 r (bit)s 29 r (setting)s 29 r (switch)s 29 r (\(EFCI\),)s 29 r (Binary)s 1972 1320 p (Enhanced)s 20 r (Switch)s 20 r (\(BES\),)s 19 r (and)s 20 r (Explicit)s 19 r (Down)s 20 r (Switch)s 19 r (\(EDS\),)s 1972 1419 p (which)s 17 r (have)s 17 r (different)s 16 r (processing)s 17 r (capabilities)s 17 r (against)s 17 r (conges-)s 1972 1519 p (tion.)s 66 r (The)s 33 r (main)s 33 r (purpose)s 34 r (of)s 33 r (this)s 33 r (paper)s 34 r (is)s 33 r (to)s 33 r (give)s 34 r (analytic)s 1972 1619 p (results)s 28 r (for)s 27 r (the)s 27 r (latest)s 27 r (EPRCA)s 27 r (with)s 27 r (EFCI)s 27 r (switch.)s 47 r (For)s 27 r (other)s 1972 1718 p (switches,)s 21 r (we)s 21 r (will)s 21 r (report)s 21 r (analytical)s 21 r (results)s 21 r (in)s 21 r (the)s 20 r (proceeding)s 1972 1818 p (papers.)s f18 SF 1972 2028 p (2)s 100 r (Analytic)s 25 r (Model)s f15 SF 1972 2157 p (W)s -5 r (e)s 20 r (\256rst)s 22 r (describe)s 21 r (a)s 22 r (basic)s 21 r (feature)s 22 r (of)s 21 r (EPRCA,)s 22 r (which)s 21 r (is)s 22 r (based)s 1972 2257 p (on)s 23 r (a)s 22 r (positive)s 23 r (feedback)s 22 r (mechanism.)s 33 r (SES)s 22 r (periodically)s 22 r (sends)s 1972 2356 p (an)s 28 r (RM)s 27 r (cell)s 27 r (every)s f4 SF 27 r (N)s f2 SF 2648 2369 p (RM)s f15 SF 2799 2356 p (data)s 27 r (cells)s 28 r (to)s 27 r (check)s 27 r (the)s 27 r (congestion)s 1972 2456 p (status)s 26 r (of)s 25 r (the)s 26 r (network.)s 41 r (The)s 26 r (RM)s 25 r (cell)s 26 r (received)s 25 r (at)s 26 r (DES)s 25 r (is)s 26 r (re-)s 1972 2556 p (turned)s 27 r (to)s 26 r (SES)s 27 r (along)s 26 r (the)s 27 r (backward)s 26 r (path)s 27 r (if)s 26 r (congestion)s 27 r (does)s 1972 2655 p (not)s 31 r (occur)s 31 r (in)s 31 r (the)s 31 r (network.)s 59 r (The)s 31 r (switch)s 31 r (can)s 31 r (notify)s 31 r (its)s 31 r (con-)s 1972 2755 p (gestion)s 28 r (occurrence)s 27 r (to)s 28 r (DES)s 28 r (by)s 27 r (marking)s 28 r (an)s 27 r (EFCI)s 28 r (bit)s 27 r (in)s 28 r (the)s 1972 2854 p (header)s 19 r (of)s 18 r (data)s 18 r (cells.)s 27 r (As)s 19 r (presented)s 18 r (in)s 18 r ([1],)s 19 r (the)s 19 r (basic)s 18 r (operation)s 1972 2954 p (of)s 16 r (the)s 15 r (rate\261based)s 15 r (congestion)s 15 r (control)s 15 r (is)s 16 r (that)s 15 r (SES)s 15 r (normally)s 15 r (in-)s 1972 3054 p (creases)s 24 r (its)s 24 r (allowable)s 23 r (cell)s 24 r (transmission)s 24 r (rate,)s 24 r (which)s 24 r (is)s 24 r (called)s 1972 3153 p (ACR)s 28 r (\(Allowed)s 29 r (Cell)s 28 r (Rate\),)s 30 r (while)s 28 r (it)s 28 r (is)s 28 r (decreased)s 28 r (when)s 28 r (the)s 1972 3253 p (network)s 28 r (falls)s 27 r (into)s 28 r (congestion.)s 48 r (However)s -3 r (,)s 28 r (a)s 28 r (notable)s 27 r (feature)s 1972 3353 p (of)s 21 r (EPRCA)s 21 r (is)s 20 r (that)s 21 r (SES)s 20 r (always)s 21 r (decreases)s 21 r (ACR)s 20 r (until)s 21 r (SES)s 20 r (re-)s 1972 3452 p (ceives)s 24 r (the)s 24 r (RM)s 24 r (cell)s 24 r (from)s 24 r (DES.)s 24 r (It)s 24 r (can)s 24 r (increase)s 24 r (the)s 24 r (rate)s 24 r (only)s 1972 3552 p (when)s 27 r (the)s 26 r (RM)s 26 r (cell)s 26 r (is)s 26 r (received.)s 44 r (If)s 26 r (the)s 26 r (RM)s 27 r (cell)s 26 r (is)s 26 r (discarded)s 1972 3651 p (at)s 27 r (DES)s 26 r (due)s 26 r (to)s 26 r (congestion)s 26 r (indication,)s 28 r (it)s 26 r (results)s 26 r (in)s 27 r (that)s 26 r (SES)s 1972 3751 p (continues)s 16 r (to)s 15 r (decrease)s 15 r (ACR.)s 16 r (This)s 15 r (control)s 15 r (mechanism)s 15 r (accom-)s 1972 3851 p (plishes)s 20 r (a)s 19 r (fast)s 20 r (rate)s 19 r (reduction)s 20 r (at)s 19 r (SES)s 20 r (even)s 19 r (if)s 20 r (RM)s 19 r (cells)s 20 r (are)s 19 r (lost)s 1972 3950 p (at)s 21 r (the)s 21 r (switch)s 21 r (due)s 20 r (to)s 21 r (congestion.)s 2055 4057 p (In)s 30 r (EPRCA,)s 29 r (three)s 30 r (types)s 30 r (of)s 29 r (switch)s 30 r (architectures)s 29 r (are)s 30 r (sug-)s 1972 4157 p (gested)s 23 r (in)s 23 r (the)s 22 r (form)s 23 r (of)s 22 r (pseudo)s 23 r (codes)s 22 r (with)s 23 r (dif)s -1 r (ferent)s 22 r (function-)s 1972 4257 p (alities)s 16 r ([6].)s 26 r (The)s 16 r (\256rst)s 15 r (one)s 16 r (is)s 16 r (an)s 16 r (EFCI)s 15 r (bit)s 16 r (setting)s 16 r (switch)s 15 r (\(EFCI\),)s 1972 4356 p (which)s 18 r (is)s 18 r (just)s 18 r (same)s 18 r (as)s 18 r (the)s 18 r (original)s 18 r (PRCA)s 18 r ([7])s 17 r (described)s 18 r (in)s 18 r (the)s 1972 4456 p (above,)s 21 r (and)s 20 r (can)s 20 r (be)s 20 r (expected)s 20 r (as)s 20 r (a)s 20 r (least)s 21 r (expensive)s 20 r (one.)s 27 r (Since,)s 1972 4556 p (in)s 26 r (the)s 26 r (EFCI)s 26 r (switch,)s 27 r (the)s 26 r (congestion)s 25 r (can)s 26 r (be)s 26 r (noti\256ed)s 26 r (to)s 25 r (DES)s 1972 4655 p (by)s 23 r (marking)s 22 r (an)s 22 r (EFCI)s 22 r (bit)s 23 r (in)s 22 r (data)s 22 r (cells,)s 23 r (forward)s 22 r (RM)s 23 r (cells)s 22 r (are)s 1972 4755 p (not)s 18 r (necessary)s -4 r (.)s 25 r (However)s -2 r (,)s 17 r (if)s 18 r (at)s 18 r (least)s 17 r (one)s 18 r (BES/EDS)s 18 r (switch)s 18 r (ex-)s 1972 4854 p (ists)s 17 r (on)s 17 r (the)s 17 r (link,)s 17 r (the)s 17 r (forward)s 16 r (RM)s 17 r (cells)s 17 r (should)s 17 r (be)s 16 r (sent)s 17 r (by)s 17 r (SES.)s 1972 4954 p (From)s 23 r (an)s 22 r (analytical)s 23 r (point)s 22 r (of)s 22 r (view)s -4 r (,)s 22 r (however)s -3 r (,)s 22 r (it)s 23 r (is)s 22 r (not)s 22 r (a)s 23 r (prob-)s 1972 5054 p (lem)s 20 r (whether)s 19 r (forward)s 19 r (RM)s 19 r (cells)s 20 r (are)s 19 r (explicitly)s 19 r (sent)s 19 r (by)s 20 r (SES)s 19 r (or)s 1972 5153 p (not,)s 21 r (and)s 20 r (both)s 21 r (cases)s 20 r (of)s 21 r (the)s 20 r (EFCI)s 21 r (switches)s 20 r (can)s 21 r (be)s 20 r (treated)s 20 r (in)s 21 r (a)s 1972 5253 p (uni\256ed)s 21 r (manner)s 21 r (as)s 21 r (shown)s 20 r (in)s 21 r (the)s 21 r (next)s 21 r (section.)s 2055 5360 p (In)s 27 r (this)s 26 r (paper)s -3 r (,)s 27 r (an)s 26 r (analytic)s 26 r (model)s 26 r (for)s 26 r (EFCI)s 26 r (switch)s 26 r (is)s 27 r (pro-)s 1972 5460 p (vided)s 25 r (for)s 25 r (a)s 25 r (rather)s 25 r (simple)s 25 r (network)s 25 r (model)s 25 r (which)s 25 r (consists)s 25 r (of)s 1972 5559 p (homogeneous)s 27 r (traf\256c)s 26 r (sources)s 27 r (and)s 27 r (a)s 27 r (single)s 27 r (bottleneck)s 27 r (A)s -8 r (TM)s 1972 5659 p (link)s 29 r (\(Fig.)s 29 r (1\).)s 51 r (The)s 28 r (number)s f4 SF 29 r (N)s f2 SF 2965 5671 p (V)s 3 r (C)s f15 SF 3092 5659 p (of)s 29 r (VC')s -4 r (s)s 28 r (share)s 28 r (it.)s 51 r (W)s -5 r (e)s 27 r (as-)s 1972 5759 p (sume)s 31 r (that)s 30 r (these)s 30 r (VC')s -4 r (s)s 29 r (behave)s 31 r (identically)s -5 r (,)s 32 r (that)s 30 r (is,)s 32 r (all)s 30 r (VC')s -3 r (s)s 1972 5858 p (have)s 18 r (identical)s 17 r (parameters,)s f4 SF 18 r (I)s -6 r (C)s -8 r (R)s f15 SF (,)s f4 SF 17 r (P)s 12 r (C)s 6 r (R)s f15 SF (,)s f4 SF 18 r (AI)s -6 r (R)s f15 SF 17 r (and)s f4 SF 17 r (M)s 9 r (D)s 3 r (F)s f15 SF 28 r (\(for)s 1972 5958 p (these)s 28 r (parameters,)s 29 r (see)s 27 r ([6]\).)s 48 r (The)s 27 r (service)s 28 r (rate)s 27 r (of)s 28 r (the)s 27 r (switch,)s EP %%Page: 3 3 BP -132 -65 p 1.000 @beginspecial 16.000000 360.000000 594.000000 691.000000 true @bbox @ecl 224.000000 @hsize @setspecial %%BeginDocument: figure/model.eps /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /arrowHeight 8 def /arrowWidth 4 def /IdrawDict 52 dict def IdrawDict begin /reencodeISO { dup dup findfont dup length dict begin { 1 index /FID ne { def }{ pop pop } ifelse } forall /Encoding ISOLatin1Encoding def currentdict end definefont } def /ISOLatin1Encoding [ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright /parenleft/parenright/asterisk/plus/comma/minus/period/slash /zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon /less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N /O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright /asciicircum/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m /n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/dotlessi/grave/acute/circumflex/tilde/macron/breve /dotaccent/dieresis/.notdef/ring/cedilla/.notdef/hungarumlaut /ogonek/caron/space/exclamdown/cent/sterling/currency/yen/brokenbar /section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot /hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior /acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine /guillemotright/onequarter/onehalf/threequarters/questiondown /Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla /Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex /Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis /multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute /Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis /aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave /iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex /otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis /yacute/thorn/ydieresis ] def /Helvetica-Oblique reencodeISO def /Helvetica reencodeISO def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { dup -1 eq { /patternGrayLevel idef /patternString idef } { /patternGrayLevel idef } ifelse false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l w add b translate w neg h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 1 printSize sub descender sub def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def /SSten { fgred fggreen fgblue setrgbcolor dup true exch 1 0 0 -1 0 6 -1 roll matrix astore } def /FSten { dup 3 -1 roll dup 4 1 roll exch newpath 0 0 moveto dup 0 exch lineto exch dup 3 1 roll exch lineto 0 lineto closepath bgred bggreen bgblue setrgbcolor eofill SSten } def /Rast { exch dup 3 1 roll 1 0 0 -1 0 6 -1 roll matrix astore } def Begin [ 0.955325 0 0 0.955325 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Rect 3 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -128 35 ] concat 358 435 438 515 Rect End Begin %I Rect 0 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.25 SetP [ 1 0 0 1 -108 35 ] concat 408 435 418 515 Rect End Begin %I Rect 0 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.25 SetP [ 1 0 0 1 -108 35 ] concat 398 435 408 515 Rect End Begin %I Rect 0 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.25 SetP [ 1 0 0 1 -108 35 ] concat 388 435 398 515 Rect End Begin %I Rect 0 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -108 35 ] concat 378 435 388 515 Rect End Begin %I Rect 0 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -108 35 ] concat 368 435 378 515 Rect End Begin %I Rect 0 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -108 35 ] concat 358 435 368 515 Rect End Begin %I Rect 0 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 0 0 1 -108 35 ] concat 348 435 358 515 Rect End Begin %I Rect 0 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 0.5 0 0 0.5 116 224.5 ] concat 228 491 248 651 Rect End Begin %I Elli 3 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.5 SetP [ 1 -0 -0 1 -128 35 ] concat 468 475 40 40 Elli End Begin %I Line 0 0 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.25 SetP [ 0.5 -0 -0 0.5 96 318.5 ] concat 288 163 288 303 Line End Begin %I Line 0 0 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.25 SetP [ 0.5 -0 -0 0.5 96 318.5 ] concat 348 163 348 303 Line End Begin %I Text 0 0 0 SetCFg Helvetica-Oblique 18 SetF [ 1 0 0 1 220 397 ] concat [ (QH) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica-Oblique 18 SetF [ 1 0 0 1 260 397 ] concat [ (QL) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica-Oblique 18 SetF [ 1 0 0 1 380 537 ] concat [ (BW) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica-Oblique 18 SetF [ 1 0 0 1 150 567 ] concat [ (Nvc) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica-Oblique 18 SetF [ 1 0 0 1 150 667 ] concat [ (Tsx) ] Text End Begin %I Line 2 0 1 [12 4] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.5 SetP [ 0.946209 -0 -0 0.416667 -117.936 431.083 ] concat 188 521 408 521 Line End Begin %I Line 2 0 1 [12 4] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.5 SetP [ 1.02995 -0 -0 0.416667 -148.635 431.083 ] concat 428 521 688 521 Line End Begin %I Text 0 0 0 SetCFg Helvetica 18 SetF [ 1 0 0 1 250 577 ] concat [ (ATM Switch) ] Text End Begin %I Elli 1 0 0 [12 4] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -128 129 ] concat 268 381 10 50 Elli End Begin %I MLine 2 0 1 [12 4] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -128 129 ] concat 418 571 688 571 688 561 188 561 4 MLine End Begin %I Text 0 0 0 SetCFg Helvetica-Oblique 18 SetF [ 1 0 0 1 410 717 ] concat [ (Txds) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica-Oblique 18 SetF [ 1 0 0 1 410 667 ] concat [ (Txd) ] Text End Begin %I Rect 2 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.5 SetP [ 1 -0 -0 1 -143 -27 ] concat 163 567 243 597 Rect End Begin %I Rect 2 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.5 SetP [ 1 -0 -0 1 -143 -27 ] concat 163 517 243 547 Rect End Begin %I Rect 2 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.5 SetP [ 1 -0 -0 1 -143 -27 ] concat 163 467 243 497 Rect End Begin %I Rect 2 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.5 SetP [ 1 -0 -0 1 -143 -27 ] concat 673 517 763 547 Rect End Begin %I Rect 2 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.5 SetP [ 1 -0 -0 1 -143 -27 ] concat 673 467 763 497 Rect End Begin %I Rect 2 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.5 SetP [ 1 -0 -0 1 -143 -27 ] concat 673 567 763 597 Rect End Begin %I Line 2 0 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.5 SetP [ 1 -0 -0 1 -143 -27 ] concat 243 527 373 527 Line End Begin %I Line 2 0 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.5 SetP [ 1 -0 -0 1 -143 -27 ] concat 243 487 373 517 Line End Begin %I Line 2 0 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.5 SetP [ 1 -0 -0 1 -143 -27 ] concat 243 577 373 537 Line End Begin %I Line 2 0 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.5 SetP [ 1 -0 -0 1 -143 -27 ] concat 523 527 673 527 Line End Begin %I Line 2 0 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.5 SetP [ 1 -0 -0 1 -143 -27 ] concat 523 537 673 577 Line End Begin %I Line 2 0 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg 0.5 SetP [ 1 -0 -0 1 -143 -27 ] concat 523 517 673 487 Line End Begin %I Text 0 0 0 SetCFg Helvetica 18 SetF [ 1 0 0 1 20 607 ] concat [ (Source End Station) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica 18 SetF [ 1 0 0 1 426 607 ] concat [ (Destination End Station) ] Text End End %I eop showpage end %%EndDocument @endspecial f15 SF 360 1177 p (Figure)s 21 r (1:)s 28 r (Analytic)s 20 r (Model.)s -188 1430 p (i.e.,)s 17 r (the)s 17 r (bandwidth)s 17 r (of)s 18 r (the)s 17 r (bottleneck)s 17 r (link,)s 18 r (is)s 17 r (denoted)s 17 r (by)s f4 SF 18 r (B)s 4 r (W)s f15 SF -188 1529 p (in)s 21 r (cells/msec.)s 31 r (Propagation)s 22 r (delays)s 22 r (from)s 22 r (SES')s -3 r (s)s 21 r (to)s 22 r (the)s 22 r (switch)s -188 1629 p (and)s 14 r (from)s 15 r (the)s 15 r (switch)s 16 r (to)s 15 r (DES')s -4 r (s)s 14 r (are)s 15 r (represented)s 15 r (by)s f4 SF 16 r (\034)s f2 SF 1427 1642 p (sx)s f15 SF 1515 1629 p (and)s f4 SF 15 r (\034)s f2 SF 1686 1642 p (xd)s f15 SF 1763 1629 p (,)s -188 1729 p (respectively)s -5 r (.)s 26 r (Propagation)s 21 r (delays)s f4 SF 21 r (\034)s f2 SF 947 1741 p (sx)s f15 SF 1040 1729 p (and)s f4 SF 21 r (\034)s f2 SF 1217 1741 p (xd)s f15 SF 1315 1729 p (may)s 20 r (differ)s 20 r (ac-)s -188 1828 p (cording)s 23 r (to)s 24 r (the)s 25 r (network)s 24 r (con\256guration)s 24 r (\(e.g.,)s 25 r (LAN,)s 24 r (MAN,)s 25 r (or)s -188 1928 p (W)s -9 r (AN)s 20 r (and)s 22 r (the)s 21 r (location)s 22 r (of)s 21 r (UNI\).)s 22 r (W)s -6 r (e)s 21 r (de\256ne)s f4 SF 21 r (\034)s f15 SF 34 r (=)s 25 r (2\()s f4 SF (\034)s f2 SF 1485 1940 p (sx)s f15 SF 1577 1928 p (+)s f4 SF 19 r (\034)s f2 SF 1679 1940 p (xd)s f15 SF 1756 1928 p (\))s -188 2028 p (as)s 15 r (a)s 16 r (round-trip)s 16 r (propagation)s 16 r (delay)s 16 r (between)s 16 r (SES)s 16 r (and)s 16 r (DES.W)s -6 r (e)s -188 2127 p (further)s 22 r (introduce)s f4 SF 24 r (\034)s f2 SF 434 2140 p (xds)s f15 SF 570 2127 p (=)s 29 r (2)s f4 SF (\034)s f2 SF 724 2140 p (xd)s f15 SF 821 2127 p (+)s f4 SF 21 r (\034)s f2 SF 925 2140 p (sx)s f15 SF 1021 2127 p (which)s 24 r (is)s 23 r (a)s 24 r (propagation)s -188 2227 p (delay)s 26 r (of)s 27 r (the)s 27 r (congestion)s 27 r (indication)s 27 r (from)s 27 r (the)s 27 r (switch)s 27 r (to)s 27 r (SES)s -188 2326 p (via)s 20 r (DES.)s -105 2426 p (The)s 24 r (congestion)s 24 r (is)s 25 r (detected)s 25 r (by)s 24 r (threshold)s 25 r (values)s 24 r (of)s 25 r (queue)s -188 2526 p (length)s 24 r (at)s 25 r (the)s 25 r (switch)s 25 r (buf)s -1 r (fer)s -4 r (.)s 39 r (The)s 25 r (EFCI)s 25 r (switch)s 25 r (has)s 25 r (high)s 25 r (and)s -188 2625 p (low)s 23 r (threshold)s 24 r (values)s 24 r (denoted)s 24 r (as)s f4 SF 25 r (Q)s f2 SF 975 2638 p (H)s f15 SF 1062 2625 p (and)s f4 SF 24 r (Q)s f2 SF 1272 2638 p (L)s f15 SF 1321 2625 p (,)s 25 r (respectively)s -4 r (.)s -188 2725 p (When)s 15 r (the)s 16 r (queue)s 15 r (length)s 16 r (at)s 16 r (the)s 15 r (switch)s 16 r (exceeds)s f4 SF 16 r (Q)s f2 SF 1349 2737 p (H)s f15 SF 1412 2725 p (,)s 17 r (the)s 15 r (switch)s -188 2825 p (detects)s 33 r (congestion)s 33 r (and)s 34 r (marks)s 34 r (the)s 33 r (EFCI)s 34 r (bit)s 34 r (in)s 33 r (the)s 34 r (header)s -188 2924 p (of)s 25 r (data)s 26 r (cells.)s 45 r (When)s 26 r (the)s 26 r (queue)s 26 r (length)s 26 r (goes)s 27 r (under)s f4 SF 26 r (Q)s f2 SF 1558 2937 p (L)s f15 SF 1607 2924 p (,)s 28 r (it)s 26 r (is)s -188 3024 p (regarded)s 31 r (that)s 32 r (the)s 32 r (congestion)s 33 r (terminates.)s 61 r (SES)s 32 r (determines)s -188 3123 p (the)s 30 r (rate)s 31 r (increase/decrease)s 31 r (by)s 32 r (RM)s 31 r (cells)s 31 r (in)s 31 r (the)s 31 r (EPRCA)s 31 r (al-)s -188 3223 p (gorithm.)s 71 r (Since)s 35 r (the)s 36 r (receiving)s 35 r (rate)s 36 r (for)s 36 r (RM)s 35 r (cells)s 36 r (is)s 35 r (in\257u-)s -188 3323 p (enced)s 19 r (by)s 20 r (the)s 20 r (congestion)s 20 r (status)s 20 r (of)s 20 r (the)s 20 r (switch,)s 20 r (we)s 20 r (require)s 19 r (an-)s -188 3422 p (other)s 25 r (analytical)s 26 r (treatment)s 25 r (different)s 25 r (from)s 25 r (the)s 26 r (one)s 26 r (presented)s -188 3522 p (in)s 20 r ([1].)s 30 r (More)s 21 r (precisely)s -5 r (,)s 21 r (the)s 21 r (rate)s 21 r (control)s 22 r (is)s 21 r (performed)s 21 r (by)s 22 r (RM)s -188 3622 p (cells)s 16 r (returned)s 17 r (from)s 18 r (DES)s 17 r (in)s 17 r (EPRCA.)s 17 r (Therefore,)s 18 r (if)s 17 r (the)s 18 r (switch)s -188 3721 p (is)s 28 r (congested,)s 30 r (the)s 28 r (returned)s 29 r (rate)s 28 r (of)s 29 r (RM)s 28 r (cells)s 29 r (is)s 28 r (bounded)s 29 r (by)s f4 SF -188 3821 p (B)s 3 r (W)s 2 r (=)s f15 SF (\()s f4 SF (N)s f2 SF 95 3833 p (V)s 3 r (C)s f4 SF 207 3821 p (N)s f2 SF 262 3833 p (RM)s f15 SF 386 3821 p (\).)s 43 r (On)s 26 r (the)s 26 r (other)s 26 r (hand,)s 27 r (the)s 26 r (rate)s 26 r (is)s 26 r (identical)s -188 3920 p (to)s 20 r (its)s 21 r (transmission)s 20 r (rate)s 21 r (when)s 21 r (the)s 21 r (switch)s 20 r (is)s 21 r (not)s 21 r (congested.)s -105 4020 p (W)s -7 r (e)s 18 r (introduce)s f4 SF 18 r (AC)s 6 r (R)s f15 SF (\()s f4 SF (t)s f15 SF (\))s 18 r (and)s f4 SF 19 r (Q)s f15 SF (\()s f4 SF (t)s f15 SF (\))s 18 r (which)s 18 r (represent)s 18 r (ACR)s 18 r (for)s -188 4120 p (each)s 14 r (SES)s 15 r (and)s 15 r (the)s 15 r (queue)s 15 r (length)s 15 r (at)s 15 r (the)s 15 r (switch)s 15 r (observed)s 15 r (at)s 15 r (time)s f4 SF -188 4219 p (t)s f15 SF (.)s 40 r (In)s 26 r (the)s 25 r (following)s 25 r (sections,)s 27 r (we)s 25 r (will)s 26 r (analyze)s 25 r (evolutions)s 25 r (of)s f4 SF -188 4319 p (AC)s 5 r (R)s f15 SF 1 r (\()s f4 SF (t)s f15 SF (\))s 14 r (and)s f4 SF 14 r (Q)s f15 SF (\()s f4 SF (t)s f15 SF (\))s 15 r (in)s 14 r (steady)s 14 r (state)s 14 r (assuming)s 15 r (that)s 14 r (\(1\))s 14 r (the)s 15 r (switch)s -188 4419 p (has)s 24 r (in\256nite)s 24 r (capacity)s 24 r (of)s 25 r (the)s 24 r (buffer)s -3 r (,)s 24 r (and)s 24 r (that)s 25 r (\(2\))s 24 r (SES)s 25 r (always)s -188 4518 p (has)s 28 r (cells)s 30 r (to)s 29 r (transmit.)s 54 r (Therefore,)s f4 SF 32 r (AC)s 5 r (R)s f15 SF 1 r (\()s f4 SF (t)s f15 SF (\))s 30 r (is)s 29 r (equivalent)s 29 r (to)s -188 4618 p (the)s 26 r (actual)s 27 r (cell)s 28 r (transmission)s 27 r (rate.)s 47 r (Last,)s 29 r (we)s 27 r (note)s 27 r (that)s 27 r (initial)s -188 4717 p (transient)s 24 r (analyses)s 25 r (of)s 25 r (those)s 25 r (switches)s 25 r (will)s 25 r (be)s 25 r (reported)s 25 r (in)s 25 r (the)s -188 4817 p (future.)s f18 SF -188 5001 p (3)s 99 r (Dynamical)s 25 r (Behavior)s 24 r (of)s 25 r (EFCI)s 25 r (Switch)s f15 SF -188 5120 p (In)s 27 r (this)s 29 r (section,)s 30 r (we)s 29 r (focus)s 28 r (on)s 28 r (the)s 29 r (EFCI)s 28 r (switch)s 29 r (to)s 28 r (analyze)s 29 r (a)s -188 5219 p (dynamical)s 17 r (behavior)s 18 r (of)s 18 r (the)s 17 r (allowed)s 18 r (cell)s 18 r (rate)s f4 SF 18 r (AC)s 6 r (R)s f15 SF (\()s f4 SF (t)s f15 SF (\))s 18 r (and)s 18 r (the)s -188 5319 p (queue)s 16 r (length)s f4 SF 18 r (Q)s f15 SF (\()s f4 SF (t)s f15 SF (\))s 17 r (in)s 18 r (steady)s 17 r (state.)s 27 r (In)s 17 r (what)s 18 r (follows,)s 18 r (RM)s 17 r (cells)s -188 5419 p (for)s 22 r (forward)s 23 r (direction)s 23 r (is)s 23 r (not)s 24 r (considered.)s 34 r (Then,)s 24 r (the)s 23 r (model)s 23 r (is)s -188 5518 p (equivalent)s 21 r (to)s 22 r (the)s 21 r (original)s 22 r (PRCA)s 22 r ([7].)s 30 r (However)s -2 r (,)s 21 r (in)s 22 r (our)s 22 r (anal-)s -188 5618 p (ysis,)s 24 r (forward)s 24 r (RM)s 24 r (cells)s 24 r (can)s 24 r (be)s 24 r (easily)s 24 r (taken)s 24 r (into)s 24 r (account)s 24 r (by)s -188 5717 p (replacing)s f4 SF 20 r (B)s 4 r (W)s f15 SF 32 r (with)s f4 SF 21 r (B)s 4 r (W)s f3 SF 644 5687 p (0)s f15 SF 688 5717 p (where)s f4 SF 21 r (B)s 4 r (W)s f3 SF 1069 5687 p (0)s f15 SF 1113 5717 p (is)s 20 r (de\256ned)s 21 r (as)s f4 SF 325 5922 p (B)s 4 r (W)s f3 SF 482 5887 p (0)s f15 SF 529 5922 p (=)s f4 SF 23 r (B)s 4 r (W)s 828 5865 p (N)s f2 SF 884 5878 p (RM)s 766 5902 p 305 3 ru f4 SF 766 5979 p (N)s f2 SF 821 5991 p (RM)s f15 SF 963 5979 p (+)s 19 r (1)s f4 SF 1080 5922 p (:)s f15 SF 584 r (\(1\))s f17 SF 1972 17 p (3.1)s 83 r (Determination)s 21 r (of)s f4 SF 21 r (AC)s 6 r (R)s f15 SF 1 r (\()s f4 SF (t)s f15 SF (\))s 2132 123 p 1.000 @beginspecial -69.000000 64.000000 599.000000 722.000000 true @bbox @ecl 199.000000 @hsize @setspecial %%BeginDocument: figure/efci-view.eps /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath arrowHeight neg arrowWidth 2 div moveto 0 0 lineto arrowHeight neg arrowWidth 2 div neg lineto } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /arrowHeight 8 def /arrowWidth 4 def /IdrawDict 55 dict def IdrawDict begin /reencodeISO { dup dup findfont dup length dict begin { 1 index /FID ne { def }{ pop pop } ifelse } forall /Encoding ISOLatin1Encoding def currentdict end definefont } def /ISOLatin1Encoding [ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright /parenleft/parenright/asterisk/plus/comma/minus/period/slash /zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon /less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N /O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright /asciicircum/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m /n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/dotlessi/grave/acute/circumflex/tilde/macron/breve /dotaccent/dieresis/.notdef/ring/cedilla/.notdef/hungarumlaut /ogonek/caron/space/exclamdown/cent/sterling/currency/yen/brokenbar /section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot /hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior /acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine /guillemotright/onequarter/onehalf/threequarters/questiondown /Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla /Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex /Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis /multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute /Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis /aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave /iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex /otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis /yacute/thorn/ydieresis ] def /Helvetica reencodeISO def /Helvetica-Oblique reencodeISO def /Helvetica-BoldOblique reencodeISO def /Helvetica-BOblique reencodeISO def /Symbol dup findfont def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { dup -1 eq { /patternGrayLevel idef /patternString idef } { /patternGrayLevel idef } ifelse false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l w add b translate w neg h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor /fontDict printFont printSize scalefont dup setfont def /descender fontDict begin 0 [FontBBox] 1 get FontMatrix end transform exch pop def /vertoffset 1 printSize sub descender sub def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 3 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def /SSten { fgred fggreen fgblue setrgbcolor dup true exch 1 0 0 -1 0 6 -1 roll matrix astore } def /FSten { dup 3 -1 roll dup 4 1 roll exch newpath 0 0 moveto dup 0 exch lineto exch dup 3 1 roll exch lineto 0 lineto closepath bgred bggreen bgblue setrgbcolor eofill SSten } def /Rast { exch dup 3 1 roll 1 0 0 -1 0 6 -1 roll matrix astore } def Begin [ 0.955325 0 0 0.955325 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Line 0 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1.03322 -0 -0 1 -159.414 105 ] concat 165 495 735 495 Line End Begin %I BSpl 2 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -22 105 ] concat 112 575 72 565 52 545 3 BSpl End Begin %I Line 0 1 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -147 38 ] concat 237 682 447 682 Line End Begin %I Line 0 1 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -147 38 ] concat 627 682 717 682 Line End Begin %I Text 0 0 0 SetCFg Helvetica 18 SetF [ 1 0 0 1 150 747 ] concat [ (ACR1) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica 18 SetF [ 1 0 0 1 290 747 ] concat [ (ACR2) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica 18 SetF [ 1 0 0 1 380 747 ] concat [ (ACR3) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica-Oblique 18 SetF [ 1 0 0 1 500 750 ] concat [ (ACR4) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica-Oblique 18 SetF [ 1 0 0 1 100 477 ] concat [ (t0) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica-Oblique 18 SetF [ 1 0 0 1 310 477 ] concat [ (t1) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica-Oblique 18 SetF [ 1 0 0 1 410 477 ] concat [ (t2) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica-Oblique 18 SetF [ 1 0 0 1 490 477 ] concat [ (t3) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica-Oblique 18 SetF [ 1.375 0 0 0.914934 580 475.554 ] concat [ (t4) ] Text End Begin %I Line 0 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1.10326 -0 -0 1 -180.969 105 ] concat 175 195 725 195 Line End Begin %I Line 0 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1.10326 -0 -0 1 -180.969 105 ] concat 175 135 725 135 Line End Begin %I BSpl 2 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -185 105 ] concat 615 55 675 105 705 195 3 BSpl End Begin %I BSpl 2 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -72 105 ] concat 592 195 602 215 622 235 642 245 4 BSpl End Begin %I Line 0 1 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -147 38 ] concat 237 372 447 372 Line End Begin %I Line 0 1 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -147 38 ] concat 627 372 717 372 Line End Begin %I Text 0 0 0 SetCFg Helvetica 18 SetF [ 1 0 0 1 170 437 ] concat [ (Q1) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica 18 SetF [ 1 0 0 1 300 437 ] concat [ (Q2) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica 18 SetF [ 1 0 0 1 380 437 ] concat [ (Q3) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica 18 SetF [ 1 0 0 1 520 437 ] concat [ (Q4) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica-Oblique 18 SetF [ 1 0 0 1 130 397 ] concat [ (Qmax) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica 24 SetF [ 1 0 0 1 -30 413 ] concat [ (Q\(t\)) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica 24 SetF [ 1 0 0 1 -70 713 ] concat [ (ACR\(t\)) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica 18 SetF [ 1 0 0 1 -30 307 ] concat [ (QH) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica 18 SetF [ 1 0 0 1 -30 247 ] concat [ (QL) ] Text End Begin %I Line 1 0 0 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -22 25 ] concat 322 475 322 385 Line End Begin %I Line 1 0 0 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -22 25 ] concat 112 655 112 385 Line End Begin %I Line 1 0 0 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -22 25 ] concat 592 655 592 385 Line End Begin %I Line 3 0 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -22 25 ] concat 32 455 642 455 Line End Begin %I Line 1 0 0 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -22 25 ] concat 112 385 112 135 Line End Begin %I Line 1 0 0 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -22 25 ] concat 322 385 322 135 Line End Begin %I Line 1 0 0 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -22 25 ] concat 502 385 502 135 Line End Begin %I Line 1 0 0 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -22 25 ] concat 592 385 592 135 Line End Begin %I Text 0 0 0 SetCFg Helvetica-BoldOblique 24 SetF [ 1 0 0 1 610 146 ] concat [ (t) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica 18 SetF [ 1 0 0 1 -70 607 ] concat [ (BW/Nvc) ] Text End Begin %I Line 1 0 0 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -75 -60 ] concat 375 710 375 570 Line End Begin %I Text 0 0 0 SetCFg Helvetica-BOblique 14 SetF [ 1 0 0 1 340 685 ] concat [ (BW) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica-BoldOblique 18 SetF [ 1 0 0 1 330 696 ] concat [ (x) ] Text End Begin %I Pict [ 1 0 0 1 -70 -10 ] concat Begin %I Text 0 0 0 SetCFg Helvetica-BOblique 14 SetF [ 1 0 0 1 330 95 ] concat [ (L2) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica-BoldOblique 18 SetF [ 1 0 0 1 320 110 ] concat [ (x) ] Text End End %I eop Begin %I Pict [ 1 0 0 1 -20 0 ] concat Begin %I Text 0 0 0 SetCFg Symbol 24 SetF [ 1 0 0 1 70 143 ] concat [ (t) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica-BoldOblique 18 SetF [ 1 0 0 1 80 140 ] concat [ (xds) ] Text End End %I eop Begin %I Pict [ 1 0 0 1 366 -4.00001 ] concat Begin %I Text 0 0 0 SetCFg Symbol 24 SetF [ 1 0 0 1 70 143 ] concat [ (t) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica-BoldOblique 18 SetF [ 1 0 0 1 80 140 ] concat [ (xds) ] Text End End %I eop Begin %I Pict [ 1 0 0 1 464 -6.00001 ] concat Begin %I Text 0 0 0 SetCFg Symbol 24 SetF [ 1 0 0 1 70 143 ] concat [ (t) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica-BoldOblique 18 SetF [ 1 0 0 1 80 140 ] concat [ (xds) ] Text End End %I eop Begin %I Pict [ 1 0 0 1 258 -32 ] concat Begin %I Text 0 0 0 SetCFg Symbol 24 SetF [ 1 0 0 1 70 143 ] concat [ (t) ] Text End Begin %I Text 0 0 0 SetCFg Helvetica-BoldOblique 18 SetF [ 1 0 0 1 80 140 ] concat [ (xds) ] Text End End %I eop Begin %I Line 2 0 1 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -283 -64 ] concat 803 364 853 474 Line End Begin %I Line 2 0 1 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -283 -64 ] concat 713 224 763 474 Line End Begin %I Line 1 0 1 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -353 -64 ] concat 633 224 683 474 Line End Begin %I Line 2 0 1 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -283 -64 ] concat 533 304 583 474 Line End Begin %I Line 1 0 0 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -283 -64 ] concat 323 364 373 474 Line End Begin %I BSpl 2 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -283 -64 ] concat 323 364 333 404 403 454 483 404 533 304 543 274 553 254 563 224 8 BSpl End Begin %I Line 0 1 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -283 -64 ] concat 583 474 613 474 Line End Begin %I Line 0 1 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -283 -64 ] concat 613 474 763 474 Line End Begin %I BSpl 2 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -283 -64 ] concat 373 744 413 724 443 674 493 604 543 574 593 544 643 614 693 664 733 694 823 734 853 744 11 BSpl End Begin %I Line 0 1 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -283 -64 ] concat 583 714 693 714 Line End Begin %I Line 1 0 1 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -283 -64 ] concat 693 664 713 224 Line End Begin %I Line 3 0 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -283 -64 ] concat 293 224 903 224 Line End Begin %I Line 0 1 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -240 -80 ] concat 280 230 330 230 Line End Begin %I Line 0 1 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -240 -80 ] concat 490 230 540 230 Line End Begin %I Line 0 1 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -240 -80 ] concat 520 220 570 220 Line End Begin %I Line 0 1 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -240 -80 ] concat 670 230 720 230 Line End Begin %I Line 0 1 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -240 -80 ] concat 770 230 810 230 Line End Begin %I Line 1 0 0 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -240 -80 ] concat 650 730 650 680 Line End Begin %I Line 1 1 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -240 -80 ] concat 490 190 520 190 Line End Begin %I Line 1 0 0 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -240 -80 ] concat 490 320 490 190 Line End Begin %I Line 1 0 0 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -240 -80 ] concat 520 240 520 190 Line End Begin %I Line 1 0 0 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -240 -80 ] concat 720 720 720 490 Line End Begin %I Line 0 1 1 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -240 -80 ] concat 540 800 570 800 Line End Begin %I Line 1 1 1 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -240 -80 ] concat 570 800 720 800 Line End Begin %I BSpl 2 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -240 -80 ] concat 810 760 840 750 860 730 3 BSpl End Begin %I BSpl 2 0 0 [] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -240 -80 ] concat 280 380 270 330 250 300 3 BSpl End Begin %I Text 0 0 0 SetCFg Helvetica-BoldOblique 24 SetF [ 1 0 0 1 618 464 ] concat [ (t) ] Text End Begin %I Line 1 0 0 [2 2] 0 SetB 0 0 0 SetCFg 1 1 1 SetCBg none SetP %I p n [ 1 -0 -0 1 -240 -80 ] concat 570 590 570 240 Line End End %I eop showpage end %%EndDocument @endspecial 1972 1926 p (Figure)s 39 r (2:)s 64 r (Pictorial)s 39 r (V)s -4 r (iew)s 37 r (of)s f4 SF 39 r (AC)s 6 r (R)s f15 SF 1 r (\()s f4 SF (t)s f15 SF (\))s 39 r (and)s f4 SF 38 r (Q)s f15 SF (\()s f4 SF (t)s f15 SF (\))s 39 r (in)s 39 r (EFCI)s 1972 2026 p (Switch.)s 2055 2201 p (Figure)s 37 r (2)s 37 r (shows)s 37 r (a)s 37 r (pictorial)s 37 r (view)s 37 r (of)s f4 SF 37 r (AC)s 6 r (R)s f15 SF (\()s f4 SF (t)s f15 SF (\))s 37 r (and)s f4 SF 37 r (Q)s f15 SF (\()s f4 SF (t)s f15 SF (\))s 1972 2301 p (which)s 18 r (have)s 18 r (a)s 18 r (periodicity)s 17 r (in)s 18 r (steady)s 18 r (state.)s 26 r (Let)s 18 r (us)s 18 r (set)s 18 r (a)s 17 r (starting)s 1972 2401 p (point)s 21 r (of)s 20 r (one)s 20 r (cycle)s 20 r (at)s 20 r (time)s 20 r (when)s 20 r (the)s 21 r (congestion)s 20 r (indication)s 20 r (is)s 1972 2500 p (received)s 23 r (by)s 23 r (SES.)s 23 r (In)s 23 r (the)s 22 r (EFCI)s 23 r (switch,)s 23 r (it)s 23 r (takes)s f4 SF 23 r (\034)s f2 SF 3547 2513 p (xds)s f15 SF 3678 2500 p (to)s 22 r (reach)s 1972 2600 p (the)s 29 r (congestion)s 28 r (indication)s 29 r (at)s 29 r (SES)s 28 r (after)s 29 r (the)s 28 r (queue)s 29 r (length)s 28 r (at)s 1972 2699 p (the)s 17 r (switch)s 17 r (buf)s -1 r (fer)s 16 r (reaches)s f4 SF 16 r (Q)s f2 SF 2873 2712 p (H)s f15 SF 2936 2699 p (.)s 26 r (W)s -5 r (e)s 15 r (divide)s 17 r (one)s 16 r (cycle)s 17 r (into)s 17 r (four)s 1972 2799 p (phases)s 17 r (following)s 16 r (behaviors)s 16 r (of)s f4 SF 16 r (AC)s 6 r (R)s f15 SF 1 r (\()s f4 SF (t)s f15 SF (\))s 16 r (and)s f4 SF 16 r (Q)s f15 SF (\()s f4 SF (t)s f15 SF (\))s 16 r (as)s 16 r (in)s 16 r (Fig.)s 16 r (2.)s 1972 2899 p (For)s 28 r (simplicity)s 28 r (of)s 27 r (presentation,)s 30 r (we)s 28 r (introduce)s f4 SF 27 r (AC)s 6 r (R)s f2 SF 3684 2911 p (i)s f15 SF 3712 2899 p (\()s f4 SF (t)s f15 SF (\))s 28 r (and)s f4 SF 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16 r (the)s 16 r (time)s 16 r (when)s 16 r (phase)s f4 SF 17 r (i)s f15 SF 16 r (terminates.)s 26 r (Fur-)s 1972 3536 p (ther)s -2 r (,)s 20 r (the)s 21 r (length)s 20 r (of)s 21 r (phase)s f4 SF 21 r (i)s f15 SF 21 r (is)s 20 r (represented)s 21 r (by)s f4 SF 2578 3693 p (t)s f2 SF 2608 3706 p (i)s f3 SF (\000)s f14 SF (1)s f2 SF (;i)s f15 SF 2783 3693 p (=)s f4 SF 23 r (t)s f2 SF 2883 3706 p (i)s f5 SF 2929 3693 p (\000)s f4 SF 18 r (t)s f2 SF 3042 3706 p (i)s f3 SF (\000)s f14 SF (1)s f4 SF 3150 3693 p (:)s f15 SF 1972 3850 p (W)s -5 r (e)s 28 r (note)s 29 r (here)s 30 r (that)s 29 r (more)s 29 r (rigorous)s 30 r (treatment)s 29 r (is)s 29 r (required)s 30 r (for)s 1972 3950 p (representing)s 20 r (system)s 20 r (behaviors)s 20 r (dependent)s 19 r (on)s 20 r (system)s 20 r (param-)s 1972 4050 p (eters)s 16 r (as)s 15 r (will)s 16 r (be)s 15 r (presented)s 16 r (in)s 15 r (the)s 16 r (next)s 15 r (subsection.)s 26 r (For)s 16 r (a)s 15 r (mean-)s 1972 4149 p (while,)s 37 r (however)s -2 r (,)s 35 r (we)s 34 r (assume)s 33 r (that)s 34 r (the)s 33 r (system)s 34 r (behaves)s 33 r (like)s 1972 4249 p (Fig.)s 21 r (2.)s f4 SF 2055 4349 p (AC)s 6 r (R)s f2 SF 2246 4361 p (i)s f15 SF 2274 4349 p (\()s f4 SF (t)s f15 SF (\))s 20 r (\(1)s f5 SF 23 r (\024)s f4 SF 24 r (i)s f5 SF 23 r (\024)s f15 SF 23 r (4\))s 20 r (is)s 21 r (determined)s 21 r (as)s 21 r (follows.)s f17 SF 1972 4448 p (Phase)s 21 r (1)s f15 SF (:)s f4 SF 28 r (AC)s 6 r (R)s f14 SF 2484 4461 p (1)s f15 SF 2517 4448 p (\()s f4 SF (t)s f15 SF (\))s 1972 4548 p (At)s 22 r (time)s f4 SF 22 r (t)s f15 SF 26 r (=)s 26 r (0,)s 22 r (Phase)s 22 r (1)s 22 r (starts)s 22 r (with)s 22 r (an)s 22 r (initial)s 22 r (value)s f4 SF 22 r (AC)s 6 r (R)s f14 SF 3815 4560 p (1)s f15 SF 3848 4548 p (\(0\))s 1972 4647 p (by)s 27 r (receiving)s 26 r (the)s 26 r (congestion)s 26 r (indication.)s 44 r (During)s 27 r (this)s 26 r (phase,)s 1972 4747 p (the)s 28 r (next)s 28 r (cell)s 28 r (emission)s 28 r (time)s 28 r (is)s 28 r 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2670 5243 p (=)s f5 SF 23 r (\000)s f4 SF 2814 5187 p (AC)s 6 r (R)s f14 SF 3005 5200 p (1)s f15 SF 3038 5187 p (\(0\))s 2814 5224 p 321 3 ru f4 SF 2901 5300 p (M)s -4 r (D)s 3145 5243 p (AC)s 6 r (R)s f14 SF 3335 5256 p (1)s f15 SF 3368 5243 p (\()s f4 SF (t)s f15 SF (\))s f4 SF (;)s f15 SF 1972 5422 p (which)s 21 r (gives)s f4 SF 2331 5602 p (AC)s 6 r (R)s f14 SF 2522 5614 p (1)s f15 SF 2555 5602 p (\()s f4 SF (t)s f15 SF (\))s 23 r (=)s f4 SF 23 r (AC)s 6 r (R)s f14 SF 2924 5614 p (1)s f15 SF 2957 5602 p (\(0\))s f4 SF (e)s f3 SF 3093 5567 p (\000)s f0 SF 3154 5534 p (AC)s 3 r (R)s f13 SF 3284 5548 p (1)s 3309 5534 p (\(0\))s 3154 5554 p 203 3 ru f0 SF 3208 5587 p (M)s -4 r (D)s f2 SF 3368 5567 p (t)s f4 SF 3397 5602 p (:)s f15 SF 1972 5759 p (Note)s 18 r (that)s 18 r (we)s 17 r (do)s 18 r (not)s 18 r (take)s 17 r (into)s 18 r (account)s f4 SF 18 r (M)s -4 r (C)s -8 r (R)s f15 SF 17 r (\(Minimum)s 18 r (Sus-)s 1972 5858 p (tained)s 29 r (ACR\))s 29 r (in)s 29 r (the)s 29 r (above)s 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(R)s f14 SF 546 1290 p (2)s f15 SF 580 1278 p (\()s f4 SF (t)s f15 SF (\))s f4 SF (AD)s -11 r (R)s f15 SF 18 r (+)s f4 SF 19 r (N)s f2 SF 987 1290 p (RM)s f15 SF 1111 1278 p (\()s f4 SF (AD)s 2 r (R)s f15 SF 20 r (+)s f4 SF 18 r (AI)s -6 r (R)s f15 SF (\))s 356 1315 p 1246 3 ru f4 SF 955 1391 p (x)s f15 SF -68 1550 p (=)s f5 SF 22 r (\000)s f4 SF 75 1494 p (AC)s 6 r (R)s f14 SF 266 1506 p (2)s f15 SF 299 1494 p (\()s f4 SF (t)s f15 SF (\))s f14 SF 384 1464 p (2)s 75 1531 p 342 3 ru f4 SF 173 1607 p (M)s -4 r (D)s f15 SF 446 1550 p (+)s f4 SF 605 1494 p (B)s 5 r (W)s 521 1531 p 325 3 ru 521 1607 p (M)s -3 r (D)s 15 r (N)s f2 SF 749 1619 p (V)s 3 r (C)s f4 SF 857 1550 p (AC)s 6 r (R)s f14 SF 1047 1562 p (2)s f15 SF 1080 1550 p (\()s f4 SF (t)s f15 SF (\))s 19 r (+)s f4 SF 1263 1494 p (B)s 4 r (W)s 1259 1531 p 165 3 ru 1259 1607 p (N)s f2 SF 1326 1619 p (V)s 3 r (C)s f4 SF 1434 1550 p (AI)s -6 r (R:)s f15 SF -188 1755 p (By)s 20 r (solving)s 21 r (this)s 20 r (equation)s 21 r (for)s f4 SF 21 r (AC)s 6 r (R)s f14 SF 949 1768 p (2)s f15 SF 983 1755 p (\()s f4 SF (t)s f15 SF (\),)s 20 r (we)s 21 r (obtain)s f4 SF 165 1974 p (AC)s 6 r (R)s f14 SF 356 1987 p (2)s f15 SF 389 1974 p (\()s f4 SF (t)s f15 SF (\))s 23 r (=)s f4 SF 577 1918 p (a)s f14 SF 621 1931 p (1)s f4 SF 654 1918 p (e)s f3 SF 693 1888 p (\000)s f2 SF (a)s f13 SF 781 1896 p (1)s f2 SF 806 1888 p (t)s f15 SF 853 1918 p (+)s f4 SF 19 r (a)s f14 SF 963 1931 p (2)s f4 SF 996 1918 p (r)s 2 r (e)s f3 SF 1074 1888 p (\000)s f2 SF (a)s f13 SF 1162 1896 p (2)s f2 SF 1187 1888 p (t)s 577 1955 p 639 3 ru f4 SF 592 2031 p (c)s f14 SF 628 2044 p (1)s f15 SF 661 2031 p (\()s f4 SF (e)s f3 SF 728 2007 p (\000)s f2 SF (a)s f13 SF 815 2016 p (1)s f2 SF 840 2007 p (t)s f15 SF 888 2031 p (+)s f4 SF 18 r (r)s 3 r (e)s f3 SF 1032 2007 p (\000)s f2 SF (a)s f13 SF 1120 2016 p (2)s f2 SF 1145 2007 p (t)s f15 SF 1174 2031 p (\))s f4 SF 1226 1974 p (;)s f15 SF 438 r (\(2\))s -188 2181 p (where)s f4 SF 20 r (a)s f14 SF 78 2194 p (1)s f15 SF 132 2181 p (and)s f4 SF 21 r (a)s f14 SF 317 2194 p (2)s f15 SF 371 2181 p (are)s 21 r (roots)s 20 r (of)s 21 r (the)s 21 r (equation)s f4 SF 388 2352 p (a)s f14 SF 431 2318 p (2)s f15 SF 483 2352 p (+)s f4 SF 19 r (c)s f14 SF 584 2364 p (2)s f4 SF 617 2352 p (a)s f15 SF 19 r (+)s f4 SF 18 r (c)s f14 SF 781 2364 p (1)s f4 SF 814 2352 p (c)s f14 SF 850 2364 p (3)s f15 SF 906 2352 p (=)s 23 r (0)s f4 SF (;)s f15 SF -188 2522 p (and)s f4 SF 20 r (c)s f14 SF -11 2535 p (1)s f15 SF 21 2522 p (,)s f4 SF 21 r (c)s f14 SF 98 2535 p (2)s f15 SF 152 2522 p (and)s f4 SF 21 r (c)s f14 SF 329 2535 p (3)s f15 SF 383 2522 p (are)s 20 r (given)s 21 r (by)s f4 SF -121 2732 p (c)s f14 SF -85 2745 p (1)s f15 SF -28 2732 p (=)s f5 SF 22 r (\000)s f15 SF 168 2676 p (1)s 115 2713 p 147 3 ru f4 SF 115 2789 p (M)s -4 r (D)s f15 SF 272 2732 p (;)s f4 SF 97 r (c)s f14 SF 428 2745 p (2)s f15 SF 484 2732 p (=)s f4 SF 648 2676 p (B)s 4 r (W)s 564 2713 p 325 3 ru 564 2789 p (M)s -4 r (D)s 15 r (N)s f2 SF 791 2802 p (V)s 3 r (C)s f15 SF 899 2732 p (;)s f4 SF 97 r (c)s f14 SF 1055 2745 p (3)s f15 SF 1111 2732 p (=)s f4 SF 1191 2676 p (B)s 4 r (W)s 26 r (AI)s -7 r (R)s 1191 2713 p 326 3 ru 1272 2789 p (N)s f2 SF 1338 2802 p (V)s 3 r (C)s f4 SF 1527 2732 p (:)s f15 SF -188 2938 p (The)s 20 r (initial)s 21 r (transmission)s 20 r (rate)s f4 SF 21 r (AC)s 6 r (R)s f14 SF 952 2950 p (2)s f15 SF 985 2938 p (\(0\))s 21 r (determines)s f4 SF 20 r (r)s f15 SF 23 r (as)s f4 SF 335 3144 p (r)s f15 SF 26 r (=)s f4 SF 478 3088 p (a)s f14 SF 522 3101 p (1)s f5 SF 574 3088 p (\000)s f4 SF 18 r (c)s f14 SF 692 3101 p (1)s f4 SF 740 3088 p (AC)s 5 r (R)s f14 SF 930 3101 p (2)s f15 SF 963 3088 p (\(0\))s 478 3125 p 582 3 ru f4 SF 478 3201 p (c)s f14 SF 514 3214 p (1)s f4 SF 561 3201 p (AC)s 6 r (R)s f14 SF 752 3214 p (2)s f15 SF 785 3201 p (\(0\))s f5 SF 18 r (\000)s f4 SF 19 r (a)s f14 SF 1027 3214 p (2)s f4 SF 1070 3144 p (:)s f17 SF -188 3352 p (Phase)s 20 r (3:)s f4 SF 27 r (AC)s 6 r (R)s f14 SF 327 3364 p 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4257 p (M)s -5 r (D)s f2 SF 1502 4237 p (x)s f5 SF 1544 4271 p (g)s f12 SF 1586 4154 p (\033)s f4 SF 1662 4271 p (:)s f15 SF -188 4486 p (However)s -3 r (,)s 22 r (it)s 22 r (is)s 22 r (dif\256cult)s 21 r (to)s 23 r (solve)s 22 r (the)s 22 r (above)s 23 r (equation,)s 23 r (and)s 22 r (we)s -188 4585 p (approximately)s 19 r (use)s 20 r (the)s 21 r (following)s 20 r (equation)s 20 r (by)s 20 r (neglecting)s 21 r (the)s -188 4685 p (second)s 20 r (term.)s f4 SF 296 4823 p (dAC)s 6 r (R)s f14 SF 530 4835 p (3)s f15 SF 563 4823 p (\()s f4 SF (t)s f15 SF (\))s 296 4860 p 352 3 ru f4 SF 435 4936 p (dt)s f15 SF 681 4879 p (=)s f4 SF 761 4823 p (N)s f2 SF 816 4835 p (R)s 1 r (M)s f4 SF 954 4823 p (AI)s -6 r (R)s 761 4860 p 348 3 ru 912 4936 p (x)s 1119 4879 p (:)s f15 SF -188 5072 p (Recalling)s 23 r (that)s f4 SF 25 r (AC)s 6 r (R)s f15 SF 25 r (is)s 24 r (decreased)s 24 r (during)s 25 r (not)s 24 r (receiving)s 24 r (RM)s -188 5171 p (cells,)s 23 r (the)s 23 r (inter)s -1 r (-arrival)s 22 r (times)s 23 r (of)s 23 r (two)s 23 r (successive)s 23 r (RM)s 24 r (cells,)s f4 SF 23 r (x)s f15 SF (,)s -188 5271 p (satis\256es)s 20 r (the)s 21 r (following)s 20 r (equation.)s f12 SF 8 5373 p (Z)s f2 SF 91 5393 p (x)s f14 SF 55 5561 p (0)s f4 SF 147 5486 p (AC)s 6 r (R)s f14 SF 338 5498 p (3)s f15 SF 371 5486 p (\()s f4 SF (t)s f5 SF 18 r (\000)s f4 SF 19 r (\034)s f15 SF 9 r (\))s f4 SF (e)s f3 SF 642 5451 p (\000)s f0 SF 704 5418 p (AC)s 3 r (R)s f13 SF 834 5431 p (3)s 859 5418 p (\()s f0 SF (t)s f1 SF (\000)s f0 SF (\034)s f13 SF 4 r (\))s 704 5438 p 284 3 ru f0 SF 798 5471 p (M)s -4 r (D)s f2 SF 998 5451 p (y)s f4 SF 1038 5486 p (dy)s f15 SF 26 r (=)s f4 SF 23 r (N)s f2 SF 1273 5498 p (RM)s f4 SF 1397 5486 p (:)s f15 SF -188 5697 p (This)s 20 r (leads)s 21 r (to)s f4 SF 295 5919 p (x)s f15 SF 23 r (=)s f4 SF 445 5850 p (M)s -4 r (D)s f15 SF 16 r (log\()s f2 SF 849 5817 p (M)s -4 r (D)s 750 5831 p 313 3 ru 750 5879 p (M)s -5 r (D)s f3 SF 1 r (\000)s f2 SF (N)s f0 SF 958 5887 p (RM)s f15 SF 1073 5850 p (\))s 445 5900 p 655 3 ru f4 SF 545 5976 p (AC)s 6 r (R)s f14 SF 735 5989 p (3)s f15 SF 769 5976 p (\()s f4 SF (t)s f5 SF 18 r (\000)s f4 SF 18 r (\034)s f15 SF 10 r (\))s f4 SF 1110 5919 p (:)s f15 SF 1972 17 p (Finally)s -4 r (,)s f4 SF 20 r (AC)s 6 r (R)s f14 SF 2434 30 p (3)s f15 SF 2468 17 p (\()s f4 SF (t)s f15 SF (\))s 20 r (is)s 21 r (solved)s 21 r (as;)s f4 SF 2433 186 p (AC)s 6 r (R)s f14 SF 2623 198 p (3)s f15 SF 2656 186 p (\()s f4 SF (t)s f15 SF (\))s f5 SF 2765 162 p (\030)s f15 SF 2774 190 p (=)s f4 SF 2852 186 p (AC)s 6 r (R)s f14 SF 3043 198 p (3)s f15 SF 3076 186 p (\(0\))s f4 SF (e)s f2 SF 3212 152 p (\014)s 3 r (t)s f4 SF 3282 186 p (;)s f15 SF 1972 355 p (where)s f4 SF 21 r (\014)s f15 SF 25 r (is)s 21 r (given)s 21 r (as)s 21 r (a)s 20 r (root)s 21 r (of)s 21 r (the)s 21 r (equation)s f4 SF 2361 563 p (\014)s f15 SF 27 r (=)s f4 SF 2676 507 p (N)s f2 SF 2731 519 p (RM)s f4 SF 2869 507 p (AI)s -6 r (R)s 2515 544 p 669 3 ru 2515 626 p (M)s -4 r (D)s f15 SF 29 r (log\()s f2 SF 2933 593 p (M)s -4 r (D)s 2833 607 p 313 3 ru 2833 655 p (M)s -4 r (D)s f3 SF 1 r (\000)s f2 SF (N)s f0 SF 3042 663 p (RM)s f15 SF 3157 626 p (\))s f4 SF 3194 563 p (e)s f3 SF 3233 528 p (\000)s f2 SF (\034)s 7 r (\014)s f4 SF 3367 563 p (:)s f17 SF 1972 797 p (Phase)s 21 r (4)s f15 SF (:)s f4 SF 28 r (AC)s 6 r (R)s f14 SF 2484 809 p (4)s f15 SF 2517 797 p (\()s f4 SF (t)s f15 SF (\))s 1972 897 p (Since)s 17 r (the)s 17 r (receiving)s 17 r (rate)s 17 r (of)s 17 r (RM)s 17 r (cells)s 17 r (at)s 17 r (SES)s 17 r (is)s 17 r (just)s 16 r (same)s 17 r (as)s 17 r (in)s 1972 996 p (the)s 19 r (case)s 18 r (of)s 19 r (Phase)s 18 r (2,)s f4 SF 19 r (AC)s 6 r (R)s f14 SF 2825 1009 p (4)s f15 SF 2859 996 p (\()s f4 SF (t)s f15 SF (\))s 18 r (is)s 18 r (given)s 19 r (in)s 18 r (an)s 19 r (equivalent)s 18 r (form)s 1972 1096 p (to)s 21 r (Eq.\(2\).)s f17 SF 1972 1277 p (3.2)s 83 r (Evolution)s 21 r (of)s f4 SF 21 r (AC)s 6 r (R)s f15 SF 1 r (\()s f4 SF (t)s f15 SF (\))s f17 SF 20 r (and)s f4 SF 21 r (Q)s f15 SF (\()s f4 SF (t)s f15 SF (\))s 1972 1378 p (In)s 25 r (this)s 24 r (subsection,)s 25 r (we)s 24 r (investigate)s 24 r (the)s 25 r (evolution)s 24 r (of)s f4 SF 24 r (AC)s 6 r (R)s f15 SF 1 r (\()s f4 SF (t)s f15 SF (\))s 1972 1478 p (and)s f4 SF 23 r (Q)s f15 SF (\()s f4 SF (t)s f15 SF (\).)s 34 r (For)s 23 r (this)s 22 r (purpose,)s 24 r (we)s 23 r (should)s 22 r (determine)s 23 r (the)s 23 r (initial)s 1972 1577 p (values)s f4 SF 31 r (AC)s 6 r (R)s f2 SF 2406 1590 p (i)s f15 SF 2434 1577 p (\(0\))s 31 r (and)s 31 r (the)s 31 r (length)s 31 r (of)s 31 r (each)s 31 r (phase)s f4 SF 31 r (t)s f2 SF 3617 1590 p (i;i)s f14 SF (+1)s f15 SF 3750 1577 p (.)s 59 r (For)s 1972 1677 p (given)s 24 r (initial)s 23 r (rates)s 23 r (of)s f4 SF 23 r (AC)s 6 r (R)s f14 SF 2860 1689 p (1)s f15 SF 2893 1677 p (\()s f4 SF (t)s f15 SF (\))s 23 r (and)s f4 SF 23 r (Q)s f14 SF 3210 1689 p (1)s f15 SF 3243 1677 p (\()s f4 SF (t)s f15 SF (\),)s f4 SF 24 r (Q)s f14 SF 3439 1689 p (1)s f15 SF 3472 1677 p (\()s f4 SF (t)s f15 SF (\))s 23 r (is)s 23 r (obtained)s 1972 1777 p (as;)s f4 SF 2035 1945 p (Q)s f14 SF 2100 1958 p (1)s f15 SF 2133 1945 p (\()s f4 SF (t)s f15 SF (\))s 83 r (=)s f4 SF 83 r (Q)s f14 SF 2497 1958 p (1)s f15 SF 2530 1945 p (\()s f4 SF (\034)s f2 SF 2594 1958 p (xds)s f15 SF 2702 1945 p (\))s 2432 2123 p (+)s f12 SF 2492 2010 p (Z)s f2 SF 2575 2030 p (t)s 2538 2198 p (x)s f14 SF (=)s f2 SF (\034)s f0 SF 2639 2207 p (xds)s f15 SF 2739 2123 p (\()s f4 SF (N)s f2 SF 2833 2135 p (V)s 3 r (C)s f4 SF 2945 2123 p (AC)s 6 r (R)s f14 SF 3136 2135 p (1)s f15 SF 3169 2123 p (\()s f4 SF (x)s f5 SF 18 r (\000)s f4 SF 19 r (\034)s f2 SF 3382 2135 p (sx)s f15 SF 3455 2123 p (\))s f5 SF 18 r (\000)s f4 SF 19 r (B)s 4 r (W)s f15 SF 12 r (\))s f4 SF (dx:)s f15 SF -34 r (\(3\))s 1972 2341 p (The)s 21 r (length)s 21 r (of)s 21 r (Phase)s 20 r (1,)s f4 SF 21 r (t)s f14 SF 2768 2353 p (12)s f15 SF 2830 2341 p (\(=)s f4 SF 23 r (t)s f14 SF 2958 2353 p (1)s f15 SF 2991 2341 p (\))s 21 r (is)s 20 r (given)s 21 r (as)s f4 SF 2594 2509 p (t)s f14 SF 2624 2522 p (12)s f15 SF 2710 2509 p (=)s f4 SF 23 r (x)s f2 SF 2827 2522 p (L)s f14 SF (1)s f15 SF 2924 2509 p (+)s f4 SF 19 r (\034)s f2 SF 3026 2522 p (xds)s f4 SF 3134 2509 p (;)s f15 SF 1972 2678 p (where)s f4 SF 28 r (x)s f2 SF 2250 2690 p (L)s f14 SF (1)s f15 SF 2357 2678 p (is)s 27 r (obtained)s 28 r (by)s 28 r (solving)s 28 r (the)s 27 r (equation)s f4 SF 28 r (Q)s f14 SF 3645 2690 p (1)s f15 SF 3678 2678 p (\()s f4 SF (x)s f2 SF 3753 2690 p (L)s f14 SF (1)s f15 SF 3832 2678 p (\))s 38 r (=)s f4 SF 1972 2778 p (Q)s f2 SF 2038 2790 p (L)s f15 SF 2088 2778 p (.)s 90 r (In)s 42 r (what)s 42 r (follows,)s 47 r (we)s 41 r (will)s 42 r (use)s 42 r (convention)s f4 SF 41 r (x)s f2 SF 3750 2790 p (L)s f14 SF (1)s f15 SF 3898 2778 p (=)s f4 SF 1972 2877 p (Q)s f3 SF 2038 2842 p (\000)s f14 SF (1)s 2038 2901 p (1)s f15 SF 2123 2877 p (\()s f4 SF (Q)s f2 SF 2216 2890 p (L)s f15 SF 2266 2877 p (\))s 21 r (for)s 21 r (brevity)s -5 r (.)s 2055 2977 p (For)s 18 r (Phase)s 17 r (2)s 17 r (and)s 18 r (later)s 17 r (phases,)s 18 r (we)s 18 r (need)s 17 r (a)s 17 r (careful)s 18 r (treatment.)s 1972 3076 p (First,)s 21 r (let)s 21 r (us)s 21 r (introduce)s f4 SF 20 r (x)s f2 SF 2746 3089 p (L)s f14 SF (2)s f15 SF 2846 3076 p (as)s f4 SF 2419 3245 p (x)s f2 SF 2467 3257 p (L)s f14 SF (2)s f15 SF 2569 3245 p (=)s f4 SF 23 r (Q)s f3 SF 2704 3210 p (\000)s f14 SF (1)s 2704 3269 p (2)s f15 SF 2789 3245 p (\(0\))s f5 SF 19 r (\000)s f4 SF 18 r (Q)s f3 SF 3053 3210 p (\000)s f14 SF (1)s 3053 3269 p (2)s f15 SF 3138 3245 p (\()s f4 SF (Q)s f2 SF 3231 3257 p (L)s f15 SF 3281 3245 p (\))s f4 SF (:)s f15 SF 1972 3414 p (That)s 29 r (is,)s f4 SF 31 r (x)s f2 SF 2307 3426 p (L)s f14 SF (2)s f15 SF 2415 3414 p (is)s 28 r (the)s 29 r (time)s 28 r (for)s 29 r (the)s 29 r (queue)s 28 r (length)s 29 r (to)s 28 r (become)s 29 r (0)s 1972 3513 p (after)s 21 r (it)s 21 r (goes)s 21 r (below)s f4 SF 20 r (Q)s f2 SF 2674 3526 p (L)s f15 SF 2724 3513 p (.)s 28 r (Further)s -3 r (,)s f4 SF 2389 3721 p (x)s f2 SF 2437 3734 p (B)s 2 r (W)s f15 SF 2588 3721 p (=)s f4 SF 23 r (AC)s 6 r (R)s f3 SF 2849 3686 p (\000)s f14 SF (1)s 2849 3745 p (2)s f15 SF 2934 3721 p (\()s f4 SF 2976 3665 p (B)s 4 r (W)s 2972 3702 p 165 3 ru 2972 3778 p (N)s f2 SF 3039 3791 p (V)s 3 r (C)s f15 SF 3147 3721 p (\))s f5 SF 18 r (\000)s f4 SF 19 r (t)s f14 SF 3306 3734 p (1)s f4 SF 3339 3721 p (;)s f15 SF 1972 3924 p (which)s 33 r (de\256nes)s 33 r (the)s 33 r (time)s 32 r (when)s 33 r (the)s 33 r (aggregate)s 32 r (ACR)s 33 r (reaches)s f4 SF 1972 4024 p (B)s 5 r (W)s f15 SF 11 r (.)s 47 r (W)s -5 r (e)s 26 r (must)s 27 r (consider)s 27 r (the)s 28 r (following)s 27 r (four)s 27 r (cases)s 27 r (depend-)s 1972 4123 p (ing)s 24 r (on)s f4 SF 23 r (x)s f2 SF 2255 4136 p (L)s f14 SF (2)s f15 SF 2334 4123 p (,)s f4 SF 24 r (x)s f2 SF 2426 4136 p (B)s 3 r (W)s f15 SF 2578 4123 p (and)s f4 SF 23 r (\034)s f2 SF 2757 4136 p (sx)s f15 SF 2854 4123 p (\(see)s 23 r (Fig.)s 23 r (2)s 23 r (which)s 23 r (corresponds)s 23 r (to)s 1972 4223 p (Case)s 21 r (1)s 21 r (in)s 21 r (the)s 20 r (below\).)s 2138 4323 p (Case)s 21 r (1:)s f4 SF 28 r (x)s f2 SF 2460 4335 p (L)s f14 SF (2)s f5 SF 2562 4323 p (\024)s f4 SF 23 r (\034)s f15 SF 10 r (,)s f4 SF 20 r (x)s f2 SF 2784 4335 p (L)s f14 SF (2)s f4 SF 2886 4323 p (<)s 23 r (x)s f2 SF 3021 4335 p (B)s 3 r (W)s f15 SF 3168 4323 p (+)s f4 SF 19 r (\034)s f2 SF 3270 4335 p (sx)s f15 SF 2138 4422 p (Case)s 21 r (2:)s f4 SF 28 r (x)s f2 SF 2460 4435 p (L)s f14 SF (2)s f5 SF 2562 4422 p (\024)s f4 SF 23 r (\034)s f15 SF 10 r (,)s f4 SF 20 r (x)s f2 SF 2784 4435 p (L)s f14 SF (2)s f5 SF 2886 4422 p (\025)s f4 SF 23 r (x)s f2 SF 3021 4435 p (B)s 3 r (W)s f15 SF 3168 4422 p (+)s f4 SF 19 r (\034)s f2 SF 3270 4435 p (sx)s f15 SF 2138 4522 p (Case)s 21 r (3:)s f4 SF 28 r (x)s f2 SF 2460 4534 p (L)s f14 SF (2)s f4 SF 2562 4522 p (>)s 23 r (\034)s f15 SF 10 r (,)s f4 SF 20 r (x)s f2 SF 2784 4534 p (L)s f14 SF (2)s f4 SF 2886 4522 p (<)s 23 r (x)s f2 SF 3021 4534 p (B)s 3 r (W)s f15 SF 3168 4522 p (+)s f4 SF 19 r (\034)s f2 SF 3270 4534 p (sx)s f15 SF 2138 4622 p (Case)s 21 r (4:)s f4 SF 28 r (x)s f2 SF 2460 4634 p (L)s f14 SF (2)s f4 SF 2562 4622 p (>)s 23 r (\034)s f15 SF 10 r (,)s f4 SF 20 r (x)s f2 SF 2784 4634 p (L)s f14 SF (2)s f5 SF 2886 4622 p (\025)s f4 SF 23 r (x)s f2 SF 3021 4634 p (B)s 3 r (W)s f15 SF 3168 4622 p (+)s f4 SF 19 r (\034)s f2 SF 3270 4634 p (sx)s f15 SF 1972 4721 p (Due)s 17 r (to)s 18 r (lack)s 17 r (of)s 17 r (space,)s 17 r (only)s 17 r (Cases)s 18 r (1)s 17 r (and)s 17 r (4)s 17 r (are)s 17 r (explained)s 17 r (in)s 17 r (the)s 1972 4821 p (below)s -4 r (.)s 27 r (In)s 20 r (Case)s 21 r (1,)s 21 r (we)s 21 r (have)s f4 SF 2390 4989 p (t)s f14 SF 2420 5002 p (2)s f15 SF 2536 4989 p (=)s f4 SF 83 r (t)s f14 SF 2696 5002 p (1)s f15 SF 2748 4989 p (+)s f4 SF 18 r (x)s f2 SF 2861 5002 p (L)s f14 SF (2)s f4 SF 2302 5114 p (Q)s f15 SF (\()s f4 SF (t)s f15 SF (\))s 83 r (=)s 83 r (0)s f4 SF (;)s 97 r (t)s f14 SF 2858 5126 p (2)s f15 SF 2909 5114 p (+)s f4 SF 19 r (\034)s f2 SF 3011 5126 p (sx)s f4 SF 3107 5114 p (<)s 23 r (t)s f5 SF 23 r (\024)s f4 SF 23 r (t)s f14 SF 3365 5126 p (3)s f15 SF 3417 5114 p (+)s f4 SF 18 r (\034)s f2 SF 3519 5126 p (sx)s f4 SF 3592 5114 p (:)s f15 SF 1972 5283 p (In)s 21 r (the)s 21 r (above)s 21 r (equation,)s f4 SF 20 r (t)s f14 SF 2761 5295 p (3)s f15 SF 2815 5283 p (is)s 21 r (given)s 20 r (by)s f4 SF 2585 5451 p (t)s f14 SF 2615 5464 p (3)s f15 SF 2731 5451 p (=)s f4 SF 83 r (t)s f14 SF 2891 5464 p (2)s f15 SF 2943 5451 p (+)s f4 SF 18 r (x)s f3 SF 3056 5417 p (0)s f2 SF 3056 5472 p (B)s 2 r (W)s f15 SF 3203 5451 p (+)s f4 SF 18 r (\034)s 5 r (;)s f15 SF 1972 5620 p (where)s f4 SF 30 r (x)s f3 SF 2252 5590 p (0)s f2 SF 2252 5643 p (B)s 3 r (W)s f15 SF 2410 5620 p (is)s 30 r (the)s 29 r (time)s 30 r (when)s 29 r (the)s 30 r (aggregate)s 29 r (ACR)s 30 r (reaches)s f4 SF 1972 5719 p (B)s 5 r (W)s f15 SF 11 r (,)s 21 r (i.e.,)s f4 SF 2389 5922 p (x)s f3 SF 2437 5887 p (0)s f2 SF 2437 5942 p (B)s 2 r (W)s f15 SF 2588 5922 p (=)s f4 SF 23 r (AC)s 6 r (R)s f3 SF 2849 5886 p (\000)s f14 SF (1)s 2849 5945 p (3)s f15 SF 2934 5922 p (\()s f4 SF 2976 5865 p (B)s 4 r (W)s 2972 5902 p 165 3 ru 2972 5979 p (N)s f2 SF 3039 5991 p (V)s 3 r (C)s f15 SF 3147 5922 p (\))s f5 SF 18 r (\000)s f4 SF 19 r (t)s f14 SF 3306 5934 p (2)s f4 SF 3339 5922 p (:)s EP %%Page: 5 5 BP f15 SF -188 17 p (Further)s -3 r (,)s 19 r (we)s 21 r (have)s 21 r (the)s 21 r (following)s 20 r (equation.)s f4 SF -76 366 p (Q)s f15 SF (\()s f4 SF (t)s f15 SF (\))s 22 r (=)s f12 SF 167 146 p (8)s 167 221 p (>)s 167 246 p (>)s 167 271 p (<)s 167 420 p (>)s 167 445 p (>)s 167 470 p (:)s f15 SF 282 203 p (0)s f4 SF (;)s 83 r (t)s f14 SF 460 215 p (2)s f15 SF 512 203 p (+)s f4 SF 18 r (\034)s f2 SF 613 215 p (sx)s f4 SF 709 203 p (<)s 23 r (t)s f5 SF 23 r (\024)s f4 SF 24 r (t)s f14 SF 968 215 p (2)s f15 SF 1019 203 p (+)s f4 SF 19 r (\034)s f2 SF 1121 215 p (sx)s f15 SF 1212 203 p (+)s f4 SF 19 r (x)s f3 SF 1325 173 p (0)s f2 SF 1325 226 p (B)s 3 r (W)s f12 SF 282 248 p (Z)s f2 SF 365 268 p (t)s 329 436 p (t)s f13 SF 354 445 p (2)s f14 SF 378 436 p (+)s f2 SF (\034)s f0 SF 442 445 p (sx)s f14 SF 507 436 p (+)s f2 SF (x)s f1 SF 577 416 p (0)s f0 SF 577 458 p (B)s 2 r (W)s f15 SF 691 361 p (\()s f4 SF (N)s f2 SF 785 373 p (V)s 3 r (C)s f4 SF 897 361 p (AC)s 6 r (R)s f14 SF 1088 373 p (3)s f15 SF 1121 361 p (\()s f4 SF (x)s f5 SF 18 r (\000)s f4 SF 19 r (\034)s f2 SF 1334 373 p (sx)s f15 SF 1407 361 p (\))s f5 SF 18 r (\000)s f4 SF 19 r (B)s 4 r (W)s f15 SF 11 r (\))s f4 SF (dx;)s 430 528 p (t)s f14 SF 460 540 p (2)s f15 SF 512 528 p (+)s f4 SF 18 r (\034)s f2 SF 613 540 p (sx)s f15 SF 705 528 p (+)s f4 SF 18 r (x)s f3 SF 817 498 p (0)s f2 SF 817 551 p (B)s 3 r (W)s f4 SF 969 528 p (<)s 23 r (t)s f5 SF 23 r (\024)s f4 SF 23 r (t)s f14 SF 1227 540 p (3)s f15 SF 1279 528 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SF 492 1249 p (+)s f4 SF 19 r (\034)s f2 SF 594 1261 p (sx)s f4 SF 690 1249 p (<)s 23 r (t)s f5 SF 23 r (\024)s f4 SF 23 r (t)s f14 SF 948 1261 p (4)s f15 SF 1000 1249 p (+)s f4 SF 18 r (\034)s f2 SF 1102 1261 p (sx)s f15 SF 1175 1249 p (\))s f4 SF (;)s f15 SF -188 1438 p (where)s f4 SF 20 r (t)s f2 SF 65 1450 p (H)s f14 SF 4 r (4)s f15 SF 180 1438 p (=)s f4 SF 23 r (Q)s f3 SF 315 1402 p (\000)s f14 SF (1)s 315 1462 p (4)s f15 SF 400 1438 p (\()s f4 SF (Q)s f2 SF 494 1450 p (H)s f15 SF 557 1438 p (\).)s -105 1541 p (In)s 37 r (Case)s 39 r (4,)s 43 r (the)s 38 r (queue)s 39 r (length)s 38 r (never)s 38 r (reaches)s 39 r (0,)s 43 r (that)s 38 r (is,)s -188 1640 p (under)s -2 r (-utilization)s 16 r (does)s 16 r (not)s 16 r (occur)s -3 r (.)s 25 r (Thus,)s 17 r (neither)s f4 SF 16 r (AC)s 6 r (R)s f14 SF 1538 1653 p (2)s f15 SF 1571 1640 p (\()s f4 SF (t)s f15 SF (\))s 16 r (nor)s f4 SF -188 1740 p (AC)s 5 r (R)s f14 SF 2 1752 p (3)s f15 SF 35 1740 p (\()s f4 SF (t)s f15 SF (\))s 21 r (appear)s -4 r (.)s 27 r (W)s -6 r (e)s 20 r (have)s f4 SF 343 1929 p (t)s f14 SF 373 1941 p (4)s f15 SF 430 1929 p (=)s f4 SF 23 r (Q)s f3 SF 565 1893 p (\000)s f14 SF (1)s 565 1953 p (4)s f15 SF 650 1929 p (\()s f4 SF (Q)s f2 SF 744 1941 p (H)s f15 SF 807 1929 p (\))s 18 r (+)s f4 SF 18 r (\034)s f2 SF 954 1941 p (xds)s f4 SF 1062 1929 p (:)s -188 2118 p (Q)s f14 SF -122 2130 p (4)s f15 SF -89 2118 p (\()s f4 SF (t)s f15 SF (\))s 20 r (is)s 20 r (then)s 21 r (obtained)s 21 r (from)s 21 r (eq.\(3\).)s -105 2221 p (By)s 20 r (setting)s f4 SF 296 2410 p (AC)s 6 r (R)s f14 SF 487 2422 p (1)s f15 SF 520 2410 p (\(0\))s 83 r (=)s f4 SF 83 r (AC)s 6 r (R)s f14 SF 1020 2422 p (4)s f15 SF 1054 2410 p (\()s f4 SF (t)s f14 SF 1111 2422 p (4)s f15 SF 1145 2410 p (\))s f4 SF (;)s 421 2534 p (Q)s f14 SF 487 2547 p (1)s f15 SF 520 2534 p (\(0\))s 83 r (=)s f4 SF 83 r (Q)s f14 SF 896 2547 p (4)s f15 SF 929 2534 p (\()s f4 SF (t)s f14 SF 986 2547 p (4)s f15 SF 1038 2534 p (+)s f4 SF 18 r (\034)s f2 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1262 5791 p (\()s f5 SF (1)s f15 SF (\))s f5 SF 18 r (\000)s f4 SF 19 r (B)s 4 r (W)s f15 SF 11 r (\))s f4 SF (dt)s f15 SF 148 5958 p (=)s f4 SF 83 r (Q)s f2 SF 344 5970 p (H)s f15 SF 425 5958 p (+)s 19 r (\()s f4 SF (N)s f2 SF 585 5970 p (V)s 3 r (C)s f4 SF 697 5958 p (AC)s 6 r (R)s f14 SF 887 5970 p (4)s f15 SF 920 5958 p (\()s f5 SF (1)s f15 SF (\))s f5 SF 19 r (\000)s f4 SF 18 r (B)s 4 r (W)s f15 SF 12 r (\))s f4 SF (\034)s 5 r (:)s f15 SF 2055 17 p (The)s 23 r (queue)s 23 r (length)s 23 r (begins)s 23 r (to)s 23 r (decrease)s 23 r (when)s 23 r (the)s 23 r (aggregate)s 1972 117 p (cell)s 19 r (arrival)s 19 r (rate)s 19 r (at)s 18 r (the)s 19 r (switch)s 19 r (is)s 18 r (below)s 19 r (the)s 19 r (bandwidth)s f4 SF 19 r (B)s 4 r (W)s f15 SF 30 r (at)s 1972 217 p (time)s f4 SF 21 r (t)s f2 SF 2171 229 p (max)s f15 SF 2307 217 p (,)s 21 r (which)s 21 r (is)s 21 r (given)s 20 r (by)s f4 SF 2249 408 p (N)s f2 SF 2316 420 p (V)s 3 r (C)s f4 SF 2428 408 p (AC)s 6 r (R)s f14 SF 2618 420 p (4)s f15 SF 2652 408 p (\()s f5 SF (1)s f15 SF (\))s f4 SF (e)s f3 SF 2829 373 p (\000)s f0 SF 2890 340 p (AC)s 3 r (R)s f13 SF 3020 354 p (4)s 3045 340 p (\()s f1 SF (1)s f13 SF (\))s 2890 360 p 239 3 ru f0 SF 2962 393 p (M)s -4 r (D)s f2 SF 3139 373 p (t)s f0 SF 3164 382 p (max)s f15 SF 3372 408 p (=)s f4 SF 83 r (B)s 4 r (W)s -1 r (;)s f15 SF 1972 576 p (i.e.,)s f4 SF 2219 778 p (t)s f2 SF 2249 791 p (max)s f15 SF 2469 778 p (=)s f4 SF 2716 722 p (M)s -4 r (D)s 2609 759 p 362 3 ru 2609 835 p (AC)s 6 r (R)s f14 SF 2799 848 p (4)s f15 SF 2832 835 p (\()s f5 SF (1)s f15 SF (\))s 2995 778 p (log)s f4 SF 3124 722 p (N)s f2 SF 3191 734 p (V)s 3 r (C)s f4 SF 3303 722 p (AC)s 6 r (R)s f14 SF 3494 734 p (4)s f15 SF 3527 722 p (\()s f5 SF (1)s f15 SF (\))s 3124 759 p 541 3 ru f4 SF 3316 835 p (B)s 4 r (W)s 3675 778 p (:)s f15 SF 1972 983 p (Then,)s 21 r (using)s 21 r (eq.\(3\),)s 21 r (we)s 20 r (have)s f4 SF 2169 1152 p (Q)s f2 SF 2235 1164 p (max)s f15 SF 2454 1152 p (=)s f4 SF 83 r (Q)s f14 SF 2650 1164 p (1)s f15 SF 2683 1152 p (\()s f4 SF (t)s f2 SF 2741 1164 p (max)s f15 SF 2877 1152 p (\))s 2454 1276 p (=)s f4 SF 83 r (Q)s f2 SF 2650 1289 p (H)s f15 SF 2731 1276 p (+)s 19 r (\()s f4 SF (N)s f2 SF 2891 1289 p (V)s 3 r (C)s f4 SF 3003 1276 p (AC)s 6 r (R)s f14 SF 3193 1289 p (4)s f15 SF 3226 1276 p (\()s f5 SF (1)s f15 SF (\))s f5 SF 19 r (\000)s f4 SF 18 r (B)s 5 r (W)s f15 SF 11 r (\))s f4 SF (\034)s f15 SF 2584 1438 p (+)s f4 SF (N)s f2 SF 2698 1451 p (V)s 3 r (C)s f4 SF 2796 1438 p (M)s -4 r (D)s f15 SF 1 r (\(1)s f5 SF 19 r (\000)s f4 SF 3127 1382 p (B)s 4 r (W)s 3123 1419 p 165 3 ru 3123 1495 p (N)s f2 SF 3190 1508 p (V)s 3 r (C)s f15 SF 3298 1438 p (\))s f5 SF 2584 1654 p (\000)s f4 SF 2681 1598 p (B)s 4 r (W)s 25 r (M)s -3 r (D)s 2659 1635 p 362 3 ru 2659 1711 p (AC)s 6 r (R)s f14 SF 2849 1723 p (4)s f15 SF 2883 1711 p (\()s f5 SF (1)s f15 SF (\))s 3045 1654 p (log)s f4 SF 3175 1598 p (N)s f2 SF 3241 1610 p (V)s 3 r (C)s f4 SF 3353 1598 p (AC)s 6 r (R)s f14 SF 3544 1610 p (4)s f15 SF 3577 1598 p (\()s f5 SF (1)s f15 SF (\))s 3175 1635 p 541 3 ru f4 SF 3366 1711 p (B)s 4 r (W)s 3725 1654 p (:)s f15 SF 1972 1860 p (where)s f4 SF 21 r (AC)s 6 r (R)s f14 SF 2387 1872 p (4)s f15 SF 2420 1860 p (\()s f5 SF (1)s f15 SF (\))s 21 r (has)s 21 r (been)s 20 r (given)s 21 r (in)s 21 r (eq.\(4\).)s 28 r (From)s 21 r (the)s 21 r (above)s 1972 1959 p (equation,)s 22 r (we)s 21 r (can)s 21 r (observe)s 21 r (that)s 21 r (the)s 21 r (number)s 21 r (of)s 21 r (VC')s -4 r (s)s 20 r (has)s 21 r (a)s 22 r (se-)s 1972 2059 p (rious)s 18 r (impact)s 18 r (on)s 17 r (the)s 18 r (maximum)s 18 r (queue)s 18 r (length)s 17 r (especially)s 18 r (when)s 1972 2158 p (the)s 21 r (propagation)s 21 r (delay)s 21 r (between)s 20 r (SES)s 21 r (and)s 21 r (DES)s 21 r (is)s 20 r (large.)s f17 SF 1972 2339 p (4.2)s 83 r (Conditions)s 21 r (of)s 21 r (A)s -5 r (voiding)s 20 r (Under)s -3 r (-Utilization)s f15 SF 1972 2441 p (As)s 24 r (previously)s 25 r (noted,)s 24 r (a)s 25 r (fully)s 24 r (link)s 24 r (usage)s 24 r (is)s 24 r (accomplished)s 24 r (by)s 1972 2540 p (ful\256lling)s 37 r (the)s 36 r (following)s 36 r (conditions,)s 41 r (which)s 36 r (corresponds)s 36 r (to)s 1972 2640 p (Case)s 21 r (4)s 21 r (in)s 21 r (the)s 20 r (previous)s 21 r (subsection.)s f4 SF 2827 2809 p (x)s f2 SF 2874 2821 p (L)s f14 SF (2)s f4 SF 3036 2809 p (>)s 83 r (\034)s 5 r (;)s 2584 2933 p (x)s f2 SF 2632 2946 p (B)s 2 r (W)s f15 SF 2779 2933 p (+)s f4 SF 18 r (\034)s f2 SF 2880 2946 p (sx)s f4 SF 3036 2933 p (<)s 83 r (x)s f2 SF 3231 2946 p (L)s f14 SF (2)s f4 SF 3310 2933 p (:)s f18 SF 1972 3118 p (5)s 100 r (Numerical)s 25 r (Examples)s f15 SF 1972 3236 p (In)s 27 r (this)s 27 r (subsection,)s 29 r (we)s 27 r (provide)s 27 r (numerical)s 27 r (examples)s 27 r (for)s 27 r (the)s 1972 3336 p (EFCI)s 23 r (switch.)s 33 r (Threshold)s 22 r (values)s f4 SF 23 r (Q)s f2 SF 3105 3348 p (H)s f15 SF 3190 3336 p (and)s f4 SF 23 r (Q)s f2 SF 3398 3348 p (L)s f15 SF 3470 3336 p (are)s 23 r (identically)s 1972 3435 p (set)s 31 r (to)s 31 r (500,)s 34 r (and)s 30 r (the)s 31 r (bandwidth)s 31 r (of)s 31 r (bottleneck)s 31 r (link)s 31 r (is)s 31 r (set)s 30 r (to)s 1972 3535 p (353.208)s 16 r (cells/msec)s 15 r (assuming)s 16 r (150Mbps)s 15 r (A)s -8 r (TM)s 14 r (link.)s 26 r (For)s 15 r (other)s 1972 3635 p (control)s 37 r (parameters,)s 40 r (the)s 37 r (values)s 37 r (suggested)s 36 r (in)s 37 r ([6])s 36 r (are)s 37 r (used)s 1972 3734 p (throughout)s 27 r (this)s 26 r (paper)s 26 r (unless)s 27 r (other)s 26 r (values)s 27 r (are)s 26 r (speci\256ed)s 26 r (ex-)s 1972 3834 p (plicitly)s -4 r (.)s 27 r (Equation)s 20 r (\(1\))s 21 r (is)s 21 r (used)s 21 r (for)s f4 SF 20 r (B)s 5 r (W)s f15 SF 11 r (.)s 2132 3946 p 1.000 @beginspecial 50.000000 50.000000 266.000000 201.000000 true @bbox @ecl 199.000000 @hsize @setspecial %%BeginDocument: figure/steady-state/efci-nvc-0.01-acr.eps /gnudict 50 dict def gnudict begin /Color false def /Solid false def 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gnulinewidth setlinewidth } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 0 1 0 DL } def /LT1 { PL [4 dl 2 dl] 0 0 1 DL } def /LT2 { PL [2 dl 3 dl] 1 0 0 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 /P { stroke [] 0 setdash currentlinewidth 2 div sub M 0 currentlinewidth V stroke } def /D { 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 P } def /A { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /B { 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 P } def /C { 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 /T { 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 P } def /S { 2 copy A C} def /F { stroke [] 0 setdash exch hpt sub exch vpt add moveto 0 vpt2 neg rlineto hpt2 0 rlineto 0 vpt2 rlineto hpt2 neg 0 rlineto closepath fill } def /I { stroke [] 0 setdash vpt 1.12 mul add moveto hpt neg vpt -1.62 mul rlineto hpt 2 mul 0 rlineto hpt neg vpt 1.62 mul rlineto closepath fill } def end gnudict begin gsave 50 50 translate 0.050 0.050 scale 0 setgray /Helvetica findfont 140 scalefont setfont newpath LTa 840 351 M 3249 0 V 840 351 M 0 2602 V LTb 840 351 M 63 0 V 3186 0 R -63 0 V stroke 756 351 M [ [(Helvetica) 140.0 0.0 true (0)] ] -46.7 Rshow 840 871 M 63 0 V 3186 0 R -63 0 V stroke 756 871 M [ [(Helvetica) 140.0 0.0 true (20)] ] -46.7 Rshow 840 1392 M 63 0 V 3186 0 R -63 0 V stroke 756 1392 M [ [(Helvetica) 140.0 0.0 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-9 V 17 -9 V 16 -9 V 16 -9 V 16 -9 V 17 -9 V 16 -9 V 16 -9 V 16 -8 V 17 -9 V 16 -8 V 16 -8 V 16 -8 V 17 -8 V 16 -8 V 16 -8 V LT3 3606 2330 M [ [(Helvetica) 140.0 0.0 true (Nvc=20)] ] -46.7 Rshow 3690 2330 M 252 0 V 840 971 M 16 -6 V 16 -5 V 17 -6 V 16 -6 V 16 -5 V 16 -6 V 17 -5 V 16 -6 V 16 -5 V 16 -5 V 17 -5 V 16 -6 V 16 -5 V 16 -5 V 17 -5 V 16 -5 V 16 -5 V 16 -5 V 17 -5 V 16 -4 V 16 -5 V 16 -5 V 17 -5 V 16 -4 V 16 -5 V 16 -4 V 17 -5 V 16 -4 V 16 -5 V 16 -4 V 17 -4 V 16 -5 V 16 -4 V 16 -4 V 17 -4 V 16 -5 V 16 -4 V 16 -4 V 17 -4 V 16 -4 V 16 -4 V 16 -4 V 17 -4 V 16 -3 V 16 -4 V 16 -4 V 17 -4 V 16 -3 V 16 -4 V 16 -4 V 16 -3 V 17 -4 V 16 -3 V 16 -4 V 16 -3 V 17 -4 V 16 -3 V 16 -4 V 16 -3 V 17 -3 V 16 -4 V 16 -3 V 16 -3 V 17 -3 V 16 -3 V 16 -4 V 16 -3 V 17 -3 V 16 -3 V 16 -3 V 16 -3 V 17 -3 V 16 -3 V 16 -3 V 16 -3 V 17 -2 V 16 -3 V 16 -3 V 16 -3 V 17 -3 V 16 -2 V 16 -3 V 16 -3 V 17 85 V 16 94 V 16 96 V 16 57 V 17 -6 V 16 -6 V 16 -5 V 16 -6 V 17 -5 V 16 -6 V 16 -5 V 16 -6 V 17 -5 V 16 -5 V 16 -6 V 16 -5 V 17 -5 V 16 -5 V 16 -5 V 16 -5 V 16 -5 V 17 -5 V 16 -5 V 16 -4 V 16 -5 V 17 -5 V 16 -4 V 16 -5 V 16 -5 V 17 -4 V 16 -5 V 16 -4 V 16 -4 V 17 -5 V 16 -4 V 16 -4 V 16 -5 V 17 -4 V 16 -4 V 16 -4 V 16 -4 V 17 -4 V 16 -4 V 16 -4 V 16 -4 V 17 -4 V 16 -4 V 16 -4 V 16 -4 V 17 -3 V 16 -4 V 16 -4 V 16 -4 V 17 -3 V 16 -4 V 16 -3 V 16 -4 V 17 -3 V 16 -4 V 16 -3 V 16 -4 V 17 -3 V 16 -3 V 16 -4 V 16 -3 V 17 -3 V 16 -3 V 16 -4 V 16 -3 V 16 -3 V 17 -3 V 16 -3 V 16 -3 V 16 -3 V 17 -3 V 16 -3 V 16 -3 V 16 -3 V 17 -3 V 16 -3 V 16 -2 V 16 -3 V 17 -3 V 16 -3 V 16 -2 V 16 -3 V 17 27 V 16 94 V 16 96 V 16 96 V 17 14 V 16 -5 V 16 -6 V 16 -6 V 17 -5 V 16 -6 V 16 -5 V 16 -6 V 17 -5 V 16 -5 V 16 -5 V 16 -6 V 17 -5 V 16 -5 V 16 -5 V 16 -5 V 17 -5 V 16 -5 V 16 -5 V 16 -4 V 17 -5 V 16 -5 V 16 -5 V 16 -4 V 17 -5 V 16 -4 V 16 -5 V LT4 3606 2190 M [ [(Helvetica) 140.0 0.0 true (Nvc=50)] ] -46.7 Rshow 3690 2190 M 252 0 V 840 636 M 16 -1 V 16 -2 V 17 -1 V 16 -1 V 16 -1 V 16 -1 V 17 -1 V 16 -2 V 16 -1 V 16 -1 V 17 -1 V 16 -1 V 16 -1 V 16 -2 V 17 -1 V 16 -1 V 16 -1 V 16 -1 V 17 -1 V 16 -1 V 16 -2 V 16 -1 V 17 -1 V 16 -1 V 16 -1 V 16 -1 V 17 -1 V 16 -1 V 16 -1 V 16 -1 V 17 -1 V 16 -2 V 16 -1 V 16 -1 V 17 -1 V 16 -1 V 16 -1 V 16 -1 V 17 -1 V 16 -1 V 16 -1 V 16 -1 V 17 -1 V 16 -1 V 16 -1 V 16 -1 V 17 -1 V 16 -1 V 16 -1 V 16 -1 V 16 -1 V 17 -1 V 16 -1 V 16 -1 V 16 -1 V 17 -1 V 16 -1 V 16 -1 V 16 -1 V 17 -1 V 16 -1 V 16 0 V 16 -1 V 17 -1 V 16 -1 V 16 -1 V 16 -1 V 17 -1 V 16 -1 V 16 -1 V 16 -1 V 17 -1 V 16 0 V 16 -1 V 16 -1 V 17 -1 V 16 -1 V 16 -1 V 16 -1 V 17 -1 V 16 -1 V 16 0 V 16 -1 V 17 -1 V 16 -1 V 16 -1 V 16 -1 V 17 0 V 16 -1 V 16 -1 V 16 -1 V 17 -1 V 16 -1 V 16 0 V 16 -1 V 17 -1 V 16 -1 V 16 -1 V 16 0 V 17 -1 V 16 -1 V 16 -1 V 16 -1 V 16 0 V 17 -1 V 16 -1 V 16 -1 V 16 0 V 17 -1 V 16 -1 V 16 -1 V 16 -1 V 17 0 V 16 -1 V 16 -1 V 16 -1 V 17 0 V 16 -1 V 16 -1 V 16 0 V 17 -1 V 16 -1 V 16 -1 V 16 0 V 17 -1 V 16 -1 V 16 0 V 16 -1 V 17 -1 V 16 -1 V 16 0 V 16 -1 V 17 -1 V 16 0 V 16 -1 V 16 -1 V 17 0 V 16 -1 V 16 -1 V 16 0 V 17 -1 V 16 -1 V 16 0 V 16 -1 V 17 -1 V 16 0 V 16 -1 V 16 -1 V 17 0 V 16 -1 V 16 -1 V 16 0 V 16 -1 V 17 -1 V 16 0 V 16 -1 V 16 0 V 17 -1 V 16 -1 V 16 0 V 16 -1 V 17 -1 V 16 0 V 16 -1 V 16 0 V 17 -1 V 16 -1 V 16 0 V 16 -1 V 17 0 V 16 -1 V 16 0 V 16 -1 V 17 -1 V 16 0 V 16 -1 V 16 0 V 17 -1 V 16 -1 V 16 0 V 16 -1 V 17 0 V 16 -1 V 16 0 V 16 -1 V 17 0 V 16 -1 V 16 -1 V 16 0 V 17 -1 V 16 0 V 16 -1 V 16 0 V 17 -1 V 16 0 V 16 -1 V 16 0 V 17 -1 V 16 0 V 16 -1 V stroke grestore end showpage %%EndDocument @endspecial 1972 5269 p (Figure)s 26 r (3:)s 37 r (Effect)s 24 r (of)s f4 SF 26 r (N)s f2 SF 2705 5282 p (V)s 3 r (C)s f15 SF 2828 5269 p (on)s f4 SF 26 r (AC)s 6 r (R)s f15 SF 1 r (\()s f4 SF (t)s f15 SF (\))s 25 r (in)s 26 r (EFCI)s 25 r (Switch)s 26 r (\()s f4 SF (\034)s f15 SF 43 r (=)s 1972 5369 p (0)s f4 SF (:)s f15 SF (02msec\).)s 2055 5559 p (Figures)s 27 r (3)s 26 r (and)s 26 r (4)s 26 r (show)s 27 r (the)s 26 r (ef)s -1 r (fect)s 25 r (of)s 27 r (the)s 26 r (number)s 26 r (of)s 26 r (VC')s -3 r (s,)s f4 SF 1972 5659 p (N)s f2 SF 2039 5671 p (V)s 3 r (C)s f15 SF 2137 5659 p (,)s 25 r (on)s f4 SF 24 r (AC)s 6 r (R)s f15 SF 1 r (\()s f4 SF (t)s f15 SF (\))s 24 r (and)s f4 SF 24 r (Q)s f15 SF (\()s f4 SF (t)s f15 SF (\),)s 25 r (respectively)s -4 r (.)s 37 r (Here,)s 25 r (we)s 24 r (choose)s 1972 5759 p (the)s 27 r (propagation)s 28 r (delay)s f4 SF 27 r (\034)s f2 SF 2768 5771 p (sx)s f15 SF 2878 5759 p (=)s f4 SF 37 r (\034)s f2 SF 2998 5771 p (xd)s f15 SF 3112 5759 p (=)s 37 r (0)s f4 SF (:)s f15 SF (005)s 54 r (msec)s 27 r (\(2km)s 27 r (be-)s 1972 5858 p (tween)s 23 r (SES)s 23 r (and)s 23 r (DES\))s 23 r (as)s 23 r (a)s 23 r (typical)s 23 r (parameter)s 23 r (for)s 23 r (a)s 23 r (LAN)s 23 r (en-)s 1972 5958 p (vironment.)s 26 r (In)s 16 r (the)s 16 r (\256gures,)s 17 r (it)s 15 r (is)s 16 r (easily)s 16 r (observed)s 16 r (that)s 15 r (as)s f4 SF 16 r (N)s f2 SF 3776 5970 p (V)s 3 r (C)s f15 SF 3889 5958 p (is)s EP %%Page: 6 6 BP -29 -65 p 1.000 @beginspecial 50.000000 50.000000 266.000000 201.000000 true @bbox @ecl 199.000000 @hsize @setspecial %%BeginDocument: figure/steady-state/efci-nvc-0.01-q.eps /gnudict 50 dict def gnudict begin /Color false def /Solid false def /gnulinewidth 5.000 def /vshift -46 def /dl {10 mul} def /hpt 31.5 def /vpt 31.5 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 /MFshow {{dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch rmoveto dup 4 get show 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 4 get stringwidth pop add} {pop} ifelse} forall} bind def /Lshow { currentpoint stroke M 0 exch R MFshow } bind def /Rshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R MFshow } def /Cshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R MFshow } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop Solid {pop []} if 0 setdash} ifelse } def /BL { stroke gnulinewidth 2 mul setlinewidth } def /AL { stroke gnulinewidth 2 div setlinewidth } def /PL { stroke gnulinewidth setlinewidth } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 0 1 0 DL } def /LT1 { PL [4 dl 2 dl] 0 0 1 DL } def /LT2 { PL [2 dl 3 dl] 1 0 0 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 /P { stroke [] 0 setdash currentlinewidth 2 div sub M 0 currentlinewidth V stroke } def /D { 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 P } def /A { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /B { 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 P } def /C { 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 /T { 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 P } def /S { 2 copy A C} def /F { stroke [] 0 setdash exch hpt sub exch vpt add moveto 0 vpt2 neg rlineto hpt2 0 rlineto 0 vpt2 rlineto hpt2 neg 0 rlineto closepath fill } def /I { stroke [] 0 setdash vpt 1.12 mul add moveto hpt neg vpt -1.62 mul rlineto hpt 2 mul 0 rlineto hpt neg vpt 1.62 mul rlineto closepath fill } def end gnudict begin gsave 50 50 translate 0.050 0.050 scale 0 setgray /Helvetica findfont 140 scalefont setfont newpath LTa 840 351 M 3249 0 V 840 351 M 0 2602 V LTb 840 351 M 63 0 V 3186 0 R -63 0 V stroke 756 351 M [ [(Helvetica) 140.0 0.0 true (0)] ] -46.7 Rshow 840 1002 M 63 0 V 3186 0 R -63 0 V stroke 756 1002 M [ [(Helvetica) 140.0 0.0 true (500)] ] -46.7 Rshow 840 1652 M 63 0 V 3186 0 R -63 0 V stroke 756 1652 M [ [(Helvetica) 140.0 0.0 true (1000)] ] -46.7 Rshow 840 2303 M 63 0 V 3186 0 R -63 0 V stroke 756 2303 M [ [(Helvetica) 140.0 0.0 true (1500)] ] -46.7 Rshow 840 2953 M 63 0 V 3186 0 R -63 0 V stroke 756 2953 M [ [(Helvetica) 140.0 0.0 true (2000)] ] -46.7 Rshow 840 351 M 0 63 V 0 2539 R 0 -63 V stroke 840 211 M [ [(Helvetica) 140.0 0.0 true (0)] ] -46.7 Cshow 1165 351 M 0 63 V 0 2539 R 0 -63 V stroke 1165 211 M [ [(Helvetica) 140.0 0.0 true (2)] ] -46.7 Cshow 1490 351 M 0 63 V 0 2539 R 0 -63 V stroke 1490 211 M [ [(Helvetica) 140.0 0.0 true (4)] ] -46.7 Cshow 1815 351 M 0 63 V 0 2539 R 0 -63 V stroke 1815 211 M [ [(Helvetica) 140.0 0.0 true (6)] ] -46.7 Cshow 2140 351 M 0 63 V 0 2539 R 0 -63 V stroke 2140 211 M [ [(Helvetica) 140.0 0.0 true (8)] ] -46.7 Cshow 2465 351 M 0 63 V 0 2539 R 0 -63 V stroke 2465 211 M [ [(Helvetica) 140.0 0.0 true (10)] ] -46.7 Cshow 2789 351 M 0 63 V 0 2539 R 0 -63 V stroke 2789 211 M [ [(Helvetica) 140.0 0.0 true (12)] ] -46.7 Cshow 3114 351 M 0 63 V 0 2539 R 0 -63 V stroke 3114 211 M [ [(Helvetica) 140.0 0.0 true (14)] ] -46.7 Cshow 3439 351 M 0 63 V 0 2539 R 0 -63 V stroke 3439 211 M [ [(Helvetica) 140.0 0.0 true (16)] ] -46.7 Cshow 3764 351 M 0 63 V 0 2539 R 0 -63 V stroke 3764 211 M [ [(Helvetica) 140.0 0.0 true (18)] ] -46.7 Cshow 4089 351 M 0 63 V 0 2539 R 0 -63 V stroke 4089 211 M [ [(Helvetica) 140.0 0.0 true (20)] ] -46.7 Cshow 840 351 M 3249 0 V 0 2602 V -3249 0 V 840 351 L stroke 140 1652 M currentpoint gsave translate 90 rotate 0 0 moveto [ [(Helvetica) 140.0 0.0 true (Queue Length: Q\(t\))] ] -46.7 Cshow grestore 2464 71 M [ [(Helvetica) 140.0 0.0 true (Time \(msec\))] ] -46.7 Cshow LT0 3606 2750 M [ [(Helvetica) 140.0 0.0 true (Nvc=5)] ] -46.7 Rshow 3690 2750 M 252 0 V 840 1003 M 16 7 V 16 6 V 17 4 V 16 3 V 16 2 V 16 0 V 17 -2 V 16 -2 V 16 -4 V 16 -5 V 17 -6 V 16 -7 V 16 -6 V 16 -4 V 17 -2 V 16 1 V 16 2 V 16 5 V 17 7 V 16 7 V 16 6 V 16 5 V 17 3 V 16 1 V 16 1 V 16 -1 V 17 -3 V 16 -3 V 16 -5 V 16 -6 V 17 -7 V 16 -6 V 16 -5 V 16 -2 V 17 1 V 16 2 V 16 4 V 16 7 V 17 7 V 16 7 V 16 4 V 16 3 V 17 2 V 16 1 V 16 -1 V 16 -2 V 17 -4 V 16 -4 V 16 -6 V 16 -7 V 16 -7 V 17 -4 V 16 -2 V 16 -1 V 16 3 V 17 4 V 16 6 V 16 8 V 16 6 V 17 5 V 16 3 V 16 2 V 16 1 V 17 -1 V 16 -2 V 16 -3 V 16 -5 V 17 -5 V 16 -7 V 16 -7 V 16 -5 V 17 -2 V 16 -1 V 16 2 V 16 4 V 17 6 V 16 8 V 16 6 V 16 5 V 17 4 V 16 2 V 16 1 V 16 -1 V 17 -2 V 16 -3 V 16 -4 V 16 -6 V 17 -6 V 16 -7 V 16 -5 V 16 -3 V 17 -1 V 16 2 V 16 4 V 16 5 V 17 8 V 16 7 V 16 5 V 16 3 V 17 3 V 16 1 V 16 -1 V 16 -1 V 16 -3 V 17 -5 V 16 -5 V 16 -6 V 16 -8 V 17 -5 V 16 -3 V 16 -1 V 16 2 V 17 3 V 16 5 V 16 8 V 16 7 V 17 5 V 16 4 V 16 3 V 16 1 V 17 -1 V 16 -1 V 16 -3 V 16 -4 V 17 -5 V 16 -7 V 16 -7 V 16 -5 V 17 -4 V 16 -1 V 16 1 V 16 4 V 17 5 V 16 7 V 16 7 V 16 6 V 17 4 V 16 2 V 16 2 V 16 0 V 17 -2 V 16 -3 V 16 -3 V 16 -6 V 17 -6 V 16 -7 V 16 -6 V 16 -3 V 17 -2 V 16 1 V 16 3 V 16 5 V 33 14 V 16 6 V 16 4 V 16 3 V 17 2 V 16 0 V 16 -2 V 16 -2 V 17 -4 V 16 -5 V 16 -6 V 16 -7 V 17 -6 V 16 -4 V 16 -2 V 16 1 V 17 3 V 16 4 V 16 7 V 16 7 V 17 6 V 16 5 V 16 3 V 16 1 V 17 1 V 16 -1 V 16 -3 V 16 -3 V 17 -5 V 16 -6 V 16 -7 V 16 -7 V 17 -4 V 16 -2 V 16 1 V 16 2 V 17 5 V 16 6 V 16 8 V 16 6 V 17 4 V 16 4 V 16 1 V 16 1 V 17 -1 V 16 -2 V 16 -4 V LT1 3606 2610 M [ [(Helvetica) 140.0 0.0 true (Nvc=10)] ] -46.7 Rshow 3690 2610 M 252 0 V 840 1003 M 16 13 V 16 12 V 17 11 V 16 10 V 16 9 V 16 8 V 17 7 V 16 7 V 16 6 V 16 4 V 17 4 V 16 4 V 16 2 V 16 2 V 17 1 V 16 0 V 16 -1 V 16 -1 V 17 -2 V 16 -3 V 16 -3 V 16 -4 V 17 -5 V 16 -5 V 16 -6 V 16 -7 V 17 -7 V 16 -8 V 16 -8 V 16 -9 V 17 -10 V 16 -10 V 16 -10 V 16 -11 V 17 -5 V 16 -1 V 16 4 V 16 8 V 17 13 V 16 12 V 16 11 V 16 11 V 17 9 V 16 8 V 16 8 V 16 7 V 17 6 V 16 5 V 16 4 V 16 4 V 16 2 V 17 2 V 16 1 V 16 1 V 16 0 V 17 -2 V 16 -1 V 16 -3 V 16 -3 V 17 -4 V 16 -4 V 16 -5 V 16 -6 V 17 -6 V 16 -7 V 16 -8 V 16 -8 V 17 -9 V 16 -9 V 16 -10 V 16 -11 V 17 -11 V 16 -7 V 16 -3 V 16 3 V 17 7 V 16 12 V 16 12 V 16 12 V 17 10 V 16 10 V 16 9 V 16 8 V 17 7 V 16 6 V 16 5 V 16 5 V 17 4 V 16 3 V 16 2 V 16 1 V 17 1 V 16 0 V 16 -1 V 16 -2 V 17 -2 V 16 -3 V 16 -3 V 16 -5 V 17 -5 V 16 -5 V 16 -6 V 16 -7 V 16 -7 V 17 -8 V 16 -9 V 16 -9 V 16 -10 V 17 -10 V 16 -11 V 16 -9 V 16 -4 V 17 1 V 16 5 V 32 24 V 17 11 V 16 11 V 16 10 V 16 9 V 17 8 V 16 8 V 16 6 V 16 6 V 17 4 V 16 4 V 16 4 V 16 2 V 17 2 V 16 1 V 16 0 V 16 -1 V 17 -1 V 16 -2 V 16 -3 V 16 -3 V 17 -4 V 16 -5 V 16 -5 V 16 -6 V 17 -7 V 16 -7 V 16 -8 V 16 -8 V 17 -9 V 16 -10 V 16 -10 V 16 -11 V 17 -10 V 16 -6 V 16 0 V 16 4 V 16 9 V 17 13 V 16 12 V 16 11 V 16 10 V 17 9 V 16 9 V 16 7 V 16 7 V 17 6 V 16 5 V 16 4 V 16 4 V 17 2 V 16 2 V 16 1 V 16 1 V 17 -1 V 16 -1 V 16 -1 V 16 -3 V 17 -3 V 16 -4 V 16 -4 V 16 -5 V 17 -6 V 16 -7 V 16 -7 V 16 -7 V 17 -8 V 16 -9 V 16 -10 V 16 -10 V 17 -10 V 16 -11 V 16 -7 V 16 -3 V 17 3 V 16 7 V 16 12 V 16 13 V 17 11 V 16 11 V 16 9 V 16 9 V 17 8 V 16 7 V 16 6 V LT2 3606 2470 M [ [(Helvetica) 140.0 0.0 true (Nvc=15)] ] -46.7 Rshow 3690 2470 M 252 0 V 840 1004 M 16 16 V 16 15 V 17 15 V 16 13 V 16 14 V 16 12 V 17 12 V 16 11 V 16 11 V 16 10 V 17 9 V 16 9 V 16 8 V 16 7 V 17 7 V 16 6 V 16 6 V 16 5 V 17 5 V 16 3 V 16 4 V 16 3 V 17 2 V 16 2 V 16 1 V 16 1 V 17 0 V 16 0 V 16 -1 V 16 -2 V 17 -2 V 16 -2 V 16 -3 V 16 -3 V 17 -4 V 16 -4 V 16 -5 V 16 -5 V 17 -5 V 16 -6 V 16 -7 V 16 -7 V 17 -7 V 16 -8 V 16 -8 V 16 -9 V 17 -9 V 16 -9 V 16 -10 V 16 -10 V 16 -11 V 17 -11 V 16 -11 V 16 -12 V 16 -12 V 17 -13 V 16 -13 V 16 -11 V 16 -4 V 17 3 V 16 10 V 16 16 V 16 15 V 17 15 V 16 14 V 16 13 V 16 13 V 17 12 V 16 11 V 16 11 V 16 10 V 17 10 V 16 8 V 16 9 V 16 7 V 17 7 V 16 7 V 16 5 V 16 6 V 17 4 V 16 5 V 16 3 V 16 3 V 17 2 V 16 2 V 16 2 V 16 1 V 17 0 V 16 0 V 16 -1 V 16 -1 V 17 -2 V 16 -2 V 16 -3 V 16 -3 V 17 -4 V 16 -4 V 16 -4 V 16 -5 V 17 -6 V 16 -6 V 16 -6 V 16 -7 V 16 -7 V 17 -8 V 16 -8 V 16 -9 V 16 -9 V 17 -9 V 16 -10 V 16 -10 V 16 -10 V 17 -11 V 16 -11 V 16 -12 V 16 -12 V 17 -13 V 16 -12 V 16 -13 V 16 -6 V 17 1 V 16 9 V 16 15 V 16 15 V 17 15 V 16 14 V 16 14 V 16 13 V 17 12 V 16 11 V 16 11 V 16 11 V 17 9 V 16 9 V 16 9 V 16 7 V 17 8 V 16 6 V 16 6 V 16 5 V 17 5 V 16 5 V 16 3 V 16 3 V 17 3 V 16 2 V 16 1 V 16 1 V 17 1 V 16 0 V 16 -1 V 16 -1 V 16 -2 V 17 -2 V 16 -2 V 16 -3 V 16 -4 V 17 -4 V 16 -4 V 16 -5 V 16 -5 V 17 -6 V 16 -7 V 16 -6 V 16 -7 V 17 -8 V 16 -8 V 16 -8 V 16 -9 V 17 -9 V 16 -10 V 16 -10 V 16 -10 V 17 -11 V 16 -11 V 16 -12 V 16 -12 V 17 -12 V 16 -13 V 16 -13 V 16 -8 V 17 -1 V 16 7 V 16 13 V 16 16 V 17 15 V 16 15 V 16 13 V 16 13 V 17 13 V 16 12 V 16 11 V 16 10 V 17 10 V 16 9 V 16 8 V 16 8 V 17 8 V 16 6 V 16 7 V LT3 3606 2330 M [ [(Helvetica) 140.0 0.0 true (Nvc=20)] ] -46.7 Rshow 3690 2330 M 252 0 V 840 1004 M 16 19 V 16 18 V 17 17 V 16 17 V 16 16 V 16 16 V 17 15 V 16 14 V 16 14 V 16 14 V 17 13 V 16 12 V 16 12 V 16 12 V 17 11 V 16 10 V 16 10 V 16 10 V 17 9 V 16 8 V 16 8 V 16 8 V 17 7 V 16 6 V 16 6 V 16 6 V 17 5 V 16 5 V 16 4 V 16 4 V 17 4 V 16 3 V 16 2 V 16 2 V 17 2 V 16 1 V 16 1 V 16 1 V 17 0 V 16 0 V 16 -1 V 16 -1 V 17 -2 V 16 -1 V 16 -3 V 16 -2 V 17 -3 V 16 -4 V 16 -4 V 16 -4 V 16 -4 V 17 -5 V 16 -5 V 16 -6 V 16 -6 V 17 -6 V 16 -6 V 16 -7 V 16 -8 V 17 -7 V 16 -8 V 16 -8 V 16 -9 V 17 -9 V 16 -9 V 16 -10 V 16 -10 V 17 -10 V 16 -10 V 16 -11 V 16 -11 V 17 -11 V 16 -12 V 16 -12 V 16 -12 V 17 -13 V 16 -13 V 16 -13 V 16 -13 V 17 -14 V 16 -14 V 16 -14 V 16 -14 V 17 -12 V 16 -1 V 16 7 V 16 17 V 17 18 V 16 18 V 16 17 V 16 16 V 17 16 V 16 16 V 16 15 V 16 14 V 17 14 V 16 13 V 16 13 V 16 12 V 17 12 V 16 11 V 16 11 V 16 10 V 16 10 V 17 9 V 16 9 V 16 8 V 16 8 V 17 7 V 16 7 V 16 7 V 16 6 V 17 5 V 16 5 V 16 5 V 16 4 V 17 4 V 16 3 V 16 3 V 16 2 V 17 2 V 16 2 V 16 1 V 16 1 V 17 0 V 16 0 V 16 -1 V 16 0 V 17 -2 V 16 -1 V 16 -2 V 16 -3 V 17 -3 V 16 -3 V 16 -3 V 16 -4 V 17 -4 V 16 -5 V 16 -5 V 16 -5 V 17 -6 V 16 -6 V 16 -7 V 16 -6 V 17 -7 V 16 -8 V 16 -7 V 16 -9 V 17 -8 V 16 -9 V 16 -9 V 16 -9 V 16 -10 V 17 -10 V 16 -10 V 16 -11 V 16 -10 V 17 -12 V 16 -11 V 16 -12 V 16 -12 V 17 -12 V 16 -13 V 16 -13 V 16 -13 V 17 -14 V 16 -13 V 16 -14 V 16 -15 V 17 -14 V 16 -7 V 16 1 V 16 12 V 17 18 V 16 18 V 16 18 V 16 17 V 17 16 V 16 16 V 16 15 V 16 15 V 17 14 V 16 13 V 16 14 V 16 12 V 17 12 V 16 12 V 16 11 V 16 10 V 17 10 V 16 10 V 16 9 V 16 9 V 17 8 V 16 7 V 16 7 V 16 7 V 17 6 V 16 6 V 16 5 V LT4 3606 2190 M [ [(Helvetica) 140.0 0.0 true (Nvc=50)] ] -46.7 Rshow 3690 2190 M 252 0 V 840 1005 M 16 28 V 16 28 V 17 27 V 16 27 V 16 26 V 16 27 V 17 26 V 16 26 V 16 25 V 16 25 V 17 25 V 16 25 V 16 24 V 16 24 V 17 24 V 16 23 V 16 23 V 16 23 V 17 23 V 16 22 V 16 22 V 16 22 V 17 21 V 16 21 V 16 21 V 16 21 V 17 20 V 16 20 V 16 20 V 16 20 V 17 19 V 16 19 V 16 19 V 16 18 V 17 18 V 16 18 V 16 18 V 16 17 V 17 18 V 16 17 V 16 16 V 16 17 V 17 16 V 16 16 V 16 15 V 16 16 V 17 15 V 16 15 V 16 14 V 16 15 V 16 14 V 17 14 V 16 14 V 16 13 V 16 13 V 17 13 V 16 13 V 16 12 V 16 12 V 17 12 V 16 12 V 16 12 V 16 11 V 17 11 V 16 11 V 16 10 V 16 11 V 17 10 V 16 10 V 16 10 V 16 9 V 17 9 V 16 9 V 16 9 V 16 9 V 17 8 V 16 8 V 16 8 V 16 8 V 17 7 V 16 7 V 16 7 V 16 7 V 17 7 V 16 6 V 16 6 V 16 6 V 17 6 V 16 6 V 16 5 V 16 5 V 17 5 V 16 5 V 16 4 V 16 4 V 17 5 V 16 3 V 16 4 V 16 4 V 17 3 V 16 3 V 16 3 V 16 3 V 16 2 V 17 2 V 16 3 V 16 2 V 16 1 V 17 2 V 16 1 V 16 1 V 16 1 V 17 1 V 16 1 V 16 0 V 16 0 V 17 0 V 16 0 V 16 0 V 16 -1 V 17 0 V 16 -1 V 16 -1 V 16 -2 V 17 -1 V 16 -2 V 16 -1 V 16 -2 V 17 -2 V 16 -3 V 16 -2 V 16 -3 V 17 -3 V 16 -3 V 16 -3 V 16 -3 V 17 -4 V 16 -3 V 16 -4 V 16 -4 V 17 -4 V 16 -5 V 16 -4 V 16 -5 V 17 -5 V 16 -5 V 16 -5 V 16 -5 V 17 -6 V 16 -6 V 16 -5 V 16 -6 V 16 -7 V 17 -6 V 16 -6 V 16 -7 V 16 -7 V 17 -7 V 16 -7 V 16 -7 V 16 -7 V 17 -8 V 16 -8 V 16 -7 V 16 -8 V 17 -9 V 16 -8 V 16 -8 V 16 -9 V 17 -9 V 16 -9 V 16 -9 V 16 -9 V 17 -9 V 16 -10 V 16 -9 V 16 -10 V 17 -10 V 16 -10 V 16 -10 V 16 -10 V 17 -11 V 16 -10 V 16 -11 V 16 -11 V 17 -11 V 16 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exch dup MFwidth neg 3 -1 roll R MFshow } def /Cshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R MFshow } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop Solid {pop []} if 0 setdash} ifelse } def /BL { stroke gnulinewidth 2 mul setlinewidth } def /AL { stroke gnulinewidth 2 div setlinewidth } def /PL { stroke gnulinewidth setlinewidth } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 0 1 0 DL } def /LT1 { PL [4 dl 2 dl] 0 0 1 DL } def /LT2 { PL [2 dl 3 dl] 1 0 0 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 /P { stroke [] 0 setdash currentlinewidth 2 div sub M 0 currentlinewidth V stroke } def /D { stroke [] 0 setdash 2 copy 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63 V 0 2539 R 0 -63 V stroke 1562 211 M [ [(Helvetica) 140.0 0.0 true (15)] ] -46.7 Cshow 1923 351 M 0 63 V 0 2539 R 0 -63 V stroke 1923 211 M [ [(Helvetica) 140.0 0.0 true (20)] ] -46.7 Cshow 2284 351 M 0 63 V 0 2539 R 0 -63 V stroke 2284 211 M [ [(Helvetica) 140.0 0.0 true (25)] ] -46.7 Cshow 2645 351 M 0 63 V 0 2539 R 0 -63 V stroke 2645 211 M [ [(Helvetica) 140.0 0.0 true (30)] ] -46.7 Cshow 3006 351 M 0 63 V 0 2539 R 0 -63 V stroke 3006 211 M [ [(Helvetica) 140.0 0.0 true (35)] ] -46.7 Cshow 3367 351 M 0 63 V 0 2539 R 0 -63 V stroke 3367 211 M [ [(Helvetica) 140.0 0.0 true (40)] ] -46.7 Cshow 3728 351 M 0 63 V 0 2539 R 0 -63 V stroke 3728 211 M [ [(Helvetica) 140.0 0.0 true (45)] ] -46.7 Cshow 4089 351 M 0 63 V 0 2539 R 0 -63 V stroke 4089 211 M [ [(Helvetica) 140.0 0.0 true (50)] ] -46.7 Cshow 840 351 M 3249 0 V 0 2602 V -3249 0 V 840 351 L stroke 140 1652 M currentpoint gsave translate 90 rotate 0 0 moveto [ [(Helvetica) 140.0 0.0 true (Maximum Queue Length)] ] -46.7 Cshow grestore 2464 71 M [ [(Helvetica) 140.0 0.0 true (Number of VCs)] ] -46.7 Cshow LT0 1562 2519 M [ [(Symbol) 140.0 0.0 true (t)] [(Helvetica) 140.0 0.0 true (=0.02)] ] -46.7 Rshow 1646 2519 M 252 0 V 840 463 M 361 13 V 361 18 V 361 23 V 4089 710 L 1730 2519 D 840 463 D 1201 476 D 1562 494 D 1923 517 D 4089 710 D LT1 1562 2379 M [ [(Symbol) 140.0 0.0 true (t)] [(Helvetica) 140.0 0.0 true (=0.20)] ] -46.7 Rshow 1646 2379 M 252 0 V 840 487 M 361 75 V 361 90 V 361 102 V 2166 806 V 1730 2379 A 840 487 A 1201 562 A 1562 652 A 1923 754 A 4089 1560 A LT2 1562 2239 M [ [(Symbol) 140.0 0.0 true (t)] [(Helvetica) 140.0 0.0 true (=0.50)] ] -46.7 Rshow 1646 2239 M 252 0 V 840 517 M 361 139 V 361 151 V 361 164 V 4089 2135 L 1730 2239 B 840 517 B 1201 656 B 1562 807 B 1923 971 B 4089 2135 B LT3 1562 2099 M [ [(Symbol) 140.0 0.0 true (t)] [(Helvetica) 140.0 0.0 true (=1.00)] ] -46.7 Rshow 1646 2099 M 252 0 V 840 560 M 361 223 V 361 228 V 361 235 V 4089 2767 L 1730 2099 C 840 560 C 1201 783 C 1562 1011 C 1923 1246 C 4089 2767 C stroke grestore end showpage %%EndDocument @endspecial 1972 1258 p (Figure)s 33 r (7:)s 51 r (Ef)s -1 r (fect)s 32 r (of)s f4 SF 32 r (N)s f2 SF 2739 1270 p (V)s 3 r (C)s f15 SF 2870 1258 p (on)s 32 r (Maximum)s 32 r (Queue)s 33 r (Length)s 32 r (in)s 1972 1357 p (EFCI)s 21 r (Switch.)s 2055 1608 p (Another)s 20 r (problem)s 19 r (of)s 19 r (the)s 19 r (EFCI)s 20 r (switch)s 19 r (can)s 19 r (be)s 19 r (found)s 20 r (by)s 19 r (let-)s 1972 1707 p (ting)s f4 SF 19 r (N)s f2 SF 2187 1720 p (V)s 3 r (C)s f15 SF 2303 1707 p (be)s 18 r (large.)s 26 r (As)s 18 r (shown)s 19 r (in)s 18 r (Fig.)s 18 r (7,)s 19 r (the)s 19 r (maximum)s 18 r (queue)s 1972 1807 p (length)s 20 r (grows)s 20 r (as)s f4 SF 19 r (N)s f2 SF 2578 1819 p (V)s 3 r (C)s f15 SF 2695 1807 p (becomes)s 20 r (lar)s -1 r (ge)s 19 r (even)s 20 r (with)s 19 r (small)s 20 r (values)s 1972 1906 p (of)s 21 r (propagation)s 21 r (delays.)s f18 SF 1972 2092 p (6)s 100 r (Conclusion)s f15 SF 1972 2211 p (One)s 25 r (problem)s 25 r (of)s 24 r (the)s 25 r (rate-based)s 25 r (congestion)s 24 r (control)s 25 r (exists)s 24 r (in)s 1972 2310 p (the)s 20 r (initial)s 19 r (transient)s 19 r (state.)s 27 r (When)s 19 r (a)s 19 r (number)s 19 r (of)s 19 r (SES')s -3 r (s)s 18 r (start)s 19 r (cell)s 1972 2410 p (transmission)s 30 r (simultaneously)s -5 r (,)s 30 r (the)s 29 r (queue)s 30 r (length)s 29 r (grows)s 29 r (very)s 1972 2510 p (large.)s 26 r (W)s -6 r (e)s 19 r (have)s 19 r (\256nished)s 20 r (its)s 19 r (analysis)s 19 r (and)s 20 r (plan)s 19 r (to)s 20 r (report)s 19 r (in)s 20 r (the)s 1972 2609 p (future.)s f18 SF 1972 2795 p (References)s f15 SF 1972 2913 p ([1])s 42 r (N.)s 18 r (Y)s -3 r (in)s 17 r (and)s 18 r (M.)s 18 r (G.)s 19 r (Hluchyj,)s 18 r (\252On)s 19 r (closed-loop)s 18 r (rate)s 18 r (control)s 2111 3013 p (for)s 30 r (A)s -8 r (TM)s 30 r (cell)s 30 r (relay)s 31 r (networks,\272)s f16 SF 33 r (Pr)s -2 r (oceedings)s 29 r (of)s 31 r (INFO-)s 2111 3113 p (COM)s 20 r ('94)s f15 SF (,)s 21 r (pp.)s 21 r (99\261109,)s 21 r (1994.)s 1972 3212 p ([2])s 42 r (P)s -8 r (.)s 27 r (Newman,)s 31 r (\252T)s -2 r (raf)s -2 r (\256c)s 28 r (management)s 28 r (for)s 29 r (A)s -8 r (TM)s 27 r (local)s 29 r (area)s 2111 3312 p (networks,\272)s f16 SF 31 r (IEEE)s 29 r (Communications)s 30 r (Magazine)s f15 SF (,)s 31 r (vol.)s 29 r (32,)s 2111 3411 p (no.)s 20 r (8,)s 21 r (pp.)s 21 r (44\26151,)s 21 r (1994.)s 1972 3511 p ([3])s 42 r (K.K.Ramakrishnan)s 45 r (and)s 46 r (R.Jain,)s 52 r (\252A)s 45 r (binary)s 46 r (feedback)s 2111 3611 p (scheme)s 47 r (for)s 48 r (congestion)s 47 r (avoidance)s 48 r (in)s 47 r (computer)s 47 r (net-)s 2111 3710 p (works,\272)s f16 SF 60 r (ACM)s 53 r (T)s -4 r (ransactions)s 52 r (on)s 52 r (Computer)s 53 r (Systems)s f15 SF (,)s 2111 3810 p (vol.)s 20 r (8,)s 21 r (no.)s 21 r (2,)s 21 r (pp.)s 20 r (158\261181,)s 21 r (1990.)s 1972 3910 p ([4])s 42 r (J.-C.)s 20 r (Bolot)s 20 r (and)s 20 r (A.)s 20 r (U.)s 21 r (Shankar)s -3 r (,)s 19 r (\252Dynamical)s 21 r (behavior)s 20 r (of)s 2111 4009 p (rate-based)s 25 r (\257ow)s 25 r (control)s 24 r (mechanisms,\272)s f16 SF 26 r (Computer)s 25 r (Com-)s 2111 4109 p (munication)s 20 r (Review)s f15 SF (,)s 21 r (vol.)s 21 r (20,)s 21 r (pp.)s 20 r (35\26149,)s 21 r (4)s 21 r (1990.)s 1972 4208 p ([5])s 42 r (J.)s 19 r (C.)s 19 r (R.)s 19 r (Bennett)s 19 r (and)s 19 r (G.)s 19 r (T)s -5 r (.)s 18 r (D.)s 19 r (Jardins,)s 20 r (\252Failure)s 19 r (modes)s 19 r (of)s 2111 4308 p (the)s 26 r (baseline)s 27 r (rate)s 27 r (based)s 27 r (congestion)s 26 r (control)s 27 r (plan,\272)s f16 SF 28 r (A)s -2 r (TM)s 2111 4408 p (Forum/94-0512)s f15 SF (,)s 20 r (July)s 21 r (1994.)s 1972 4507 p ([6])s 42 r (L.)s 54 r (Roberts,)s 63 r (\252Enhanced)s 54 r (PRCA)s 55 r (\(Proportional)s 54 r (Rate-)s 2111 4607 p (Control)s 21 r (Algorithm\),\272)s f16 SF 21 r (A)s -2 r (TM)s 20 r (Forum/94-0735)s f15 SF (,)s 21 r (September)s 2111 4707 p (1994.)s 1972 4806 p ([7])s 42 r (A.)s 35 r (W)s -7 r (.)s 34 r (Barnhart,)s 38 r (\252Baseline)s 35 r (performance)s 34 r (using)s 35 r (PRCA)s 2111 4906 p (rate-control,\272)s f16 SF 20 r (A)s -2 r (TM)s 20 r (Forum/94-0597)s f15 SF (,)s 21 r (July)s 21 r (1994.)s EP %%Trailer %%Pages: 6 END %%EOF