{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "u := proc(f, c) f/(c -f);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG:6$%\"fG%\"cG6\"F)F)*&9$\"\"\",&9%F,F+!\"\"F/F)F) " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "delay := proc(f, c) 1/( c-f); end; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&delayG:6$%\"fG%\"cG6 \"F)F)*$,&9%\"\"\"9$!\"\"F/F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "flow := [3, 1, 6, 2, 4, 5];\nlinkname:=[`SF-LA`, `SF-NY`, `LA- NY`, `LA-Dal`, `NY-Phi`, `Phi-Dal`];" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%%flowG7(\"\"$\"\"\"\"\"'\"\"#\"\"%\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)linknameG7(%&SF-LAG%&SF-NYG%&LA-NYG%'LA-DalG%'NY-Phi G%(Phi-DalG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "costperlink \+ := [700, 1600, 1500, 1100, 500, 1300];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,costperlinkG7(\"$+(\"%+;\"%+:\"%+6\"$+&\"%+8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "Cprop:=proc(f, C) f*C/sum(flow[k], \+ k=1..6); end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&CpropG:6$%\"fG%\"C G6\"F)F)*(9$\"\"\"9%F,-%$sumG6$&%%flowG6#%\"kG/F4;F,\"\"'!\"\"F)F)" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "Cprop(3, 42); linkname[2]; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&SF-NYG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 644 "Proportional:= proc(Capacity)\nlocal Tcap, Tdelay, Tcost, capa, i, de l, cost,avgdelay, variance;\nTcap:=0; Tdelay:=0; Tcost:=0;\nprintf(` \+ Cap=%f, Power=0 (Proportional Assignment Rule)\\n`, Capacity);\np rintf(` Link Flow Cost Cap Util Delay TotalC ost\\n`);\nfor i from 1 to 6 do \n capa:= Cprop(flow[i], Capacity); Tcap:=Tcap+capa;\n del:=delay(flow[i],capa); Tdelay:=Tdelay+del*fl ow[i];\n cost:=capa*costperlink[i];Tcost:=Tcost+cost;\n printf(` %8s %8.3f %8.3f %8.3f %8.3f %8.3f %8.2f\\n`, \n linkname [i], flow[i], costperlink[i], capa, flow[i]/capa,\n del, cos t);\n " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 365 " od;\nprintf(` Total cap Average Delay TC= Delay Deviation\\n`);\navgdelay:=Tdelay/(sum(flow[k],k=1..6) );\nvariance:=evalf(sqrt(sum((avgdelay-delay(flow[k],Cprop(flow[k],Cap acity)))^2,k=1..6)/6));\nprintf(` %8.3f \+ %8.3f %8.2f %8.3f\\n`,\n Capacity, avgdelay, Tcost, v ariance\n ); end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%-Proporti onalG:6#%)CapacityG6+%%TcapG%'TdelayG%&TcostG%%capaG%\"iG%$delG%%costG %)avgdelayG%)varianceG6\"F2C,>8$\"\"!>8%F6>8&F6-%'printfG6$%W~~~~~~~Ca p=%f,~Power=0~(Proportional~Assignment~Rule)|+G9$-F<6#%^o~~~~Link~~~~F low~~~~~~Cost~~~~~~Cap~~~~~~Util~~~~Delay~~~TotalCost|+G?(8(\"\"\"FE\" \"'%%trueGC)>8'-%&CpropG6$&%%flowG6#FDF?>F5,&F5FEFJFE>8)-%&delayG6$FNF J>F8,&F8FE*&FTFEFNFEFE>8**&FJFE&%,costperlinkGFPFE>F:,&F:FEFfnFE-F<6*% M%8s~%8.3f~~%8.3f~%8.3f~%8.3f~%8.3f~~~~%8.2f|+G&%)linknameGFPFNFhnFJ*& FNFEFJ!\"\"FTFfn-F<6#%^p~~~~~~~~~~~~~~~~~~~~~~~~~~~~Total~cap~~~~~~~Av erage~Delay~~~~TC=~~~Delay~Deviation|+G>8+*&F8FE-%$sumG6$&FO6#%\"kG/F^ p;FEFFFbo>8,-%&evalfG6#-%%sqrtG6#,$-Fjo6$*$,&FgoFE-FV6$F\\p-FL6$F\\pF? Fbo\"\"#F_p#FEFF-F<6'%\\o~~~~~~~~~~~~~~~~~~~~~~~~~~~~%8.3f~~~~~~~~~~%8 .3f~~~~%8.2f~~%8.3f|+GF?FgoF:FbpF2F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Proportional(42);" }}{PARA 6 "" 1 "" {TEXT -1 682 " \+ Cap=42, Power=0 (Proportional Assignment Rule)\n Link Flow \+ Cost Cap Util Delay TotalCost\n SF-LA 3.000 \+ 700.000 6.000 .500 .333 4200.00\n SF-NY 1.000 16 00.000 2.000 .500 1.000 3200.00\n LA-NY 6.000 1500 .000 12.000 .500 .166 18000.00\n LA-Dal 2.000 1100.0 00 4.000 .500 .500 4400.00\n NY-Phi 4.000 500.000 8.000 .500 .250 4000.00\n Phi-Dal 5.000 1300.000 \+ 10.000 .500 .200 13000.00\n Tot al cap Average Delay TC= Delay Deviation\n \+ 42.000 .285 46800.00 .311" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "C:=proc(i, D, p)\nflow[i]+( D-sum(flow[k], k=1..6))\n*(flow[i])^(1/(p+1))\n/sum((flow[j])^(1/(p+1) ), j=1..6); \nend;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"CG:6%%\"iG% \"DG%\"pG6\"F*F*,&&%%flowG6#9$\"\"\"*(,&9%F0-%$sumG6$&F-6#%\"kG/F9;F0 \"\"'!\"\"F0)F,*$,&9&F0F0F0F=F0-F56$)&F-6#%\"jGF?/FGF;F=F0F*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "costperlink:=[1,1,1,1,1,1];e valf(C(1, 42, 1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,costperlinkG7 (\"\"\"F&F&F&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+5B)zN'!\"*" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 612 "GeneralCA:= proc(Capacity , p)\nlocal Tcap, Tdelay, Tcost, capa, i, del, cost;\nTcap:=0; Tdelay: =0; Tcost:=0;\nprintf(` Cap=%f, Power=%f (Square Root)\\n`, Capa city, p);\nprintf(` Link Flow Cost Cap Util De lay TotalCost\\n`);\nfor i from 1 to 6 do \n capa:= evalf(C(i, Ca pacity, p)); Tcap:=Tcap+capa;\n del:=delay(flow[i],capa); Tdelay:=T delay+del*flow[i];\n cost:=capa*costperlink[i];Tcost:=Tcost+cost;\n printf(`%8s %8.3f %8.3f %8.3f %8.3f %8.3f %8.2f\\n`, \n \+ linkname[i], flow[i], costperlink[i], capa, flow[i]/capa,\n \+ del, cost);\n " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 212 "od;\nprintf(` Total cap \+ Average Delay TC=\\n`);\nprintf(` % 8.3f %8.3f %8.2f\\n`,\n Capacity, Tdelay/(sum(flow[k ],k=1..6)), Tcost); end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*Genera lCAG:6$%)CapacityG%\"pG6)%%TcapG%'TdelayG%&TcostG%%capaG%\"iG%$delG%%c ostG6\"F1C*>8$\"\"!>8%F5>8&F5-%'printfG6%%G~~~~~~~Cap=%f,~Power=%f~(Sq uare~Root)|+G9$9%-F;6#%^o~~~~Link~~~~Flow~~~~~~Cost~~~~~~Cap~~~~~~Util ~~~~Delay~~~TotalCost|+G?(8(\"\"\"FE\"\"'%%trueGC)>8'-%&evalfG6#-%\"CG 6%FDF>F?>F4,&F4FEFJFE>8)-%&delayG6$&%%flowG6#FDFJ>F7,&F7FE*&FTFEFXFEFE >8**&FJFE&%,costperlinkGFZFE>F9,&F9FEFinFE-F;6*%M%8s~%8.3f~~%8.3f~%8.3 f~%8.3f~%8.3f~~~~%8.2f|+G&%)linknameGFZFXF[oFJ*&FXFEFJ!\"\"FTFin-F;6#% \\o~~~~~~~~~~~~~~~~~~~~~~~~~~~~Total~cap~~~~~~~Average~Delay~~~~TC=|+G -F;6&%en~~~~~~~~~~~~~~~~~~~~~~~~~~~~%8.3f~~~~~~~~~~%8.3f~~~~%8.2f|+GF> *&F7FE-%$sumG6$&FY6#%\"kG/Fbp;FEFFFeoF9F1F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "GeneralCA(42, 1);" }}{PARA 6 "" 1 "" {TEXT -1 637 " Cap=42, Power=1 (Square Root)\n Link Flow Cost \+ Cap Util Delay TotalCost\n SF-LA 3.000 1.000 6. 357 .471 .297 6.35\n SF-NY 1.000 1.000 2.93 8 .340 .515 2.93\n LA-NY 6.000 1.000 10.748 \+ .558 .210 10.74\n LA-Dal 2.000 1.000 4.741 \+ .421 .364 4.74\n NY-Phi 4.000 1.000 7.877 \+ .507 .257 7.87\n Phi-Dal 5.000 1.000 9.335 .5 35 .230 9.33\n Total cap A verage Delay TC=\n 42.000 \+ .266 42.00" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 165 "Gener alC:=proc(i, D, p)\nflow[i]+(D-sum(flow[k]*costperlink[k], k=1..6))\n* (flow[i]/costperlink[i])^(1/(p+1))\n/sum((flow[j]*costperlink[j]^p)^(1 /(p+1)), j=1..6); \nend;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)General CG:6%%\"iG%\"DG%\"pG6\"F*F*,&&%%flowG6#9$\"\"\"*(,&9%F0-%$sumG6$*&&F-6 #%\"kGF0&%,costperlinkGF9F0/F:;F0\"\"'!\"\"F0)*&F,F0&FF@F0F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 649 "GeneralCAwithCostConstraint:= proc(CostCon straint, p)\nlocal Tcap, Tdelay, Tcost, capa, i, del, cost;\nTcap:=0; \+ Tdelay:=0; Tcost:=0;\nprintf(` Cost=%f, Power=1 (Min-cost)\\n`, \+ CostConstraint);\nprintf(` Link Flow Cost Cap Uti l Delay TotalCost\\n`);\nfor i from 1 to 6 do \n capa:= evalf( GeneralC(i, CostConstraint, p)); Tcap:=Tcap+capa;\n del:=delay(flow [i],capa); Tdelay:=Tdelay+del*flow[i];\n cost:=capa*costperlink[i]; Tcost:=Tcost+cost;\n printf(`%8s %8.3f %8.3f %8.3f %8.3f %8.3f \+ %8.2f\\n`, \n linkname[i], flow[i], costperlink[i], capa, fl ow[i]/capa,\n del, cost);\n " }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 208 "od;\nprintf(` \+ Total cap Average Delay TC=\\n`);\nprintf(` \+ %8.3f %8.3f %8.2f\\n`,\n Tcap, Tdel ay/(sum(flow[k],k=1..6)), Tcost); end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%8$\"\"!>8%F5>8&F5-% 'printfG6$%D~~~~~~~Cost=%f,~Power=1~(Min-cost)|+G9$-F;6#%^o~~~~Link~~~ ~Flow~~~~~~Cost~~~~~~Cap~~~~~~Util~~~~Delay~~~TotalCost|+G?(8(\"\"\"FD \"\"'%%trueGC)>8'-%&evalfG6#-%)GeneralCG6%FCF>9%>F4,&F4FDFIFD>8)-%&del ayG6$&%%flowG6#FCFI>F7,&F7FD*&FTFDFXFDFD>8**&FIFD&%,costperlinkGFZFD>F 9,&F9FDFinFD-F;6*%M%8s~%8.3f~~%8.3f~%8.3f~%8.3f~%8.3f~~~~%8.2f|+G&%)li nknameGFZFXF[oFI*&FXFDFI!\"\"FTFin-F;6#%\\o~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~Total~cap~~~~~~~Average~Delay~~~~TC=|+G-F;6&%en~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~%8.3f~~~~~~~~~~%8.3f~~~~%8.2f|+GF4*&F7FD-%$sumG6$&FY6#%\"kG/Fbp; FDFEFeoF9F1F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "GeneralCAw ithCostConstraint(46800,1);" }}{PARA 6 "" 1 "" {TEXT -1 640 " Co st=46800, Power=1 (Min-cost)\n Link Flow Cost Cap \+ Util Delay TotalCost\n SF-LA 3.000 1.000 7483.145 . 000 .000 7483.14\n SF-NY 1.000 1.000 4319.663 .00 0 .000 4319.66\n LA-NY 6.000 1.000 10584.523 .000 .000 10584.52\n LA-Dal 2.000 1.000 6109.513 .000 \+ .000 6109.51\n NY-Phi 4.000 1.000 8641.327 .000 \+ .000 8641.32\n Phi-Dal 5.000 1.000 9661.826 .000 . 000 9661.82\n Total cap Average D elay TC=\n 46800.000 .000 \+ 46800.00" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "GeneralCA(42, 100);" }}{PARA 6 "" 1 "" {TEXT -1 639 " Cap=42, Power=100 (Squar e Root)\n Link Flow Cost Cap Util Delay Tota lCost\n SF-LA 3.000 1.000 6.500 .461 .285 6 .50\n SF-NY 1.000 1.000 4.462 .224 .288 4.4 6\n LA-NY 6.000 1.000 9.524 .629 .283 9.52 \n LA-Dal 2.000 1.000 5.485 .364 .286 5.48\n NY-Phi 4.000 1.000 7.509 .532 .284 7.50\n P hi-Dal 5.000 1.000 8.517 .587 .284 8.51\n \+ Total cap Average Delay TC=\n \+ 42.000 .284 42.00" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "GeneralCA(42,0);" }}{PARA 6 "" 1 " " {TEXT -1 637 " Cap=42, Power=0 (Square Root)\n Link Flow Cost Cap Util Delay TotalCost\n SF-LA 3.000 \+ 1.000 6.000 .500 .333 6.00\n SF-NY 1.000 \+ 1.000 2.000 .500 1.000 2.00\n LA-NY 6.000 \+ 1.000 12.000 .500 .166 12.00\n LA-Dal 2.000 1. 000 4.000 .500 .500 4.00\n NY-Phi 4.000 1.00 0 8.000 .500 .250 8.00\n Phi-Dal 5.000 1.000 \+ 10.000 .500 .200 10.00\n To tal cap Average Delay TC=\n 42.0 00 .285 42.00" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 574 "EqualCA:= proc(Capacity)\nlocal Tcap, Tdelay, Tcost, capa, i, del, cost;\nTcap:=0; Tdelay:=0; Tcost:=0;\nprintf(` Ca p=%f (Equal)\\n`, Capacity);\nprintf(` Link Flow Cost \+ Cap Util Delay TotalCost\\n`);\nfor i from 1 to 6 do \n c apa:= Capacity/6; Tcap:=Tcap+capa;\n del:=delay(flow[i],capa); Tdel ay:=Tdelay+del*flow[i];\n cost:=capa*costperlink[i];Tcost:=Tcost+co st;\n printf(`%8s %8.3f %8.3f %8.3f %8.3f %8.3f %8.2f\\n`, \n \+ linkname[i], flow[i], costperlink[i], capa, flow[i]/capa,\n \+ del, cost);\n " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 212 "od;\nprintf(` Total cap \+ Average Delay TC=\\n`);\nprintf(` % 8.3f %8.3f %8.2f\\n`,\n Capacity, Tdelay/(sum(flow[k ],k=1..6)), Tcost); end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(EqualC AG:6#%)CapacityG6)%%TcapG%'TdelayG%&TcostG%%capaG%\"iG%$delG%%costG6\" F0C*>8$\"\"!>8%F4>8&F4-%'printfG6$%7~~~~~~~Cap=%f~(Equal)|+G9$-F:6#%^o ~~~~Link~~~~Flow~~~~~~Cost~~~~~~Cap~~~~~~Util~~~~Delay~~~TotalCost|+G? (8(\"\"\"FC\"\"'%%trueGC)>8',$F=#FCFD>F3,&F3FCFHFC>8)-%&delayG6$&%%flo wG6#FBFH>F6,&F6FC*&FNFCFRFCFC>8**&FHFC&%,costperlinkGFTFC>F8,&F8FCFYFC -F:6*%M%8s~%8.3f~~%8.3f~%8.3f~%8.3f~%8.3f~~~~%8.2f|+G&%)linknameGFTFRF enFH*&FRFCFH!\"\"FNFY-F:6#%\\o~~~~~~~~~~~~~~~~~~~~~~~~~~~~Total~cap~~~ ~~~~Average~Delay~~~~TC=|+G-F:6&%en~~~~~~~~~~~~~~~~~~~~~~~~~~~~%8.3f~~ ~~~~~~~~%8.3f~~~~%8.2f|+GF=*&F6FC-%$sumG6$&FS6#%\"kG/F\\p;FCFDF_oF8F0F 0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "EqualCA(42,1);" }} {PARA 6 "" 1 "" {TEXT -1 622 " Cap=42 (Equal)\n Link Flow \+ Cost Cap Util Delay TotalCost\n SF-LA 3.000 \+ 1.000 7.000 .428 .250 7.00\n SF-NY 1.000 \+ 1.000 7.000 .142 .166 7.00\n LA-NY 6.000 1 .000 7.000 .857 1.000 7.00\n LA-Dal 2.000 1.0 00 7.000 .285 .200 7.00\n NY-Phi 4.000 1.000 7.000 .571 .333 7.00\n Phi-Dal 5.000 1.000 \+ 7.000 .714 .500 7.00\n Tot al cap Average Delay TC=\n 42.00 0 .530 42.00" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "GeneralCAwithCostConstraint(46566.28,1);" }}{PARA 6 "" 1 "" {TEXT -1 643 " Cost=46566.28, Power=1 (Min-cost)\n Link Fl ow Cost Cap Util Delay TotalCost\n SF-LA 3.00 0 1.000 7445.772 .000 .000 7445.77\n SF-NY 1.000 \+ 1.000 4298.086 .000 .000 4298.08\n LA-NY 6.000 \+ 1.000 10531.670 .000 .000 10531.67\n LA-Dal 2.000 \+ 1.000 6078.998 .000 .000 6078.99\n NY-Phi 4.000 1 .000 8598.173 .000 .000 8598.17\n Phi-Dal 5.000 1.0 00 9613.578 .000 .000 9613.57\n \+ Total cap Average Delay TC=\n 465 66.280 .000 46566.28" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "20 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }