This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
8s(+Q/:!=!6/5JEJ!#83Nj¿5JEJ! 6 !3!=E 8j(+5X(+:+">6 8H,-*'( Î $5>LsE/"4(V"g!=Z>!=:@ V *0*%>7Np¿T 5JEJ! i6/!3!#E/8(5(:V"%6 8,-*v( Î Ã $5%LsE "4(+"!3Z7!3:+@I(*/*/>7N¿5JEJ! X6/!=!=E/8(+5g(+:+">6 8H,-*'( Î Ã $ 5>LzE "4(+"9!=Z>!3:+@ (/*/*%>7NjS!3$0!=1("98I/*'(+">A/$'!OOzOÀLM5>:(+Q/!6/!3( T 57:x;">6 Eb15>,-./I/(!p(Q !p(5>x7!36bQ/57$0EJ*06/?9(*0,-!LM5>:!#">1VQ 6/5J EJ!7N »<É)²«µ#·Y»C±`½sn/:+5>, "%6!à {/*0"%* ,-*06 "4(+*'576;5%L(Q/!f,-!=8+8">?>!#83l7(Q/!p8Q/5>:(!#8U(EJ!="7EJ$0*'6/!p"%,-576/?i">$'$y,-!=8+8">?>!#8j*28R/à */*/>7NzORQ/!3:+!LM57:!7l T ! 1="%6b8H!=$'!#1e())A à Π*0*%>>N]ORQ/!1VQ ">6/6/!=$kIJ(*0$'*0m="%(*05>6oEJI/!p(+59(Q/!EJ*'dy!3:+!36^(6/5JEJ!=8 T 5>I $0EAC!> Î V */* , 5oA +4,-8 à , 5oA +4,-8 Î ( *0* à , 5oA +4,-8 Ã/*/* à , à , V :0: = 5oNA +[,h8 Î V */* , Î (/ */* à *0* V */*/* 8*06/?h]{J./:#N = , N Î lS(Q/!pV *0(+*/5>* x7!36Q/5>$2EJ*06/?9(*0,9!#85%L(Q/!E/*vdy!3:+!36^(6/5JEJ!#813"%6bAC!EJ!(+!3:+,-*'6/!#E;(+5hA Î */* (. */ = * V V :0*0: */* = Î ( /à (%> * 0 * / * Î 1 = V Î */* à */* V :0: = =/V ( = > U
Î(
Version 2 CSE, IIT Kharagpur
]> j£b¤9 bji£ u_(f(Q/!9EJ!=8*0?>6o(+*',-!>l|"EJ!(V"%*0$'!#EoxS6/5 $0!=EJ?7!5%L](+Q/!i,-!#88+"%?7!X8H!3(*28f5%La(!=6qI/6 "[Z4">*'$2"%A/$0!>Nf¬5 !3Z7!3:#l/(Q !9EJ!#8H*0?>6 !3:V85%L`"g:!#"%$'& (+*',-!b6/!( T 5>:+xDI 8HI<"%$0$'@ªQ "[Z7!">6F!=8H(*0T,h"4(+!5>L(Q/!(:V"4;1?>!=6/!3:V"4(+!=EªAS@P(Q !EJ*'dy!3:+!36^(9:+!=">$vT &c(*0,-!85>I :+13!=8*06G(!3:+,h895%L(+Q/! :+!=8.$0$'5 T *06/?p( T 5fI/(*0$'*0m="%(*05>6J&A ">8!=E9,-!(+:*2138`"%:+!_,-!#"%6/*06/?%LMI $ T Q/*0$'!15>,-. ">:*06/? (+Q/!.6 1!p5%LzEJ*'dC!=:!=67(. :5>(5J157$08=N E ¹ =»CÉY²µ=Å X¶4ÅS¯ |Æ» !h±µ=·)ÉY·7¯Jµ=·)»<± #U¹ &[½ORQ *08g,9!3(:+*01b*06 EJ*213"%(!#8h(Q !q!{J.C!=1e(+!=EZ4"%$0I/!q5>LfIJ(+*'$0*0m="4(+*'576 5%L" ,-!=8+8">?>!p8H!3("%( T Q/*01VQ,-!=8+8">?>!#8_8H(+">:H(,-*288*'6 ?-E/!=">E/$'*06/!=8=N 5 T,XQ/I !31V:+Q! ( :V"4;*28j1p(+13Q/">!f68*0ACm3!!f">5%1=L«1,-57,9!=8+,-8+"%5J?>E/! "%(!= E R*06blJ"%"96 6/E !3 ( 57*28`:x *'(+8_.C*'(!3Q :+5>*'5JIJEk(Nz(+Q/}D!!p,-1=!="%8+6g8">">?>$v(+!=!38_:+6 Q "4"[(+ZS!3*06/$0@-?9Z^(*05-! T ,-(+*08+Q/8_*28R(Q ,9!3!3*0:(:+EJ*01!="7(EJ59$0*'*'6/6I ">:+">6^(!3!. :57A "%A/*0$0*v(U@-"4(R1VQ "%6/6 !3$ I/(*0$'*0m="%(*05>6 Á 6 Á ÄÄj*06 EJ*213"%(!#8j(+Q/! ./:+5>A ">A/*'$0*'(U@-(Q "%("i,-!#88+"%?7!f8!( T *'(QbIJ(+*'$0*'m#"4(+*'576 °,-!3!3(+8">$'$k,-!=8+8+"%?>!pEJ!#">EJ$0*'6 !>N
Unsaturated Saturated
Unschedulable
n *0?>I/:+! Î ÃJjJ1VQ !3,h"4(+*01!=./:+!=8!36^(+"%(*05>6g5>L 5q!=8+8">?>!S!(V8 }D!6/5 ./:+54ZS*0EJ!">6o*'6^(+I/*v(+*'Z7!X!3{S. $0">6 "4(+*'5765>Lz(Q/!i,9!3(:+*01=83NORQ !!36^(*0:+!.<57./I/$2"4(+*'576o5%L`8@^6<1VQ/:576/5>I<8R,9!#88+"%?7!=81="%6oAC! EJ*0ZS*0E/!=Ei*'6^(T 5f(+Q/:!=!_13$0"788!=8zEJ!=.6X(Q/!8+1VQ/!=EJI $0">A/*'$0*'(U@5%dy!3:+!=E9">8z8HQ 5 T 6X*069n*0? N Î ÃJNORQ/!=8!s(Q/:+!3!1$2">8+8!=85%L<,-!#88+"%?7!=8 ">:!pA/:+*'! @;!3{S. $0">*'6/!#Eg*06(Q/!pLM57$'$05 T *06/? N ± #¯Jµ#²«¶4¯Jµ#Å^Æ ´[ÈÅSƲÉ)¯ zÉYÅC½ORQ/!X,-!=8+8+"%?>!i8H!3(f*06o(Q *08p1$2">8+8f"%:+!X81VQ !=EJI/$2"%A $'!9"%6 Eo:+!3,h">*'6r8+1VQ/!#EJI/$2"%A/$0!X!=Z>!36B"4La(!=:f">6S@ ,-!=8+8+"%?>!p8*'m=!f*288$'*0?>Q^(+$'@;*06 13:!#">8!=EkN ¯Jµ=²¶4¯Jµ=ÅSÆ ´[ÈÅSƲÉ)¯ zÉYÅC½XORQ/!9,-!=8+8">?>!-8H!3(f*06r(+Q/*281$2">8+8">:!-81VQ !=EJI/$2"%A $'!9A/IJ("%6S@o*06 1:+!="78H!i*'6B(Q !9,-!#88+"%?7!i8*'m=!i5>Ls" ,-!=8+8+"%?>! T 5>I/$2Eg$0!="7E(5h8H57,-!f,-!#88+"%?7!=8_,-*08+8H*06/?9(Q !3*0:EJ!="7EJ$0*'6/!#83N ± #´[ÈÅSƲÉ)¯ zÉYÅC½ 6 81VQ !=EJI/$2"%A $'!f8H!3(s:+!LM!3:V8](+5(Q 578!,-!=8+8">?>!#8zLM5>: T Q/*21VQ;EJ!="7EJ$'*06/!#8`5>L«8H57,9!,9!#88+"%?7!=8 T 5>I $0EhAC!,-*288!=E|N }D! 57I/$2E!3{J.6b$05 T !=:R(Q ">6qu °">6 Eb"%././:+57"71VQ *h"78IJ(*0$0*'m#"4(*05>6o*06 13:!#">8!=8 AC!3@75>6 ET u N w6P$05 A ">6 E *2ES(Qª6/!3( 57:xJ8=l|./:+*'57:*'(U@^&cA<">8!=Eq. :5>(5J157$ 5>:+xJ8pA8"%(Q/*0?>Q/!=:A "%6 E *0ES(+Q 8=l«(+Q/!;AC5>I/6 E/!=E "7131!#88s./:+T 5%(+5S135>$ TT 57:xJ8`A:+,h"%6 13!5%L(Q/!f./:+*'T57:*'(U@^&E/:*0Z>!=6h./:T 5>(5J157$<*06/*'(*2"%$0$'@h*0,-./:+54Z>!=8_T ">8`(Q !fA<"%6 E T *2ES(+Qg*28 *06 1:+!="78H!#EklSA/IJ(8H(+"%:(+8`(5-EJ:+5>.5%doA576 Eg"91!=:H(V"%*06g.C5>*067(#NjORQ/*28s*28R"%?^"%*06 8U(_(Q !*06^(I/*'(*05>6(Q "%(.L"i./:5>(5J157$ 8Q/5>I $0E*',-./:+54Z>!"78`(+Q/!A ">6 E T *2ES(Qo*28R*'6<1:+!=">8!=E|N
Î1=
Version 2 CSE, IIT Kharagpur
low Bandwidth 802.5
GP(U) 802.4
U high Bandwidth 802.4
GP(U)
802.5
U
n *0?>I/:+! Î1V 6 Á Ä_Z7!3:V8HI<8 (*0$0*'m#"4(*05>6o"%(¾«5 T ">6 E¬*'?7Q _">6 E T *2ES(Q<8 } Q/!=6ª(Q !gA ">6 E *2ES(QG*08X*'6 13:!#">8!=EPAC!3@75>6 Eª"B1!3:(+">*'6ªZ4">$'I/!7lz(Q/!EJ!=13:!#">8!h*'6F(:V"%6 8,-*08+8*'576B(+*',-!13"%I<8H!#8(Q !gLM:V"%,-! (+:+">6 8H,-*288*05>6(*0,9!nKT (5hAC!$'!#88(Q ">6(+Q/!p(57x>!=6:+5%(V"4(+*'576;(*0,-f! E/Njw6(+Q/*0813"78H!7lJA:+!f:+!3$0!="78H*06/?h"96/! T (57x>!=6|lJ(Q !p(:V"%6 8H& ,-*'(H(*06/?96/5JEJ!Q<">8`(5 T "%*'(`LM57:`(+Q/!(5>x7!36-(+5i:+!(+I/:6h!=Z>!=6g"4La(+!3:s(Q/!(:V"%6 8,-*08+8*'576h5%Lk(Q !LM:V"%,-!*28_15>,-./$0!(+!(+5X(+:+">6 8H,-*'(`(+Q/! 6/!3{S(. ">1Vx7!(#NsORQSI 8=lJ(Q/!X!dy!=1e(+*'Z7!LM:V"%,-!p(:V"%6 8,-*08+8*'576g(+*',-!X*06b(Q *081=">8!*08 E;"%6 E(+Q/!LM:V">1e(+*'576b5%Lz(Q/! T "78U(+!=EA "%6<E T *0EJ(Q *28Á4E%&n]Ä+%n_N.<"%?7"%(*05>6g(*0,9!*28*06 EJ!=.L(+Q/!A ">6 E *2ES(Qo">6 EQ/!36 13!13">6AC!1576 8*0EJ!=:!#E"78"-1576 8U(V"%6^(=NsORQ/! (+5>x>!=6r(+:+">6 8,9*28+8H*05>6B(*0,-!;EJ!=13:!#">8!=8 T *v(+QP*'6 13:!#">8*'6 ?A<"%6 E T *2ES(+Q|T NgORQ/!=:!3LM5>:+!>ly(Q !;.?>!95%L T "78U(+!=EBA "%6<E T *0EJ(QP*'6/& 13:!#">8!=8 T *v(+Qb*'6 13:!#">8!*06bA "%6<E T *0EJ(Q|N ORQ/!X(*0,-!=Er(5>x7!36q. :5>(5J157$EJ5S!#86/5>(f!3{JQ/*'A *v(f(Q/*28p"%6/57,h"%$0@>lyAI 8H!9"g6 5SE/!i*28.C!3:+,-*v((!#Eq(+5g(+:+">6 8H,-*'(f135>6^(*06SI/5>I 8$0@ EJI :*06/?-*v(V8">8+8*'?76/!=E;(*0,9!8$05%(=N w6"%$0$C1=">8!=8=l7*'(13"%6gAI ">:+">67(+!3!. :57A "%A/*0$0*v(U@-:+!3,h"%*06 8_1$0578!(5 Î "78`$05>6 ?i">8s(+Q/!I/(*0$'*0m="%(*05>6g*28_$'!#88`(Q<"%6 u XN/ORQ/!3:+!f*08R"98HQ ">:.EJ:57.g*06g(+Q/!f?>I ">:+">67(+!3!./:57A "%A *'$0*v(U@h"%(_IJ(+*'$0*0m="4(+*'576Z4">$'I/!#8R1$0578!(5-u XN/ORQ/*08E/!3,-5>6 8H(:V"4(+!=8`(Q "%( u *28s":+5>A I 8U(_,-!=">8I/:+!5%L«"[Z7!3:V"%?7!.L|:!#"%$'&)(+*',-!6/!3( 57:xJ8=N¿5 l !1="%6;8I/,-,h"%:+*'m=!5>I :`5>A<8H!=:Z4"4(+*'576 8`"78 LM57$'$05 T 83N]u_($05 T (:V"%6<8H,-*288*'5768.:+*v(U@h*06SZ>!=:+8*'576 8_13"%I<8H!#T EgAS@h(+Q/!p:T57I/6 T ES&:57A/*068+1VQ/!=EJI $'*06/?h"%./. :5^">1VQh(+!36 E/8_(+5 "7EJZ>!=:+8!3$0@*0,-. ">1(f,-!#88+"%?7!=8 *'(QP8Q/5>:(fEJ!#">EJ$0*06/!=8=NORQSI 83lk"%(f$05 A "%6<E *0EJ(Q 8f./:+*'57:*'(U@^&E/:*0Z>!=6o./:5>(5J157$*28Ax7!36./:+5%(5J13T 5>$CLM5>::+!=">$v&c(*0,-!p">././$0*01="4(+*'576 83N T T
802.5 802.4
ABU Bandwidth
n*'?7I/:! Î $ ]uA 85>$0IJ(+! s:+!=">xJEJ5 T 6 (*0$'*0m="%(*05>6 ]!3:V8HI 8 _">6 E T *2ES(Q
Î;:
Version 2 CSE, IIT Kharagpur
+C3 i ¡o£o¤f¥]9£i |£9¥ j£bR¥ n :57,"D,95JEJ!#8U(hAC!3?7*'6/6 *'6/?K"D$0*v(($0!o54Z>!=:9"PEJ!#13">E/!b">?>58-AC!=135>,-!o"BZ4"78U(h:+!3.C578*v(+5>:+@ª5%L*06JLM57:,h"4(+*'576|ls">6 E !=6 "%A/$0!3:`5%Lk8H!=Z>!3:V"%$J6 ! T "%./. $'*213"%(*05>6 8]8I 1VQh">8]!3&135>,-,-!3:V1!7N«w6^(!=:6/!3(`./:+54ZS*0EJ!#8 b'&' 5"' 8!3:+ZS*013!R(5"%. ./$'*213"%(*05>6 8=l>,-!#"%6/*06/? (+Q "4(p(:V"4;1i*08f./:+5J1!#88!=EB">8f~7I *01VxS$0@q">8f.<5^88*0A/$'!9A/IJ(p(+Q/!3:+!-*08f6/5?>I ">:+">6^(!3!i5%Lj(+*',-!=$'*06/!=8+8p5>:"71e(I<"%$]EJ!3$0*0Z>!3:+@>N} *'(QD(+Q/! *06 1:+!="78H*06/?D15>,-,-!3:V1*2"%$_I 8+"%?7!g5%Lw67(+!3:+6/!(#l](Q !3:+!*28-"q6/!=!=EF(5P8HI/. .<57:H(h8H5>La(-">6 EªW<:, :+!=">$v&c(*0,-!"%. ./$'*213"%(*05>6 8=NPw6F(+Q/*28 8!=1(*05>6|l T !W<:+8H(_. :54ZS*2EJ!f85>,-!fA ">8*21135>6 13!3.J(V8_">A<57IJ(w6^(!3:+6/!3(=N`SI/A<8H!#~7I !36^($0@>l T !:+!3ZS*0! T (+Q/!p:!#1!=67(_(:+!36<E/8R*'6g(Q/*28"%:+!=" N
A EM
HJ
LBE MN
B
C
ORQ/!A<">8*01fw6^(!=:6/!3(8H!=:ZS*21!p,-5SE/!3$kQ "7881VQ/!=,h"4(*213">$'$0@;AC!3!=6b8Q/5 T 6*'6on*0? N Î (/N physical link Host (Sender)
Host (Receiver)
Edge router
Edge router
n *0?>I :! Î (/]u°S*',-./$0! 5o5JEJ!=$k5%L(Q/!w6^(!=:6 !( ORQ/!Rw6/?7:!#88:+5>IJ(+!3:]*28(Q/!:+5>I/(!3:]"%(H(+"71VQ/!=E9"4(z(+Q/!8H!=6 EJ!=:=© 8z!36 E|N(j*28(Q/!RW<:+8H(]*'6^(!=:HLY"71!_(5p(+Q/!E/"4(V"p8H!=67(jAS@(+Q/!8!36 EJ!=: Q/5^8U(#NORQ/!-([email protected]!;5%LR./QS@J8H*213">$]$'*06/xDI 8!=EP"4(X"b$0*'6 xB,h"[@qAC!g"( T *28U(+!=ED. "%*0:X1="%A/$0!>l"W A./(*21;13">A/$'!7l">6 ED!3Z>!=6 T *':+!3$0!=8+8 $0*'6 xCNjORQ !fw6^(+!3:+6/!(8!3:+Z^*21!*08R. :54ZS*2EJ!=EgA^@"%6gw6^(+!3:+6/!(S!=:ZS*21! j:+54Z^*2EJ!=:fÁYH sÄN/ORQ/!3:+!LM57:!7l7(+Q/!E/"4(V"9. ">8+8H!#8s(Q/:+5>I/?7Q;(+Q/! H © 8s:+5>IJ(+!3:V83NzORQ/!=8!p"%:+!(!=:,-!=E">8_157:!:57IJ(!=:+8=NORQ !EJ!=6 8H*'(U@h5%L«(Q/!#8H!:57IJ(!=:+8s*08sZ>!=:@-Q/*0?>Q"4(s(Q/!fH G!36 EklJ8*'6<1!fQ^I ?>! ">,957I/6^(f5>L_E/"%(+"b"%6<Eq$0*'6/xJ8f(U@S./*213">$'$0@q1576^Z7!3:+?>!9"4(p(Q/!-H zN|n :57,(Q/!h135>:+!i:+5>IJ(+!3:V83ly(+Q/!hE/"4(V"*08LM5>: T "%:VEJ!=Eq(Q/:+5>I/?7Qq(+Q/! !=?>:+!=8+8s:+5>I/(!3:V8pÁY"%((Q/!:+!=13!3*0Z>!3:R!=6 E Äs(59(+Q/!157::+!=8.<576 EJ*06/?9:!#1!3*0Z>!=:+8=N !#"%$'&OR*0,-!X157,-,XI/6/*213"%(*05>6o13">6qAC!i8I/./.C5>:(!=Eb576b(Q/!iw6^(!3:+6/!3(AS@. :54ZS*2EJ*'6 ?h./:!3LM!3:+!36^(*2"%$«(:+!="%(,-!36^((+5gE/"4(V"h5%L`13!3:& (V"%*06D8!36 E/!3:V8(+Q "4(Q "[Z7!X!=67(+!3:+!=Er*'6^(5o"15767(+:+"71e( T *v(+QB(+Q/!-H zN _IJ(pLM5>:f(Q "%(E/"4(V"g. "71Vx>!3(+8p8HQ 5>I/$2EqQ "[Z7!iAC!3!=6D13$0"788*'W !=E AC!LM57:!-(+:+">6 8H,-*288*05>6|Nhu_((Q !;15>6 6/!=1(*05>6P8H!3(H&I/.D(*0,9!7l«(+Q/!;8!36 EJ!=:./:+54Z^*2EJ!#8f(Q/!hH T *'(QP( T 5b. "%:V"%,-!(+!3:V83(Q !h(:V"4;1 8.6"%6 E;(Q/!p8H!=:ZS*21!f8H.C!=13*vW<1="4(+*'576|N]ORQ/!H FI 8!=8`(Q *08_(+59EJ!3(!=:,-*06/! T Q !(Q !3:R*v(13">6"7131!=.J(s57:RQ ">8`(59:!3LMI 8!(+Q/! 13$'*0!36^(:+!=~^I/!=8H(=N9(X1VQ/!#1VxS8LM57:p(Q/!h:+!=85>I/:V1!#8f5>6B(Q/!h.C578+8H*0A/$0!-:57IJ(!#85>Ls(+Q "4(.<">1Vx>!3(pE "4(+" Nhu$'(!3:+6 "%(*0Z>!3$0@>l !h13">6D8+"[@q*'( (+:*0!=8(5W 6 ED". "4(+QGÁYI/6/*213">8H(5>:f,XI/$'(*213"78U(:+5>IJ(+*'6 ?^Ä(Q "%(pQ<">8(Q/!-6/!#1!#88+"%:+@:+!=85>I :+13!=8(5b8"%(*28ULM@b(+Q/!-:!#~7I T *':+!=E T 5^bLM57: (+Q/!8H.C!=13*vW!=6/!3:V"4(+!=E;AS@g(Q/!85>I/:V1!7N Lf(Q/!b6/!3( 57:xG">1313!3.J(V89(Q/!o135>6/6/!#1e(+*'576:+!=~^I/!#8U(#lj(+Q/!36Í*'(;./:57,-*08!=8i(Q<"4(h(Q !qE/"4(V"r(+:+">6 8,9*28+8H*05>68H!=:ZS*21! *'$0$,-!3!3( ÁY5>:!3{/1!3!#E ÄR(+Q/T !i13$'*0!36^(&8.I/6 E 83Nf¬5 T !3Z>!=:=l/(Q/!i?>*0Z>!36o?7I "%:V"%6^(+!3!:+!3,h"%*06 8Z4">$'*2Eo5>6 $'@*vL](+TQ/!i13$'*0!36^(& ?7!36/!=:+"%(!=EF(:V"4;1:+!3,h"%*06 8 T *'(Q/*06Í(Q/!q8.C!=1*'W !#E(:V"4;1A<57I/6 E/8=NLp(Q/!q13$'*0!36^(h(+:+"%h1bZS*05>$2"4(+!=8i(Q/!r./:!#8H.C!=13*vWI/6<E/83l/(Q/!=6(+Q/!6/!3( T 57:xh,h"[@gEJ:+5>.. "71Vx>!(V83lS57::!#8HQ ">.:(+">67(p157,9.C5>6 !36^(f5>L](Q/*28p"%./. :5^">1VQo*28(+Q/!i. :5>(!=1(*05>6q?7*'Z7!36o(+5;(+Q/!i:+!=">$v&c(*0,-!i135>6/6/!#1e(+*'576 83Np¿5>(!i(Q "%( (+Q/!g6/!3( T 57:xD8H!=:ZS*21! T *0$0$`,-!3!3(X(Q !g?>*0Z>!=6ª.6 1!;AC5>I 6 E/8X"78$05>6/?B">8(+Q/!13$'*0!36^(i(:V"4;1h:+!3,h"%*06 8 T *'(Q/*06K(+Q/!;(+:+"%La& W<1h8.C!=1*'W<1="4(*05>6«l«*0::+!=8.Ls(+Q/!hA:+,h"%6 13!-1="%6/6 5%(AC!h?>I ">:+">67(+!3!#Eklk*vLR(+Q/! 135>6/6/!#1e(+*'576 8"%:+!-6/5%(./:+5%(+!=1(!=EBLM:+5>,(+Q/!;,-*28HAC!3Q "[ZS*06/?ªÁM57:,-">$'*21*05>I<8+Äf:+!=">$v&c(*0,-!-">6 ED6/5>6D:+!="%$'&c(*0,9!;85>I :+13!=8=N-O5q"[Z>57*0E ZS*05>$2"4(*06/?(Q !h?>I ">:+">67(+!3!#8,h">E/!i(+5o:!#"%$'&)(+*',-!-1576/6/!=1(*05>6 8=l|(+Q/!h6/!3( T 57:xo,iI 8U(!=*v(+Q/!3:!3{J./$'*21*'($0@B135>6^(:+5>$(+Q/!h*'6 ./IJ(:V"4(!#8 576"D.C!3:&135>6/6/!#1e(+*'576GA "78H*28-*cN !7N8HQ ">./*06/?ª"%6 EG.<57$'*21*06/?P5%Lf(Q !qE/"4(V"/l_5>:h">EJ57.J(g8+1VQ/!=EJI $'*06/?ª"%$0?>57:*'(Q/,h8i(Q<"4( T *0$'$EJ5K85 core router
Î1,
Version 2 CSE, IIT Kharagpur
">IJ(57,-"%(*213">$'$0@h*'6(+Q/!6/5JEJ!=8XÁM!>N ? N0l/n ">*': T I !3I/*06/? lJ}D!3*0?>Q^(+!=Ebn ">*': T I/!=I/*06/? lJ!3(+1%N ÄeN ORQ/!#8H!(!=1VQ 6/*0~^I/!#8">:!"h.<"%:(5%L]*067(+!3?7:+"%(!=Eb85%La( "%:+!"%:V1VQ/*'(!=1(I/:+!=8R$0*0x>!w6^(VJ!3:+ZCl !*vd|S!3:+Z!(+1>N'l Q/*21VQoQ "[Z>!XA!=!3./*06/?f*'69,-*'6 EiZ4"%:+*'57I 8*08+8HI !=8.$v&c(*0,-!_135>,-,XI 6/*01="4(+*'576|N«}D!EJ*08+1I<88(Q !=8!_*28+8HT I/!#8«*06i(Q/!_LM5>$0$05 T *'6/?
A M 4 A ADM
E A E
O:+"%;11VQ ">:+"71e(+!3:+*'m#"4(*05>6h*28"i,95JEJ!=$k5%L(Q/!E/"%(+"i?>!36 !3:V"4(*05>61VQ "%:V">1(!=:*28U(+*01=8j5>L"98H57I/:+13!>Nz¿57:,h"%$0$0@;"X(+:+"%;1*28R1VQ "%:V">1(!3:& *0m3!#ErAS@qAC5>I/6<EJ*'6 ?*'(+8Z>5>$0I/,-!>N-uA<57I/6 ED5>6B(Q !9Z75>$0I/,-!-5%L`(+Q/!9(:V"4;1-13">6BAC!-I 8H!#EB(5bA<57I/6 Er(Q/!;">,-5>I/6^(p5%Ls6 !( T 5>:+x :+!=85>I/:V1!#8z(Q<"4(R,-"[@9Q "[Z7!(5iA$'*'(U@95%L8!3:+ZS*013!=8=N !I/:*06/?915>6 6/!=1(*05>6;!#8U(V"%A/$0*08Q/,-!36^(#l :+!=85>I/:V1!#8j"%:+!./:+54ZS*0E/!=E-A "78H!#E-5>6h(+Q/!(+:+"%h11VQ "%:V">1(!=:*0m="%(*05>6-"%6 Eh:+!=85>I :+13!:!#~7I *':+!3,-!36^(V83NzORQ/!3:+!">:!,h">6^@-8.6 ,-5JEJ!3$28./:+5>.C578!=Eg*'6(+Q/!$'*'(!=:+"%(I/:+!fLM5>:R(+:+"%h1p1VQ ">:+"71e(+!3:+*'m#"4(*05>6«N«}D!EJ*08+1I<88"iLM! T *0,9.C5>:(+">6^(5>6/!#83N # 0&i¼K»|ÆÅ^ÉH½ ORQ/!-Á kl 7Ä`,95JEJ!=$yA<57I/6 E/8"(:V"4;185>I :+13! T *'(Qb".C!="%xh:V"4(+!>N]u 15>6 6/!=1(*05>68+"4(+*08HW !#8Á kl 7Ä`,-5SE/!3$clJ*vdo(+Q/! *06^(!3:&w"%:+:*0Z4"%$k(+*',-!=8fAC!( T !3!=6q( T 5;. ">1Vx7!(V8*28">$ T "[@J8$0!=8+8(+Q "%6 klk"%6 Er8H*0m3!95%L](+Q/!i$2"%:+?>!#8U(. ">1Vx7!(*28A<57I/6 EqAS@ N _5%(+Qg(+Q/!.C!="%x"%6 E"[Z>!=:+">?>!:+"%(!=8R5>L«(+:+"%h1f*06(Q/*28,-5JEJ!3$|*28R?>*0Z>!=6AS@ N
n *0?>I/:+! Î1= jÌs576 8H(+"%6^( _*v(&"4(!O:V"4;1 ORQ/*289,-5SE/!3$./:+54ZS*0EJ!#8i"B(+*'?7Q7(-AC5>I/6 EGLM57:;Ì R (:V"4;1%Nn/:+5>,n*0? N Î-= *'(g13">6FAC!b8!3!=6F(+Q "4(-LM57:;Ì R (:V"4;1A<5>(Q (+Q/! T 57:+8H(f1=">8!9">6 Eo(+Q/!h"[Z>!3:V"%?7!. ">1Vx7!("%:+:*0Z4"%$«(*0,9!#8"%:+!X(+Q/!-8">,9!7NX¬5 T !3Z7!3:#lCLM5>:pA/I/:V8U(U@(+:+"%h1iI 8!-5%Lj(+Q/*08p,-5JEJ!=$(+5 8.:+"71e(+!3:+*08H(*21j:+!=8I/$'(+8z*069Z7!3:+@1576 8H!=:Z4"%(*0Z>!_:!#8H57I/:+13!s:+!=8!3:+Z4"4(+*'576|l4$'!#">EJ*06/?f(5p$05 T IJ(+*'$0*0m="4(+*'576-5%L (+Q/!:+!=8!3:+Z>!=E :+!=85>I/:V1!#83N #U¶ &i¼K»|ÆÅSÉU½ w6B(Q/*28,-5JEJ!3$z(+Q/!-(*0,-!;"4{J*28*28EJ*0ZS*0EJ!#ED*'6^(5b*06^(!3:+Z4"%$28f5%Ls$0!36 ?%(QPO !=">1VQ«l|13"%$0$0!=ED"gLM:V"%,-!7N9u 135>6/6/!#1e(+*'576B8+"4(*28HW !=8hÁY:=l OÄ ,-5JEJ!3$clC*vL]*'(?>!=6/!3:V"4(+!=86 5;,-5>:+!p(Q ">6o:=N O A/*v(V85>L](:V"4;1p*'6B"%6S@g*06^(!3:+Z4"%$OpN w6b(Q *08,-5SE/!3$cl<:*28(+Q/!XI ./.I/6<Eo5>6b(+Q/! "[Z7!3:V"%?>!9:V"4(!g54Z>!3:p(+Q/!"[Z7!3:V"%?7*'6/?*067(+!3:+Z4"%$sOpNORQ/*28,-5JEJ!3$_*08X*'6K85>,-!g8!36<8H!g8*0,9*0$2"%:(+5o(Q/!DÁ l Ä,-5JEJ!3$cNqORQ/*28 ,-5JEJ!3$y"%$285./:+54Z^*2EJ!#8j"p(*0?>Q^(_A<57I/6 E-LM57:RÌ RÍ(:V"4;1>N¬5 T !=Z>!3:#l%LM57:`A/I :+8H(U@X(+:+"%;1*v(_:!#8HI $v(V8j*06;Z>!=:@-1576 8H!=:Z4"%(*0Z>!:+!=85>I/:V1! :+!=8!3:+Z4"4(*05>6«l^$0!="7EJ*06/?9(5-$'5 T IJ(*0$0*'m#"4(*05>6b5>L(+Q/!:!#8H!=:Z7!=Eh:+!=85>I :+13!=8=N # 1&i¼K»«ÆÅSÉU½ w6P(+Q/*08i,-5JEJ!3$cl ª8H.C!=13*vW::+*0Z[">$z(*0,-!gAC!( T !3!36P( T 5q. "71Vx>!3(+8=N r8H.C!=13*vW !#8(+Q/!;,h"4{J*0,XI/, . "71Vx>!3(p8*'m=!9">6 Eq*08p"1!=:H(V"%*06r*067(+!3:+Z4"%$z54Z>!=: T Q/*21VQB(Q/!-5>A<8H!=:Z4"4(+*'576 8">:!9Z4"%$0*0E|N *28f(Q !-"[Z7!3:V"%?7!*'6^(!=:H&w"%:+:+*'Z4"%$(*0,-! AC!( T !3!=6r. "71Vx>!(p54Z>!=:f">6S@o*'6^(+!3:+Z[">$)N9S5"b135>6/6/!#1e(+*'576B8+"4(*28HW !=8(Q/*28p,-5JEJ!3$]*'Ls*'(8"%(*28UW !#8-Á D 7Ä,-5JEJ!3$]"%6<Eq(+Q/! "[Z7!3:V"%?>!`*'6^(!=:H&w"%:+:+*'Z4"%$>(*0,-!5%LC135>6 8!=13IJ(*0Z>!s. ">1Vx7!(V8*28z$2"%:+?>!3:(Q<"%6 sEJI/:+*06/?f">6S@*'6^(!=:Z4">$J5%L $0!36/?>(Q9eN%¬!=:!R*06X(+Q/*08z,-5JEJ!=$ (+Q/!h.:! + D"%6 E + #Nh¿5>(!=8f(+Q "4((+Q/*28,-5SE/!3$j./:+54ZS*0E/!=8 AC5>I/6<E/8]LM57:`AC5%(Qg.6 Eh"[Z>!=:+">?>!_:+"%(!5>LC(+Q/!(+:+"%;1%NzORQ/*08s,-5JEJ!3$<./:54ZS*2EJ!=8jA1e(+!3:+*'m#"4(+*'576i5>L RÍ(:V"4;1 135>,-. "%:+!=E;(5hAC5%(+QPÁ l ÄR">6 EPÁM:#l OÄs,-5JEJ!3$283N # D &9¼K»|ÆÅ^ÉH½ w6D(Q *08X,95JEJ!=$ *08(Q/!;,h"%{S*0,XI ,tA/I/:V8H(X8H*0m3!;">6 E q*08(Q/!;$05>6 ?(+!3:+, "[Z7!3:V"%?>!i:+"%(!h5>Ls(+Q/!g85>I/:V1!9(:V"4;1>l«:+!=8.!=$'@7N uZ>!3:V"%?7!(+:+"%h1i*2813"%$21I $0"%(!=EBAS@KÁM6SI/,iA1Vx>!3(+8f?>!=6/!3:V"4(+!=Eo54Z7!3:p$2"%:+?>!iE/I/:+"%(*05>6<Ä +JÁY$0">:?7!iEJI/:V"4(+*'576<ÄeN9u 1576/6/!=1(*05>6 8+"4(+*08HW !=89Á D SÄl|*'LsEJI/:+*'6 ?"%6S@b*067(+!3:+Z4"%$5%L`$0!36/?>(Qr((+Q/!i6SI/,iAL`A/*'(+8f?>!=6/!3:V"4(+!=EbAS@b(Q !9135>6/6/!#1e(+*'576q*'6r(Q "%(f*06^(!=:Z4"%$*28 $0!=8+8_(Q ">6 7(=N _I/:V8U(,h"[@g135>,-!54Z7!3:_(EJI/:V"4(+*'57657:_6 5%(AI 8H!p*'(*08RZ7!3:+@h*'6JLM:+!=~^I/!=6^(8H596/5-5%LA/*v(V8?>!=6/!3:V"4(+!=Eg*08R$0!=8+8
!
"
"
#
#
$ %
&$
'%
$ (%
)$
*%
Î1.
Version 2 CSE, IIT Kharagpur
(+Q "%6b5>:R!#~7I<"%$ 7(=NjORQ/*28,-5JEJ!3$|1="%6bAC!8"%(*28ULY"71e(57:*0$0@hAI :+13!=8=N ®°²ÉMµ#· zÉYÅg¶[¯/µ=Å `»C²±Æ·Y±¸«½_uÀ,-5>:+!"71313I/:+"%(!f"%././:+5[{J*',h"%(*05>6-LM5>:RA/I :+8H(U@9(:V"4;185>I :+13!=8_13"%6gAA/(+"%*06/!#E;AS@h1VQ "%:V">1(!3:& *0m3*06/?i(Q/!f(:V"4;1 T *v(+Qg,iI/$v(+*'. $'!pAC5>I/6 E/*'6/?h"[Z7!3:V"%?>!:V"4(+!=8=lS!=">1VQg54Z>!3:REJ*'dC!=:!=6^(R"[Z7!3:V"%?>*06/?*06^(!3:+Z4"%$283N]u (:V"4;1 T 57I/$2E;8"%(*28ULM@ ÁM: Î l O Î ÄÁY:VÃ/l OÃ7ÄeN0N'N 7lS*'L Î Ã V l ">6 E54Z>!3:">6S@g*067(+!3:+Z4"%$|s(Q/!X6^I ,XAC!3:5>LzA *v(V8?>!=6/!3:V"4(+!=E*08A<57I/6 EJ!#EbA^@:* 4OR*«*vL #Ii Î #VN_u8(+Q/!i"[Z7!3:V"%?>*06/?9*'6^(+!3:+Z[">$|?>!3(+8$'576/?>!=:=l "g8H57I/:+13!*08A<57I/6 EJ!#EbAS@"h:V"4(+!$'5 T !3:(Q ">6o*v(V8.C!="%x:V"4(!">6 E 13$'5^8H!=:s(+5h*v(V8$05>6/?i(!=:, "[Z>!3:V"%?7!:V"4(+!>N i¡¥z=£ \6 13!;"(:V"4;1h85>I/:V1!hQ "788.1(!=:*28U(+*01=8p"%6 ED*'(+8 T 5SB:!#~7I *':+!3,-!36^(V8f(5o(+Q/!;6/!3( 57:xyl«*'( "%*'(+8pLM57: (+Q/!X6/!3( T 57:x(5">1313!3.J((Q/!i:!#~^I/!=8H(AC!LM57:!*'(f1="%6r8H(+">:H(*v(V8(+:+">6 8H,-*288*05>6 8=NORQ/!X6 !( T 5>:+x576o*v(V8. ">:H(p1VT Q/!=1VxJ8*'Ls"7T EJ!=~^I "%(! :+!=85>I/:V1!h*28X"[Z4">*'$2"%A/$0!;"%$05>6 ?q"%6S@B.<"4(QPLM:+5>,Â85>I/:V1!h(+5rEJ!#8U(+*'6 "%(*05>6P(+5q,-!3!(i(Q/!EJ!3,h">6 EkNq57IJ(!8H!=$'!#1e(*05>6 ÁYI/6/*213">8H(i57: ,iI/$v(+*01=">8H(VÄsLM57:"98!=8+8*'576EJI :*06/?9(Q/!135>6/6 !=1e(+*'576!#8U(V"%A/$0*28HQ/,-!=67(./Q<">8!>N ?QH @B E ÌsI/:+:+!36^(jw6^(!3:+6/!3(`./:+5%(5J135>$28zI 8H!:+5>I/(*06/?"%$0?>57:*'(Q/,h8j8I 1VQh">8](Q/!8Q/57:H(+!=8H(j. "4(+Qh:57IJ(*06/?*06 Q/*01VQ-(+Q/!:+5>IJ(+*'6 ?13"%6-AC!5>./(*'& ,-*0m3!=E9LM57:j8H57,-!,9!3(:+*01 T *v(+Q/5>IJ(](V"%xS*06/?*'6^(+5">13135>I/6^( T Q/!3(Q/!=:](Q !:!#~^I/*':+!=Ei:+!=85>I/:V1!R*28j">1(T I ">$'$0@i"[Z4"%*0$2"%A/$0!>N]Ìs5>6 8!=~^I/!=67(+$'@7l (+Q/!B 5 T 8j,9*0?>Q^(`AC!:+5>I/(!=E954Z7!3:](+Q/!. "%(Q 8j(Q "%(s"%:+!I/6 ">A/$0!(598HI/. .<57:H(j(+Q/!3*0:`:+!=~^I/*0:+!3,-!36^(+8 T Q/*'$0!5>(Q/!=:`. "%(Q 8`,9*0?>Q^(`!3{J*08H( T135>Q/6/*26/1VQP!#1e1(+*'5>57I 6 $083ErNzQ !"[#Z>8H!-!#"%8:V"%1V(Q/*28U!3W<:V!=8zEoQ "[(+Z>Q/!!h6/8H5.C!=13./*vW<:!=57EB.<5^:8H!#!#~7E I *':+!3 ,-!3"$6^(V83N9
AORQQ/5>*0_:8 LT %5> I/&'$2EB"$#$'
!# a"> EoFb#\(+5b&1ONA/:"$!#">1VQq
A5>Q L_13Q/5>,-*21VQh,-54*v(Z>(!3!=:VE 157T ,-5^!Rr(Q/?>!#I<8H"%!:V"%./6^:(57!=A/!=$08!3,b(+5 N T ORQ/!. :*0,h"%:+@h?>57">$08_5>L T 5S;:+5>IJ(+*'6 ?9T ">:!7 E O«5h8!3$0!=1(R:+5>I/(!=8_(+Q "4(1="%6,-!3!(13!3:(+">*'6 T 5^g:!#~^I/*':+!3,-!=67(V83l E O«5-*06 1:+!="78H!(Q !IJ(*0$'*0m="%(*05>6b5%L(Q/!6 !( T 5>:+xCN } Q/*0$0!-E/!(!=:,-*06/*06/?":+5>IJ(+!>l T 5So:+5>IJ(+*'6/?b8+1VQ/!3,-!=8f6/5>(f576/$0@r1576 8H*2EJ!=:(+Q/!9(5>.C5>$05>?7@o5%Ls"6/!3( 57:xylyA/IJ(">$085g(+Q/!-:!3& ~^I/*0:!=,-!36^(5%L(Q/! 5 T lS(+Q/!:+!=85>I/:V1!p"[Z4"%*0$0">A/*'$0*'(U@h5%L«(+Q/!$0*'6/xJ8=l "%6<Eg5>(Q/!=:.<57$'*21*0!=8R(+Q "4(,h"[@hAC!8H.CT!=13*vW:+x "7EJ,-*'6/*28H(:V"4(57:+8=NORQ !3:+!LM5>:+!>l T 5^9:+5>IJ(+*'6 ? 57I/$2E-A!=:`"%6 E-$0*0?>Q^($0@^&c$057"7EJ!=E9. "%(Q;:V"4(+Q/!3:`(Q ">6-(Q/!f8HQ/57:H(& !#8U(. "%(QB(Q "%(,h"[@qAIJ(+*'6 ?b8+1VQ/!=,9!#8"%:+!9(Q/!=:!3LM5>:+!i!3{S.C!=1(!#Er(+5oAI/(*06/?h81VQ/!=,-!=8_*'6b,-!3!3(*06/? T 5^g?>I<"%:V"%6^(!=!=8=N $
%
@B E C EF P ORQ/!9157,9. $'!3{S*'(U@5%Lj" T 5^:+5>I/(*06/?g"%$0?>57:*'(Q ,EJ!=.6o(+Q/!i1VQ/5^8H!=6 T 5^b1576 8H(:V"%*067(V88I 1VQq">8Q/5>.r135>I/6^(#l6 E T *2ES(Q«l EJ!=$0"[@7l/EJ!3$2"[@^& U*'(H(+!3:!3(+1%NjORQ ! T 5Sg135>6 8H(:V"%*06^(+81="%6AE1$2">8+8!=8 8 Î-.;< N ¾«!(fE«ÁM*cl ÄpEJ!=6/5%(+!i"1VQ/578!36q135>6 8H(:V"%*06^(LM57:(+Q/!-$'*06/xªÁM*cl ÄNXn/57:f">6S@.<"4(Q ?ÁY*)l lkxyl0N'N0N$clC,;Äl«"g135>6 8H(:V"%*06^(fE 5>I $0E AC!p(!=:,-!=E #/O:O
`\3l *'L]E|Á _Ä °E|ÁM*cl Ä ºE|Á l x/Ä N0N0N ºE|ÁY$)l ,;ÄeNjn/57:!{/"%,-./$0!>lJ!=6 ES&c(5>&c!=6 EgEJ!=$0"[@g*08">6">E EJ*v(+*'Z7!15>6<8UT (+:+">*'6^( ">6 E*08R!#~7I<"%$y(5-(+Q/!8I/,5>L(+Q/!EJ!3$2"[@;5>L«(Q !*'6<EJ*'ZS*2EJI ">$k$'*06/xJ8*06(+Q/!. "%(Q|N 7*'(H(!=:=l/13578H("%6 EQ/57.b135>I/6^("%:+!"%$28H5-">E EJ*v(+*'Z7! 135>6 8H(:V"%*06^(+8=N u 1576 8H(:V"%*067(R*28_(!3:+,-!=ME ([C *#
`\3l *'L CÁ #Ä CÁ D SÄ CÁ :D /Ä CÁ -D$>bÄNjn/57:_!3{/"%,-./$0!>lJ:+!3$0*0">A/*'$0*'(U@;15>6<8U(+:+">*'6^( *28R,XI/$'(*0./$0*01="4(+*'Z7!>NjORQ/!:+!3$0*0">A/*0$'*'(U@;5%Lz"9. "4(+Q*28?7*'Z7!36gAS@g(Q/!./:+5JEJI 1(R5>L(+ Q/ !:+!3$0*0">A/*'$0*'(U@;5%L(Q/!*06 EJ*0ZS*0EJI<"%$|$0*'6 xS8=N S*0,-*'$2"%:+$0@>lj"D15>6<8U(+:+">*'6^(i*28i(!=:,-!=E L#%`\3l`*'LE|Á sÄ ,-*06 E|ÁY*)l Äel_E|Á l x/ÄelfN'N0N0l`E|ÁM$cl ,hÄ 7Nu6F!3{/"%,-./$0!5>L"B135>6 1="[Z>! 135>6 8H(:V"%*06^(z*28jA<"%6 E T *2ES(+Q|N _">6 E T *2ES(Q-576-"p.<"4(Qh*28]!#~7I<"%$J(+5p(Q/!,-*06/*0,XI/,A "%6<E T *0EJ(Qh5%Lk"p$0*'6/x95>69(+Q "4(`.<"4(Q«N}P"%6/?">6 E Ìs:+5 13:5>La(j./:+54Z>!=E9(+Q "4(_(Q !./:+5>A/$0!3,5>LkW 6 EJ*06/?9. "4(+Qg8HI A U!=1(`(5X( 5i5>:s,957:!f">E/E/*v(+*'Z7!"%6<E +[57:j,XI/$'(*0./$0*01="4(+*'Z7!1576 8H(:V"%*067(V8 *06i">6^T @p.C578+8H*0A/$0!s135>,XA *'6 "%(*05>6*28¿ ]&w157,-./$'!3(! 8 Ã Î < Nz¬5 T !3Z7!3:#l3(+Q/!_./T :5S5>L/5%L ¿ j&UÌs57,-./$'!3(!=6/!=8+8«*28A ">8!=EX5>6(+Q/!_"788I/,-.J(+*'576 8 Ã* >
Version 2 CSE, IIT Kharagpur
(+Q "4(# Î ÄR"%$0$y(Q !15>6<8H*2EJ!3:+!=E1576 8H(:V"%*067(V8R"%:+!f*06 EJ!=.6 EÃ7Äs(Q/!E/!3$2"[@g"%6 E U*'(H(!=:5%Lz!3Z7!3:+@h$'*06/x"%:+!fxS6/5 T 6b"9./:+*'57:*cN u$v(+Q/5>I/?7Qr(+Q/!-W :V8U("788I/,-.J(*05>6D*28p6/5>:+,h"%$0$'@b(+:I/!-LM57:1*0:+13I/*v(&8 *'(+1VQ/!#Er6/!3( 57:xJ8=lkA "%6<E *0EJ(Q|lEJ!3$2"[@>l«">6 E U*v((!3:i"%:+!i6/5>( *06 EJ!=.8!5%Lz. ">1Vx7!(8 T *v(V1VQ/!=Eb6 !( T 5>:+xS8=T N`u8"h:+!=8I/$'T (=l/.C5>$0@S6/5>,-*2"%T $">$'?75>:+*v(+Q/,h8R$'*0x>! _!=$'$0,h"%6J&wn/57:+E ">6 E(Q/!X!{S(!=6 EJ!=E !* UxS8H(:V"/© 8">$'?75>:+*v(+Q/, 8 ;Î :1< !{J*28U(LM57:157,-./IJ(*06/?;:+5>I/(!=8 *v(+QoQ/5>.q135>I/6^(=lCEJ!3$2"[@>l<"%6 E U*'(H(+!3:135>6 8H(:V"%*06^(+8=N w6^(!=:!#8U(+*'6 ?>$0@>l«A<"%6 E T *2ES(+QP">6 EDQ/5>.ª135>I/6^(X1576 8H(:V"%*067(V8"%:+!-,957:!-*0,-.<57:H(V"%T6^((Q ">6D(Q/!gE/!3$2"[@q5>: U*'(H(+!3:i135>6 8H(:V"%*06^(+8=l«8*'6 13! (+Q/!=8!;( T 5r"%:+!-(5D"o$2"%:+?>!;!3{^(+!36^(9E/!(!=:,-*06/!=EPAS@D(Q !gA ">6 E T *2ES(QF">6 EªQ/57.K157I/6^(91576 8H(:V"%*067(V8"%6<EK"%$28H5o,-5^8U(9:!#"%$'&)(+*',-! 8!3:+ZS*013!=8p:+!=~^I/*0:!hA ">6 E T *2ES(QK"78X">6D!#88!36^(+*0">$`1576 8U(+:+">*'6^( T Q/*0$0!h(Q/!gQ/5>.ª157I/6^(i1576 8H(:V"%*067(XE/!(!=:,-*06/!=8!dy!=1e(+*'Z7!;:+!=85>I/:V1! IJ(+*'$0*0m="4(+*'576|N w6b(+Q/!$2">8H(( 5;E/!=13"7EJ!=8=l<8!3Z7!3:V"%$|">$'?75>:+*v(+Q/,h8Q "[Z>!AC!3!=6o./:+5>.C578!=E(5g"7E/EJ:+!=8+8R(Q !XZ4"%:+*'57I 8R./:+5>A/$0!3,h8">8+8H5J1*2"4(+!=E *'(Q I/6 *01=">8H(s"%6 E-,iI/$'T (*213">8H(`:+5>IJ(+*'6 ? NjÌs5>,-./:+!3Q/!=6 8H*0Z>!R:+!3ZS*0! T 8j5>LkI/6/*213">8H(`"%6<E-,XI/$'(*213"78U(s">$'?75>:+*v(+Q/,h8zLM5>: T 5^i:+5>IJ(+*'6/?">:!"[T Z4">*'$'& ">A/$'!X*'Q6 8 ÃJl =;< BN 5qI/$v(+*',-!#EJ*0""%./. $'*213"%(*05>6 8=l T Q/*21VQo:!#~^I/*':+!,XI $v(+*01=">8H( T 5^:+5>IJ(+*'6 ? l<">:!AC!=135>,-*06/?hZ>!=:@*',-.C5>:(+"%6^(">6 Eo"%:+! TT *25SEJ;!3$0:+@;5>IJAC(+!3*'*06 6/? ?-l/I "%86*0La?7("%:(!#!"%"i$'&)(+LM*'! ,-!p*',-"%./.C./5>$0*2:13(+"4"%(+6^*'(576 ./8=:+N5%(+w5S613(5>Q $283!N LM57$'$05 T *06/? l T !fEJ*28+1I 8+88H57,-!*288I/!#8s:+!3$0!3Z4">67(_(5-,iI/$v(+*01=">8H( T
¡oV¥z3¤|¥i¡¥]3£ w6^(!=:6 !(*08W 6 EJ*06/?-?>:+5 T *'6 ?iI 8!p*'6b,h"%6S@;85%La(:+!=">$v&c(*0,-!f">././$0*01="4(*05>6<83Nzw6o">E/E/*v(+*'576g(+5hZ^*2EJ!=5%&5>6J&wEJ!3,h">6 EklJ"%6 Eg(!=$'!#1576JLM!3:& !=6 1*06/? ly,h"%6S@bEJ*28U(+:*0A/IJ(+!=Er">././$0*01="4(+*'576 8:+!=~^I/*0:+!,XI/$'(*213"78U(p157,9,iI/6/*213"%(*05>6|N 6 *'ZS*06/?g!#">1VQr85>I/:V1!i"%6q*06 EJ!=.6/6 !=1e(+*'576o(5!="71VQrEJ!=8H(*06 "%(*05>6q*28">6qI/6 "71313!3.J(V"%A/$0!i">././:+57">1VQbAC!=1="%I 8!X5>L](Q/!9.<5>(!=67(+*0">$ T ">8H(+">?>!5>Lj:!#8H57I/:V1!=8=N ORQ/!i15>,-,-5>6q">././:+57"71VQ*28(+5g1576 8U(+:I<1e(LM57:!="71VQo8H57I/:+13!"h,XI $v(+*01=">8H((:+!3!X135>6/6 !=1e(+*'576|N`"71VQZ7!3:(!3{576b";,XI/$'(*213"78U((+:!=! :+!3./:+!=8!36^(V8s!=*v(+Q/!3:"i:+5>I/(!3:R57:"iQ 578H(=N \6/!1="%6b8"[Z7!f"9?>:+!="%(RE/!="%$«5%L:+!=85>I :+13!=8_AS@;Q "[ZS*'6 ?i(+Q/!8H57I/:V1!=88Q ">:!f:!#8H57I/:V1!=8 Q/!=6/!3Z7!3:R.C578+8H*0A/$0!>Njn/57:!{/"%,-./$0!>lJ*06 ">6b">I EJ*05;1576JLM!3:+!36 13!>l/576/!;ÁM57:"4(A. $'!8.6^@g(*0,-!>N_w6b8I 1VQq"hT 8+1!=6 "%:+*'58H( ?7:57I/."78R5>6/! T Q/!=:!f(+:+"%h1LM:+5>,"-8!(5>L85>I/:V1!#8`(+:+"[Z7!3:V8H!p85>,-!15>,-,-5>6:+5>IJ(+!3:V8_">6 E(:V"%6 8,-*08+8*'576g$0*'6/xJ8=N ORQ/! T 5Si:57IJ(*06/?pLMI/6 1(*05>6h*06;"p,XI/$'(*213"78U(_"%././$0*213"4(+*'576-*'6SZ>57$'Z7!=8W 6 E/*'6/?i"f(:+!3!:+5S5%(!#Ei"%(s"85>I/:V1!">6 E-154Z>!=:*06/?p"%$0$/(+Q/! :+!=13!3*0Z>!3:V8=l T *'(Q!3Z7!3:+@h. "4(+QgLM:+5>, (+Q/!8H!=6 EJ!=:s(+59(Q/!p:+!=1!=*'Z7!3:V8s8+"4(+*08HLM@S*'6 ?X(+Q/! T 5^g:!#~7I *':+!3,-!36^(#NORQ/!f(+:!=!p135>6 8H(:+I 1(*05>6g*06 ,iI/$v(+*01=">8H(*06/?">:!XI 8HI<"%$0$'@b.C!3:LM5>:+,9!#Eo*06o( T 5gA ">8*01 T "[@J8=8H57I/:+13!&A ">8!=Eb">6 Eq157:!3&cA<">8!=EkN}D!X6 5 T EJ*08+1I<88f"-LM! T :57IJ(*06/? ./:+5%(+5J15>$28_A*06/?9(5-(+Q/!=8!f( T 5-A/:+57"7Eg1="4(!=?>57:*0!=8=N B H @B MN SA
@ E D MN C w6(Q !pLM5>$0$'5 T *06/? l T !EJ*2813I 88_( T 5-*',-.C5>:(+">67(85>I/:V1!3&cA<">8!=Eh:+5>IJ(+*'6 ?9. :5>(5J157$08=N U ® # U· =µ=¯/±´>Å ÅS´%µ#» ¶®°²ÉMµ=·)´>¯ =µ g»C²«µ#·Y±¸ p¶4»<µ=»|´7»<É & ! 5q 8 V < *0,9. $'!=,9!=6^(+8;85>I/:V1!3&cA<">8!=EP(+:!=!=8 *'(QÍ:!=Z>!=:+8!g. "%(QLM5>: "%:VEJ*'6 ? l]./:+I/6/*06/?ª"%6 EG?>:V"4La(+*'6 ? N(;:!=$'*0!=8-576F(+Q/! !3{J1VQ<"%6/?7!5>L>E/*08H(+">6 1!pZ>!#1e(+5>:RI/.yE/"4(+!=8+9">,-5>6/?-T 6/5JEJ!#83N]`"71VQZ7!=1(5>:R!=T 67(+:@15>6^(V"%*06 8s(Q/!EJ!#8U(+*'6<"4(*05>6b"%6<EE/*08H(+">6 1!p*06JLM5>:& ,h"4(+*'576b!{J./:+!=8+8H!#Eg*06(!3:+,h85%L]6SI/,iA.<83N`ORQ !=8!I/.CE "4(!#8"%:+!8H!=6^(5>6!="71VQ$0*06/xyNsORQ/!,iI/$v(+*01=">8H(EJ*28U(+:*0A/IJ(+*'576(+:!=! *28_(Q/!=6q1:+!="%(!=E|N ® Ê #U®°²ÉMµ#·Y´7¯ 3µ sÅ^± È»<¶[µ=Å =µ ¯Jµ=ÈÀÊ·M¶ 3µ & »<²µ=·)±¸ p¶4»<µ=»|´7»<É 5B\p `n 8 Î Ã < *08i"q,XI $v(+*01=">8H(X!{S(!=6 8*'576ª(5r(Q/!o\p `n I/6/*213"78U(9$'*06/x^&8H(+"%(!;:+5>I/(*06/?q./:+5%(+5S135>$cNqw6\p snÀ!#">1VQª:+5>IJ(+!3:i.$'$0@P8H!=6 E/8$0*06/xª8U(V"4(!#8(+5r"%$0$`5>(Q/!=:X:+5>IJ(+!3:V8*06ª(Q/!g6/!( T 5>:+xJ83Nqs">1VQP:57IJ(!=:A/I/*0$2E/8XI .F"q157,-./$'!3(!6/!( T 5>:+xr,h"%.«N } *'(Qg(Q/*28`*06JLM57:,h"4(+*'576h!="71VQ;:57IJ(!=:`*28`">A/$'!(5915>,-./I/(!(+Q/!8Q/57:H(+!=8H(`. "4(+Q;(+5!3Z7!3:+@9EJ!#8U(+*'6<"4(*05>6g*'6h(+Q/!f6/!( T 5>:+xXI 8*06/?(+Q/! !* UxJ8H(:V"/© 8p8HQ/57:H(+!=8H(. "%(QD"%$0?>5>:+*'(Q/, 8 Î :1< N 5B\p `nÍ!3{S(!36<E/8(Q/!#8H!9$'*06/xq8H(+"%(!=8(5b"%$285g*06 1$0I EJ!9*'6/LM5>:+,-"%(*05>6r">A<57IJ(p?>:+5>I/. ,-!3,iA1VQD:+5>IJ(+!3:">EJZ7!3:(*28H!#8(Q/!;. :!#8H!=6 1!-5%L_,XI/$'(*213"78U(?7:57I/.D:!#1!3*0Z>!=:+8f"4((+"71VQ/!=EB(5b*'(=NgORQ !3:+!LM5>:+! 5B\p sn 1="%6r135>6 8H(:+I 1e(p"g8Q/5>:(!#8U(&c.<"4(Qr,XI/$'(*213"78U((:+!3!>ly*cN !7Nf(Q/!9. "4(+QoLM:+5>,(Q !985>I/:V1!(5g!#">1VQq:+!=13!3*0Z>!=:*06q(Q !i,iI/$v(+*01=">8H((+:!=!X*28
ÃÎ
Version 2 CSE, IIT Kharagpur
(+Q/!I/6/*213"78U(f8HQ/57:H(+!=8H(H&. "4(+Q|Njw6 8H(!#">Eb5>L:+!3$0@S*'6/?h576 5S5JEJ*'6 ? +[. :I/6 *'6/?-*06JLM5>:+,h"4(+*'576$0*0x>! ! 5q zl *06I5B\p snK!#">1VQb:57IJ(!=: x7!3!3.<8`*06JLM5>:+,h"4(+*'576;"%AC5>IJ(R"%$0$7:57I/.;,-!3,iAIJ(+!3:V8j*06h(Q !6/!3( T 57:xyNuÀ$0*',-*'(+"%(*05>6g5>L 5B\p snB*28`(Q "%(s*'(REJ5S!#8`6/5>( 8+13">$'! T !3$0$y(5h$2"%:+?>!f6/!( T 5>:+xJ83N B ) A
$ K PO QR 9@SCFE MNAD 0 @ E w6h(+Q/!135>:+!&A ">8!=EX(:+!3!1*'(!3A<"%$0$)l A "%$0$ Î "%./. :5^">1VQ|l4W<:+8H(s"135>:+!LM5>:_",XI/$'(*213"78U(`(:+!3!*28s8!3$0!=1(!#EkNORQ !EJ*'dC!=:!=6^(s:+!=1!=*'Z7!3:V8]8H!=6 E (+Q/!3*0:8I/A 8+1:+*'AC!X:+!=~^I/!#8U((+5;(+Q/*08f157:!7N`">1VQb*06^(!3:+,-!=EJ*2"4(+!X:+5>IJ(+!3::+!3,-!=,XAC!3:V8(Q !*'6^(+!3:LY">1!LM:57, T Q/*21VQo(+Q/*08:+!=~^I/!=8H(Q "78 AC!3!=6:+!=13!3*0Z>!=E;*'65>:VEJ!3:_(+5i*06 1$0I EJ!p*'(*'6^(5i(Q !pE/*08H(:+*'A IJ(*05>6(:+!3!7N} Q !36b"i85>I/:V1!p8!36 E/8RE/"%(+"X(59(Q !,iI/$v(+*01=">8H(?>:+5>I/.|l^(+Q/! . "71Vx>!3(:!#">1VQ/!#8f"oW :+8H(5>6/&)(+:!=!9:+5>I/(!3: Q/*01VQD(+Q/!36ª:+!3./$0*213"4(+!=8p(+Q/*28. "71Vx>!(576K"%$0$](Q/!g5>6J&c(:+!3!-*067(+!3:LY">13!=8!3{J13!3.J(X(Q/!h576/! LM:+5>, T Q *01VQ(Q !. ">1Vx7!(13"%,-!pLM:+5>,bN T ® U® ® ¶4»C²«µ#·Y±¸ p¶[»<µ=»«´>»CÉ `:5>(5J157$kw6 EJ!3.C!36<EJ!36^S( 5oI $v(+*01=">8H(XÁ j 5BÄ 8 $ < ">8(Q/!6<"%,-!*v(V8H!=$vLj8I/?>?7!=8H(+8R*28*06 EJ!3.C!36<EJ!36^(5>Lz">6S@gI/6 E/!3:+$'@S*06/?h./:+5%(5J135>$cNj( 135>6 8*08H(+85%L]( 5g,iI/$'(*213">8H(:+5>I/(*06/?g./:+5%(+5J15>$28= !!36<8H! 5o5JEJ!bÁ ! 5rÄ ` 5">6 ErS. ">:+8! 5q5SE/!Á) 5rÄ ` 5ªNy}B!96/5 T EJ*28+1I 8+8 (+Q/!=8!p( T 59./:+T 5%(+5S135>$283N UÅS± #ÅP®°»|ÆÅ # U® & ® ½(p*08f*06^(!36<EJ!=EqLM5>:p*'6^(+!3:&EJ57,h"%*06q:57IJ(*06/?"%6 EB">8+8HI/,-!#8(+Q "4(?>:+5>I .q,-!3,XAC!3:V8f"%:+!iEJ!=6 8H!=$'@ EJ*28H(:+*'A/I/(!=EG*06F(+Q/!o6/!( 5>:+xyNF¬!=6 1!7l`*'(;*089:+!="78H576 "%A/$0!;(+5ª">8+8HI/,-!(Q "%(h!=">1VQ"%6 EG!3Z7!3:+@ª:57IJ(!=:98Q/57I/$0EGAC!*06SZ>57$'Z7!=EK*06 ,iI/$v(+*01=">8H(=NjORQSI 8=l/"%6o"%. T ./:5^">1VQ;$0*0x>!!3Z7!3:V8H! ]"%(Qn$05S5SE/*'6/?-(+Q "4 ( <5^5JE/8E "4(+">?>:V"%,h8s(5-!3Z7!3:+@h,XI/$'(*213"78U(:+5>I/(!3:#N ¯/¶ #Åo®°»|ÆÅ # ® & 3® ½<( ">8sW :V8U(R*067(+!36 E/!=EgLM5>: *0E/!&w"%:+!=",iI/$'(*213">8H(:57IJ(*06/?8H(?>:+5>I/.;,-!=,XAC!3:V8 ">:!;8. "%:V8!3$0@rEJ*28U(+:*0A/IJ(+!=Eª*06P(Q/!6/T !( T 5>:+xyNu6F">8+8HI ,9./(T *05>6D(Q "%(X*28,h">EJ!g*08(Q "%(i"o:+5>IJ(+!3:X8Q/5>I $0ED6/5>(XQ "[Z>!-(+5rEJ5r">6S@ T>,95>:+!#xb88+I/"%6/?7!=$0!=8=8+l78pA *vIJ( (T "%"%:+!f6^(+5%8(Q (5 !3: U57*'*06P8!p"g6/5%,i(I/*0$'6S(Z>*2135>">$0Z>8H(!#E;?>:+*05>6bI/,X.«NXI/$'OR(*2Q/13"7*28p8U(R*08pLM5>"b: 1"%!=67:VEJ(+!3*'6 :&c? A 8!=Eq">././:+57">1VQ«l T Q !3:+!i:+5>IJ(+!3:V8p8H!=6 Eq!3{S. $'*21*'( U5>*06 T T "%(Q/!=:j(+Q "%6;715>:+!= l ` 5b&w 5I 8H!#8](+Q/!6/5>(*05>6h5>L«":!=6 EJ!=m3Z>57I 8].C5>*06^(fÁY sÄeNS`"71VQ-?>:+5>I/.h*28`"7885J1*2"4(!#E95>6/!9ÁM5>:s,-5>:+!#Ä zN|¿! T ?>:+5>I/.D:+!=1!=*'Z7!3:V88!36<ED U5>*06 ,9!#88+"%?7!=8(5b(+Q/!h zN«¾«*'x7!;Ì ROplk!#">1VQD*'6^(!=:,-!#EJ*0"%(!-:+5>IJ(+!3:p(+">x>!#8f"7EJZ4"%6^(+">?>!95%L (+Q/!=8!i U5>*06 ;,-!=8+8+"%?>!#8(+5gI/.yE/"4(+!X(+Q/!-EJ*08H(:+*0A/IJ(*05>6r(:+!3!7N !f"4(V";*288I/!=EqA^@o"8H57I/:V1!*28W<:+8H(!=6 13">. 8HI $0"%(!=Eq*'6BI/6/*213">8H(f">6 E (+Q/!36o8!36^((5-(+Q/! A:+!A6 ">$2ÄN`n/57:R(Q/5^8H!pZ7!3:+@g">1(*0Z>! 85>I/:V1!#83l/">6 EbAC!=13">I 8!?>5>*06/?-(+Q/:57I/?>Qo"h ÍAC!LM57:! U5>*06/*'6 ?;"-:!#1!3*0Z>!=:*08,-5SE/!3:V"4(!=$'@!;1*0!36^(#l jU¿ +% 5 !=6 "%A/$0!=8(Q/!X13:!3& "%(*05>65%L]"9 `nP(+:!=!:5S5%(+!=E"4((Q *0885>I :+13!>Nz(*08R(+QSI 8$0!=8+8EJ!3.C!36 E/!36^(5>6(Q/!13!36^(!=:$'5J1="4(*05>6(Q<"%6rÌ ROpN
">$'?75>:+*v(+Q/,:!#~7I *':+!=8!3Z7!3:+@6/5JEJ!9(+5g,h"%*06^(+"%*06B"EJ*28U(V"%6 13!iZ7!=1(5>: T Q/*21VQB8H(5>:+!=8(Q !9,-*06/*0,XI/,tE/!3$2"[@(+5!=Z>!=:@5%(+Q/!3:p6/5JEJ!7N ^(V"%:(*06/? *'(Q(Q/!i8H57I/:+13!p6/5JEJ!>lJ(+Q/!X">$'?75>:+*v(+Q/,1576 8H(:+I 1e(V8_(Q/!,iI/$'(*213">8H((:+!3!*'(!=:+"%(*0Z>!=$'@;AS@">E/EJ*06/?;"-$0*'6 xg*067(+5-(Q/!p(+:!=! !#">1VQh(+*',-!>T Njs">1VQ;*'(!=:+"%(*05>65%L|(+Q/!"%$0?>5>:+*'(Q/, 1576 8*08H(+8s5%L(Q/:+!3!f./Q "78H!#8`5>L«,-!=8+8">?>!.<">8+8H*06/? Nzw6g(Q/!fW :V8U(R./Q "78H!7l^(Q/!p8H57I/:V1! 6/5JEJ!pA/:+57"7E/13"78U(V8s" O7'&&1#1QAREJ5 T 6;(+Q/!p. "%:(*2"%$0$0@;15>6<8U(+:I 1(!#Eh(:+!3!7N]} Q/!36b"i6/5JEJ!p:!#1!3*0Z>!#8j(+Q/!p,-!=8+8">?>!>lS*'(RW 6 E/8R57IJ( (+Q/!">E H"71!=67($0*'6 x T Q/*21VQ| E $'!#">E/8_(+5h"9E/!=8H(*06 "4(+*'57657IJ(5%L(Q/!p(+:!=!>l E EJ5S!=8R6/5>(Z^*05>$2"4(+!f(Q/!EJ!=$0"[@15>6<8U(+:+">*'6^(=lJ">6 E E ,-*'6/*0,-*'m=!"-8H!=$'!#1e(*05>6LMI/6 1(*05>6|N w69(Q !R8!=135>6 Ei./Q "78H!7l4(Q !8H!=$'!#1e(!#E9$'*06/xJ8]"%:+!_8!36^(](+5(+Q/!85>I/:V1!_6/5JEJ!>l Q/!3:+!_(Q/!RAC!=8H(j$'*06/xi$ Q/*21VQi,-*06/*',-*0m3!#8z(Q/!8!3$0!=1(*05>6 LMI/6<1e(*05>6*2891VQ 578!36|NPw6G(Q/!(Q/*0:VEF./Q<">8!>lj"%6u ! !,-!=8+8">?>!;*28-8H!=6^(iT (+5D"7E/EK$R(+5r(+Q/!g(+:!=T !>NFORQ *089./:+5J1!=E/I/:!15767(+*'6SI/!#8 I/6^(+*'$z!3Z7!3:+@E/!=8H(*06 "4(+*'576q*08*06 1$0I EJ!#Eq*06q(Q !X(+:!=!>NpORQ/*08f"%$0?>57:*'(Q ,:+!=~^I/*0:!#8*06^(!36<8H*0Z>!i,XI/$'(*0./$0!i,-!=8+8+"%?>!X!{/1VQ "%6 ?>!=8=NO T 5 *0,-.<57:H(V"%6^(]./:57A/$0!3, T *'(Q B*08(Q<"4(](Q !R135>,-,XI 6/*01="4(+*'576X54Z>!=:Q !=">E*08Z>!=:@Q *'?7Q9">6 E(+Q "4(j!=Z>!3:+@p6/5JEJ!R6/!3!#E/8(5f,h"%*06^(+"%*06 "9?>$05>A<"%$|8H(+"4(+!>N Ã>Ã B
?QH SA
9@4C E MNAD 0 @ E p57,9.C!3$0$2"o!(h"%$cN 8 Î $ < ./:+5>.C578!=EK"rEJ*08H(:+*0A/IJ(!#EKQ/!=I/:+*08H(*21g">$'?75>:+*v(+Q/,tLM57:9135>6 8H(:+I 1(*06/?r"r135>6 8H(:V"%*06/!#EK^(!=*'6/!=:X(+:!=!>NDORQ/!
Version 2 CSE, IIT Kharagpur
4j
B
?QH J S
E
¬5>I 1.#_1576 1!=67(+:+"%(!#E 5>6 !36/Q ">6 1!=,-!36^(+8g(5 U5>*06 +[$0!="[Z7!q,-!=8+8">?>!q. :5J1!#88*06/?F576:57IJ(!=:+8=l">*',-*06/?"%((+Q/!D?>I ">:+">67(+!3! 5>LfEJ*'dC!=:!=6^( T 5Sª:+!=~^I/*0:!=,-!36^(+8=lj5>6 !"%(h"B(+*',-! 8 Ã/* < Ns">1VQF:+5>I/(!3:9x>!=!3. 89*06JLM5>:+,h"4(+*'576G:+!3?^"%:VEJ*'6 ?o(Q/! T 5Sª$0!3Z7!3$R5%Lf*v(V8 EJ5 T 6<8U(+:!#"%, ,9!=,XAC!3:V83NP} Q/!=6F*'(9:+!=13!3*0Z>!#8X" U57*'6G,-!=8+8">?>!>lz*'(-1VQ !=1VxJ8X*'L(+Q/! T 5SP$0!3Z>!=$s:+!=~^I/*0:+!=EDLM5>:9(+Q/!6 ! T ,-!3,iA!3$_5%LR(+Q/!g5>(Q/!=:X,-!3,iA*'6/!#E ÁaLM57: U57*'6B,9!#88+"%?7!=85>6/$0@/ÄeNORQ/! U57*'6B,9!#88+"%?7!XQ T"78(+5g(+:+"[Z7!3$(5(Q/!h135>:+!X5%L`(Q/!9(:+!3!iA:+!X(+Q/! U5>*06B1="%6B8I 1=1!3!#Ekl|8*'6 13!i!#">1VQ :+5>IJ(+!3:px>!=!3. 8 T 5So*06JLM5>:+,h"4(*05>6D"%AC5>IJ(EJ5 T 6<8U(+:!#"%,,-!3,XAC!3:V8p5>6 $'@7NiORQ/!hEJ!=$0"[@q">6 Er$0578+8f:!#~^I/*':+!3,-!=67(p5%Ls,9!=,XAC!3:V8p,h"[@ AC!iEJ*'dy!3:+!36^(=lCA/IJ(f(Q/!iA "%6<E T *0EJ(Qq:+!=~^I/*0:!=,-!36^(*28">8+8I/,-!=E(5A,-!>NORQ/! T 5^:+!=~^I/*0:!=,9!=6^(+8">:!6 5%(f135>6 8*2EJ!3:+!=E *06P(Q/!h:+5>I/(*06/? l«(Q/!=@D">:! UI 8H(X?>I<"%:V"%6^(!=!=EDEJI/:+*'6/?b(+Q/!h(+:!=!;15>6<8U(+:I 1(*05>6P"%6 EB(+Q/!36ª*'(X*28,h"%*067(V"%*06/!=EDAS@r:+!=8H(:+*21e(*06/?b(+Q/! 8I 1313!=8+8R5%L U5>*06,-!#88+"%?7!=8=N i i¡ ]¤¢ pf¥]9£ u 6/!( 5>:+x-13"%6g./:54ZS*2EJ! T 5S9?>I ">:+">6^(!3!#8](+5i1576/6/!#1e(*05>6<83lS5>6 $'@-*'L«*v(RQ "78`:+!=8!3:+Z>!#E9">././:+5>./:+*2"4(!:!#8H57I/:+13!=8s"%$05>6/?(+Q/!f*0EJ!=6^(*'& W !#EX:+5>T I/(!=8=N 5q!3:+!3$0@W 6 EJ*06/?":57IJ(!_(Q<"4(]Q ">8z8IJ;1*0!36^(]:!#8H57I/:V1!=8=l[,h"[@6/5%(j"%I/(5>,h"%(*213"%$0$0@8H57$'Z7!`(+Q/!R./:57A/$0!3,°5>L ./:+54Z^*2EJ*06/? T 5SX?7I "%:V"%6^(+!3!=8=N|Lk6/5:+!=8!3:+Z4"4(+*'57698+1VQ/!3,-!*28]I/6 E/!3:(+"%x7!36|l>(Q/!=6-(Q/!(:V"4;1RA6 E-1576/?>!#8U(](+Q/! 8@J8U(+!3,(Q "%(_*06h(+I/:6 T *'$0$CQ^I :H(s(Q/! T 5^-?7I "%:V"%6^(+!3!=8jA ">EJ$0@>NjS5I/:V1!#8]Q/!=$'. 8_*06g8+"4LM!3?7I "%:VEJ*06/?(+Q/! T 5SX?7I "%:V"%6^(+!3!=8=N|w6-(+Q/*08s8H!#1e(+*'576 T !EJ*2813I 8+8j"p.<57./I/$2"%:`">6 E T *0E/!3$0@iI 8!=E9./:+5%(+5J15>$ 6 "%,-!=E-!#8H57I/:V1!R:![S!3: j"4(+*'576 j:+5%(5J135>$ Á) _Ä 8 Î-= l<Ã7à < N }D!o13"%68H57,-!(*0,-!=8-:+!=EJI<1!(Q/!bA ">6 E *2ES(Q "%6<EKA/IJdy!3:;8. "71!:!#8H!=:Z7!=EªLM57:h"r,iI/$v(+*01=">8H(h?>:+5>I/."4(9(Q/!o:+5>IJ(+!3:V8i">6 E $0*'6 xS8(:V"[Z>!=:+8!=EAS@b,957:!p(+Q "%6r5>6/!i,XI/$'(*213T "78U((+:!=!XI 8*06/?g"h:+!=85>I/:V1!:+!#J!3: j"4(*05>6o. :5>(5J157$k(Q "%(f135>6 8*0E/!3:V8(Q !i"%?7?>:+!3?^"4(! :+!=~^I/*0:!=,-!36^(5%L«(+Q/!,XI $v(+*01=">8H(?>:+5>I/.">8" T Q/5>$0!>N]w6oEJ!=!=EklS(+Q/*28*08(Q/! ./:+5%(5J135>$cN
@4 MN
K L A E D MN C O H R Í*288H57$'!=$'@g"9:+!=85>I/:V1!:!#8H!=:Z4"%(*05>6g. :5>(5J157$)Nz(">8+8I/,-!=8s(Q "%((Q/!,iI/$'(*213">8H(R(:+!3!Q "78RAI/(!3:V8_5%L (+Q/!6/!( T 5>:+xyNuEJ,-*08+8*'5765>L"-6/! T ,iI/$v(+*01=">8H(1576/6/!=1(*05>6*08RQ<"%6 EJ$0!=EAS@h(+Q/!">EJ,-*288*05>6b15>6^(+:57$C,-5JEJI/$0!*06b"9$05 T !=:R$0"[@7!3:#N ">8EJ!#8H*0?>6/!#E*'6 -Î ././V "4B( 3!3:+5[{ ]"%$05hu$'(5;!#8H!#"%:V1VQoÌs!=6^(!3:#NsORQ !*0EJ!#" "78_(5;EJ!#8H*0?>6o"-:+!=85>I/:V1!p:+!=8!3:+Z4"4(*05>6 ./:+5%(+5J15>$C(+Q T "4(1="%6b81="%$0!(+5h,XI/$'(*213"78U(135>,-,XI/6 *01="4(*05>6b"%6<E1="%6*'6<15>:+.C5>:V"4(!fQ/!3(!3:+5>?7T !36/!=5>I 8s:+!=1!=*'Z7!3:V83N !#8U(V"%A/$0*08Q/!#8"%6 Eb,h">*'6^(+">*'6<8" &'
Z0."$_LM5>:!=">1VQoEJ!#8U(+*'6<"4(*05>6q">6 EbI 8!=8*'((+5;8H!=6 Eo1576^(:+5>$|,-!=8+8+"%?>!#8_LM:57,!#">1VQ EJ!#8U(+*'6<"4(*05>6«Nu 8*'6 x(:+!3!R*28j"p8H. ">6/6/*06/?f(:+!3!_(Q<"4(]*08j:5S5%(+!=Ei"4(](Q !EJ!=8H(*06 "4(+*'5769">6 E915>6 6/!=1(+8]"%$0$J(+Q/!8H57I/:+13!=8*06-"f,iI/$v(+*01=">8H( ?7:57I/.|N(*08f57AJ(+">*'6/!#EqAS@o(+:+"71*06/?g*06r(+Q/!9:!=Z>!3:V8!iEJ*0:!#1e(+*'576qLM:+5>,(Q !-E/!=8H(*06 "4(+*'576q(5!3Z7!3:+@o8H57I/:+13!9">$'576/?;(+Q/!-. "4(+Q 8f*'6D" ,iI/$v(+*01=">8H((:+!3!7N p¶4»<µ=»|´7»<É `Å^¶4¯Jµ#·Y»C±`½o`"71VQª:57IJ(!=:iI<8H!#EKAS@ª"r,iI/$v(+*01=">8H(i?7:57I/.K,h"%*06^(+"%*06 8X( T 5r(U@S.L*06JLM5>:+,h"4(*05>6« ¯Jµ#È 3µ#¯Jµ=Å "$!&1!"'`# * NiORQ/!-. "%(QP8U(V"4(!95%L_!="71VQB85>I/:V1!9*08p135>6 13!3:+6/!=EB"%AC5>IJ(p(Q !9.<"4(QDI 8!=ErA^@q(Q/!h85>I/:V1!7NX ÀI 8!=8f(+Q/*28 *06JLM5>:+,h"4(+*'576g(+59,h">*'6^(+">*'6(+Q/!8H*06/xh(+:!=!=8R5>L(+Q/!EJ!=8H(*06 "%(*05>6|N *08X":+!=13!3*0Z>!=:H&5>:+*'!=6^(!=Eq./:5>(5J157$)NhORQ "%(*08=l|(+Q/!h:!#1!=*'Z7!3:p5%L"bE/"4(V%" <5 *06/*v(+*0"%(!#8"%6 ED,h"%*06^(+">*'6 8f(+Q/!h:+!=85>I/:V1! :+!=8!3:+Z4"4(*05>6rI 8H!#EqLM57:p(Q "%( 5 T N9¿5%(+!i(+Q "4(!#">1VQD:57IJ(!=:f:+!=13!3*0Z>!#8":+!=8!3:+Z["%(*05>6qT ,-!#88+"%?7!XLM:+5>, !#">1VQB5%L`(+Q/!hEJ5 T 6 8H(:+!=">, $0*'6 xS8f*06q(+Q/!i,iI/$'(*213">8H(f(:+!3!-"%6 Eq8!36<E/8f5>6/$0@b5>6/!9:!#8H!=:Z4"%(*05>6o,-!=8+8">?>!*06^(5*v(V8fI/. 8H(:+!="%,$0*'6 xCNORQ !i:+!=8!3:+Z4"4(*05>6q8H(+"%(!95%L !#">1VQE/!=8H(*06 "4(+*'576*281576 1!=:6/!#E *'(Qb:+!=85>I/:V1!#8s8!(">8*2EJ!LM57:R(Q/!EJ!#8U(+*'6<"4(*05>6(5h8I/./.C5>:(R(Q/!:+!=~^I/*0:!#E T 5SyNJORQ/!p6 "%,-!p5%L (+Q/!EJ!=8H(*06 "%(*05>6PÁM:+!=8!3:+Z>!3:eÄs"%6 ET (Q !"%,-5>I/6^(:+!=8!3:+Z>!=Eg"%:+!p">,-5>6/?9(Q !*'6JLM57:,h"%(*05>6g. :54ZS*2EJ!=EAS@h(Q/!:+!=8!3:+Z4"4(+*'576;(+">A/$0!>N u. "%(QP,-!=8+8">?>!9*08"o135>6^(:+5>$z,-!=8+8+"%?>!h8!36^(AS@B"b8H57I/:V1!h"%6 ErLM5>: "%:VEJ!=ErA^@r(Q/!h:+5>I/(!3:V8f*'6ª"b,iI/$v(+*01=">8H(p(:+!3!>N;s">1VQ 85>I/:V1!i8H!=6 E/8*v(V8W :V8H(. "%(Qr,-!#88+"%?7!A:+!X*'(p135>,-,-!36 13!=8(:V"%6 8,-*08+8H*0T 5>6q">6 Eq8!36 E 88I/A 8!=~^I/!=67(f. "4(+Qq,-!=8+8">?>!#8.:+,h"4(*05>6;1="%:+:*0!=Ei*06;!="71VQ9.<"4(Qh,-!#88+"%?7!5%L|"85>I/:V1!R*28](Q B! 5 T 8H.C!=13*vWC13"4(+*'576h5%Lk*'(+8j,-!#88+"%?7!8U(+:!#"%,bN ÃV
Version 2 CSE, IIT Kharagpur
u :+5>IJ(+!3:RI/.yE/"4(+!=8R(+Q/!. "%(Qo8U(V"4(+!fI .<576:+!=13!3*0ZS*'6/?9(+Q/!. "4(+Q,-!#88+"%?7!LM:+5>,"985>I :+13!>N s">1VQbEJ!=8H(*06 "4(+*'576o8H!=6 E/8:+!=8!3:+Z4"4(+*'576:+!=~^I/!#8U(,-!=8+8">?>!;ÁY:!#8HZ,9!#88+"%?7!fLM5>:8Q/5>:(VÄ Q *01VQo"%:+!pLM5>: "%:VEJ!=E"%$05>6/?9(+Q/!X8*'6/x (+:!=!5%Lk(+Q/!E/!=8H(*06 "4(+*'576|N]u,-5>6/?(Q/!f*'6/LM5>:+,-"%(*05>6;135>6^(+">*'6/!#E-*'6!="71VQh:!#8H!=:Z4"4(+*'576-,9!#8T 8+"%?7!*28j(+Q/!B 5 T T 8.6;?7*'ZS*06/? (+Q/! T 5^g:!#~^I/*':+!3,-!=67(5>L«(Q !8H!=6 EJ!3:#N (p*08p13$'!#"%:(+Q "4(f(Q !-">,-5>I/6^(5>L`A ">6 E *2ES(Qr(Q "%("g:57IJ(!=::+!=8!3:+Z>!#88Q/5>I/$2Eq6 5%(p!{/1!=!=Eb(+Q/!-$'*06/xy© 8p1="%. "71*'(U@>NpO«5 "%:VE/8 (+Q/*08=l T Q/!=6/!3Z7!3:_(Q !:57IJ(!=::!#1!3*0Z>!#8R"i6 ! T T :+!=8!3:+Z4"4(+*'576g,-!=8+8">?>!7l^*'(EJ!3(!3:+,-*'6 !=8*'L*'(+8E/5 T 6 8U(+:!#"%, $0*06/xJ8R5>6(Q/!,iI/$vT (+*01=">8H( (+:!=!i13">6q./:+54ZS*0EJ!(Q/!9:!#~^I/*':+!=Eb:+!=8!3:+Z4"4(+*'576|NLj(+Q/!-">EJ,-*288*'576b(!#8U(fLY"%*0$08=lC(Q/!9:+5>IJ(+!3::+! U!#1e(V8(+Q/!i:+!=8!3:+Z4"4(+*'576q"%6 Eo:+!(+I/:+6 8 ">6r!3:+:+5>:,-!#88+"%?7!(5(Q/!h">././:+5>./:+*0"%(!:+!=13!3*0Z>!=:#Á)8+ÄNf EJ5S!=8f6/5%(EJ!3W 6/!-"%[email protected]!=13*vWC1i"7EJ,-*08+8H*05>6q(!=8H(=lkA IJ(*v(">8+8HI ,9!#8 (+Q "4((+Q/!:57IJ(!=:R.1e( T *'(Q(Q !p(!=8H(=N ORQ/!pEJ!#8U(+*'6 "%(*05>68H!=6 E/8_*v(V8_W :V8U(R:!#8H!=:Z4"%(*05>6;,-!=8+8+"%?>! Q/!36*'(R:+!=13!3*0Z>!#8s"i. "4(+Qg,-!=8+8+"%?>!LM:57, "i85>I :+13! Q/5^8H!,-!=8+8">?>! 8H(:+!=">, *v( T *28HQ !=89(5P:+!=13!3*0Z>!>NÍuLa(+!3: T ">:+E 8i*'(;8H!=6 E/8-:+!=8!3T :+Z4"4(*05>6G,-!=8+8">?>!=8i.C!3:+*'5JEJ*213">$'$0@ª(5P,h"%*06^(+">*'6:!#8HT !=:Z4"%(*05>6|NORQ/! ,h"%*06^(!=6 "%6 13!5>L:+!=8!3:+Z["%(*05>6P(+Q/:57I/?>QG.!#8*28 T Q "4(h8H!3(+8- "%. ">:H(iLM:57, ,95^8U(-5%L(Q/!5%(+Q/!3:-:+!=85>I/:V1! :+!=8!3:+Z4"4(*05>6./:+5%(+5S135>$283NsORQ/*08*08R(+Q/!X85;13">$'$0!=ME &1-,H&'3#%3"%6 E*28R(Q/!X./:!3LM!3:+:!#EE/!=8*'?76b1VQ 5>*21!pLM5>:"%././$0*213"4(+*'576 8_(Q<"4(">:!"%:+! EJ@S6 ">,-*01p*06o6 "4(+I/:+!>N`¬5 !=Z>!3:#lS(Q !6/!3!#ELM5>:!#">1VQQ/578H((5h.C!3:+*'5JEJ*213">$'$0@;(+:+">6 8,9*'(,-!=8+8">?>!#8_LM5>:(+Q/!./I/:+.<5^8H!5>L:+!LM:+!=8Q/*06/? *'(+8_8U(V"4(+!=8s,-">*'6^(V"%*06/!=EhAS@-T :+5>IJ(+!3:V8j$0!=">E 8](59"Q/*0?>Q !3:`. :5>(5J157$ 54Z>!=:Q !=">E|NORQ/*28`54Z7!3:+Q/!="7E9*08_8H57,-! T Q "%(s$0!=8+8H!=6/!=EhAS@i(Q/!LY">1( (+Q "4(1576^(:+5>$,9!#88+"%?7!=8:!#~7I *':+!i$05 T !3:54Z7!3:+Q/!="7Eb(Q<"%6BE "4(+",-!=8+8">?>!#83N5o!=:?7*'6/?5%LR15>6^(+:57$,-!=8+8+"%?>!#8LM:+5>, ">$'$zQ/5^8U(V8f">6 E LM57: T "%:VEJ*06/? T Q !36/!=Z>!3:_(+Q/!3:+!*08R6 596 ! T 8U(V"4(!p*06JLM5>:+,h"4(+*'576|lS(Q/!. :5>(5J157$k54Z>!3:+Q/!#">E;1="%6LMI/:H(+Q/!3:AL6 ">,9!#8_5%L85>I :+13!=8 Q/578!,-!#88+"%?7!8H(:+!="%,h8R13">6gI 8!f(Q/!p:+!=85>I/:V1!#8j:+!=8!3:+Z>!#E-LM5>:_(Q !pE/!=8H(*06 "4(+*'576|Nju EJ!#8U(+*'6<"4(*05>6(+Q "4( T "%6^(V8"9W $v(+!3:*06 13$'I E/!=8T (+Q/!pW $'(!=:*06*'(+8:!#8H!=:Z4"%(*05>6g,-!#88+"%?7!>Nj} Q/!=6o6/5-W $'(!=:*08"%././$0*0!=EklC"%$0$«8H57I/:V1!=8R*06 (+Q/!,XI/$'(*213"78U(?7:57I/.g,h"[@;I<8H!p*'(+8:+!=85>I/:V1!#83N ] ¤ o3£ £ 93¤=£ u8`"%$0:+!=">E/@iEJ*2813I 8+8H!#Ekl^85>,-!,-!#1VQ "%6/*28, (+5:!=?>I/$2"4(+!R(Q/4! 5 5%Lk. "71Vx>!(V8]*06h(Q/!6/!( 5>:+xX*28j6 !3!=E/!=EklS8H5(Q "%(`(Q !?>:+!3!#EJ@X57: ,h"%$0*21*05>I 8_:+!="%$'&c(*0,9!f5>:R6/576:+!=">$v&c(*0,-!f85>I :+13!=8_EJ5i6 5%(6/!3?^"4(+T *'Z7!3$0@;"4dy!=1e(R(+Q/! T 5^h?7I T "%:V"%6^(+!3!=8s?>*0Z>!=6;(+595>(Q/!=:15>6 6/!=1(*05>6 8=N SQ<"%./*06/?r">6 EP.<57$'*21*06/?r">:!;(Q/!,9!#1VQ "%6 *08,h8I 8!=EP(+5q!36 8I/:+!h(Q *08=NqO">A/$0! = N Î 8I/,-,-">:*0m3!#8(+Q/!;x>!=@DE/*vdy!3:+!36 13!=8XA6 E.<57$'*21*06/? NsORQ/!1VQ/5>*21!AC!( T !3!=6 T Q/*01VQb576/!f(5hI 8!EJ!3.C!36<E/8576g(+Q/!(U@S.Lz">././$0*01="4(+*'576">6 E*v(V88.·Y±¸ ȯ ·)±¸ #Å^´>µ=D· C<Å ! " $#%'&( )*+# , ! " -# &+ .*0/( . %12*0/( , ,*+343456" 74' 8 *+343456" 74' 89),*: $*%-1! 78 ;o¯/±ÆÉ)·Y±¸ 9²¶ =µ <= " -?>@ 7&:AB1'&( *4! >CA DE*+#F(0 1 G 8 "'H4%I 5C /!5@FJ? "34*:*%5CF? 78 ),*: $* "34*:*%5CF8 ¹g=Æ C/¯/±yµ=¯ ¸<Å K/(*%5C "' "345@ " "5@*+L =* K/+*+5C $! >C7AB =*4: 5@F!8 EJ:+5>. .1Vx>!3(+8=N U· =¯ Æ C/¯/±yµ#¯/¸CÅ M%N5@:"* O >PA! - =*4: 5@F8 M% 7 =*%F%#!$*%Q 7B G" 734 8 O"%A $'!7N = N Î ]O«:V"4;1SQ ">./*'6 ?hZ>!3:V8I 8 z5>$0*013*'6/? S!=Z>!=:+">$z(:V"4;1;8Q "%./*06/?q">6 EP.<57$'*21*06/?o(+!=1VQ/6 *0~^I/!#8X"%:+!;"[Z4"%*0$0">A/$0!>Nw6P(Q/!gLM5>$0$'5 T *06/? l T !;EJ*08+1I<88i"%6ª*0,9.C5>:(+">6^((:V"4;1 8Q "%. *'6/?h">6 Eg.C5>$0*21*06/?-(!#1VQ/6/*2~7I !>N
Ã$
Version 2 CSE, IIT Kharagpur
r tokens / second
Packets
if sufficient tokens, remove tokens and transmit packet
Packet Wait
outgoing link
n*'?7I/:! Î : ]O«57x>!=6 _I 1Vx7!(} *v(+Qo¾|!=">xS@g"4(+!XÌs5>6^(:+5>$ @4M Q E 7 KA A C u .C5>. I/$0">:](!#1VQ/6/*2~^I/!I 8!=E-*06-8Q ">./*'6 ?"%6 E-.C5>$0*013*'6 ?*08z(+5>x7!36-A/I 1Vx7!( *'(Qh$0!="%xS@i:+"%(!1576^(:+5>$K8 Î;:1< N]u8j8Q/5 6-*'6;n*0? N Î;: l>" A/I<1Vx>!(_13"%6hQ 5>$2EhI/.h(+5X1!=:H(V"%*06h./:!#8H.C!=13*vWx>!=6 8=NO5>x7!3T 6 8j">:!">E/EJ!#E9(5X(Q/*28jA/I<1Vx>!(R">8zLM57$'$05 TT 8=N¿! T (57x>!=6 8 (+Q "4(,-*0?>Q^(A!(#l">:!h"%$ T "[@S8?>!=6/!3:V"4(+!=ED"4(X":V"4(!-5>L_:p(+5>x>!=6 8p.C!3:X8!=135>6 EkN-LR(Q !hA/I 1Vx>!3(15>6^(V"%*06 8 $0!=8+8j(+Q/!36A;(+5>x>!=6 8 T Q/!36g"(57x>!36g*08_?>!=6/!3:V"4(+!=Ekl7(Q !6/! T $'@-?7!36/!=:+"%(!=Eh(5>x7!36h*28R">E/EJ!#E-(5i(Q !A/I<1Vx>!(#S5%(Q !3: T *08!(Q !6/! T $'@ ?7!36/!=:+"%(!=E;(57x>!36*28*'?76/5>:+!=E|lS">6 E(Q/!p(+5>x7!36A/I 1Vx>!3(:!=,-">*'6<8_LMI/$'$ T *v(+QA(+5>x>!=6 8=N w6b$0!="%xS@;:V"4(+!15767(+:57$)l/" "%*'(*06/?-. "71Vx>!(*28R(+">x>!=6LM57:(:V"%6<8H,-*288*'576576/$0@;*vLz(+Q/!3:+!*08"4($0!=">8H(5>6 !p(5>x7!36*'6b(+Q/!A/I 1Vx7!(#N Lz!36/57I/?>Q(+5>x>!=6 8"%:+!p6/5%("[Z4T">*'$2"%A/$0!f*'6b(+Q/!A/I 1Vx7!(=l/(Q/!=6(+Q/!. "71Vx>!3(R!=*v(+Q/!3: T "%*'(+8I/6^(*0$k(Q/!A I 1Vx>!3(Q ">8R!=6/5>I/?7Q(5>x7!36 8R*06 1=">8!i5>L_"b8HQ<"%.C!3:#Niw6P13"78H!95%L"g.C5>$0*21!3:#lk(+Q/!h. ">1Vx7!(p*08p!=*v(+Q/!3:E/*08+13">:+EJ!#Eq57:f*28p,h"%:+x>!#ErEJ5 6|N-ORQ/!9(57x>!=6B*28p:!=,-54Z>!=E|lk*vL (+:+">6 8H,-*288*05>6q5>L`(Q !i. "71Vx>!3((V"%x>!#8. $0"71!>N _!=13">I 8!(Q !3:+!91="%6rAC!h"4(,-578H(fAB(57x>!=6 8*06B(Q/!-T A/I 1Vx7!(#ly(Q/!-,h"4{J*0,XI/,A/I :+8H( 8*'m=!5%Lj"h$0!=">xS@7&A/I 1Vx7!(&c.C5>$0*013!=%E 5 *08Aq. ">1Vx7!(V83NRn/I/:(Q !3:+,957:!7l AC!=1="%I 8!p(Q/!X(57x>!36b?7!36/!=:+"%(*05>6b:+"%(!*28:#l/(+Q/!,h"4{J*0,XI/, 6SI/,iA!(V8(Q "%(s13">6-!36^(!=:]T (Q/!6/!( T 5>:+x5%L|">6^@X*'6^(!=:Z4">$/5%Ly(*0,-!5%Ly$0!36/?>(Q-(`*28]:( A«NzORQSI 8=l%(+Q/!(+5>x>!=6-?>!36 !3:V"4(*05>6 :V"4(+!>l>:#lS8H!=:Z7!=8z(+5X$0*',-*'(`(Q !$05>6/?>&)(+!3:+, "[Z>!=:+">?>!R:V"4(!"%( T Q/*21VQ-(Q !. "71Vx>!(_13"%6h!=6^(!3:`(Q/!6/!( T 5>:+xyNORQ/*28`(!=1VQ 6/*0~^I/!13"%6;">$085 AC!I 8!=E(5-.C5>$0*013!p(Q/!.C!=">x;:+"%(!"%$05>6 ? T *'(Qb$05>6/?>&)(+!3:+,"[Z>!=:+">?>!:V"4(+!>N
¤ q ¡o=3£
¤ £oz
Switch
Service Discipline
Switch
Output Buffers fixed delay Switch Switch
n *0?>I/:+! Î1, ]u 5o5JEJ!=$|5%L]u ]">1Vx7!( T *v(V1VQ/!=Eb¿!( T 5>:+x u8H*0,-./$'!,-5SE/!3$_5%L"%6Kw6^(+!3:+6/!(9*08i"r157$'$0!=1(*05>6ª5>L8H!=6 EJ*06/?r"%6<Eª:!#1!=*'ZS*06/?q6/5JEJ!#8X"%6<Eª6/!( 5>:+xB8 *'(+1VQ/!#83Nru_(9!3Z7!3:+@ 8 T *v(V1VQ|l](+Q/!3:+!,h"[@PAC!,h"%6S@ª*06 157,-*'6/?D"%6 EF,h"%6S@P5>IJ(+?>5>*06/?D15>,-,iI/6/*213"4(+*'576K$0*'6/xJ8-">898Q/5 T 6KT *06n*0? T N Î1, N !!3.C!36<EJ*'6 ? /Ã (
Version 2 CSE, IIT Kharagpur
I/.C5>6PEJ!#8U(+*'6 "%(*05>6B5%L_". "71Vx>!(#ly*v(*28~7I !3I/!#Eq5>6DA/IJdy!3:~^I/!=I/!-5%L`. ">:H(+*013I/$2"%:f5>IJ(+?>5>*06/?$'*06/xyNiu8+1VQ/!=EJI $'!=:p8!3$0!=1(+8f. "71Vx>!(V8 (+59AC!f(:V"%6 8,-*v((!#E;LM:+5>,(+Q/!A/IJdy!3:"%(s(+Q/!p5>IJ(+./IJ($0*'6/xgA ">8!=Eg5>6b8H57,9!p8+1VQ/!=EJI $'*06/?9.<57$'*21@7Nju 8!3:+ZS*013!fE/*08+1*0./$0*'6/!8+1VQ/!=E/I/$'!#8 *06 157,-*'6/?. "71Vx>!(V8LM57:f(:V"%6 8,-*08+8H*05>6«NXn/57:f:+!=">$«(+*',-!h1576/6/!#1e(*05>6«lk:+"%(!9A ">8!=EB8H!=:ZS*21!-EJ*08+1*0./$0*'6 !=8p"%:+!iI<8H!#Eo(5b./:+5%(+!=1((+Q/! ?7I "%:V"%6^(!=!=8`?>*0Z>!36;(5-15>6 6/!=1(*05>6 8`LM:57, 6/!( T 5>:+x-$'5^">E I ">:+">6^(!3!#8`"i,-*'6/*0,XI ,8H!=:ZS*21!:+"%(!(+5i*06 EJ*0ZS*0EJ& I ">$|1576/6/!=1(*05>6 8R:+!3?^"%:VEJ$0!=8+8`5>L(+Q/!p(:V"4;1f?>!=6/!3:V"4(+!=E;AS@5%(Q !3:1576/6/!#1e(*05>6<83N ORQ/! sI/dC!=:X:+!=~^I/*0:!=,9!=6^(+8X"%(i"q8 *v(V1VQKEJ!3.C!36<E/8X576ª,h"4{J*',iI/,Â. ">1Vx7!(X">::+*'Z4">$j:+"%(!7l,h"%{S*0,XI , . "71Vx>!3(X8H*0m3!g">6 EP(+Q/! !3{S.C!=1(!#Er85 U5>I :6o(+*',-!-5%Ls. ">1Vx7!(+8=NXT\6o(Q !95>(Q/!=:Q<"%6 Ekly(+Q/!-A/IJdy!3:p:+!=~^I/*0:!=,9!=6^(+8f"4(f(Q/!9:!#1!=*'ZS*06/?g!=6 Eq*28f!=~^I "%$(+5g(+Q/! ./:+5JEJI 1(5%LE/!3$2"[@ U*v((!=:=l ">6 Eg(Q/!,h"4{J*0,XI/,. ">1Vx7!("%:+:*0Z4"%$k:V"4(+!f">6 E. ">1Vx7!(8H*0m3!7N ORQ/!h8!3:+ZS*013!9EJ*28+1*0./$'*06/!h"4(">6^@b(+*',-!hEJ!#1*2EJ!=8 Q/*21VQD5>IJ(+./IJ(A/IJdy!3:V8 5>I/$2EqAC!-(+">x>!36BI/.BLM5>:p(:V"%6<8H,-*288*'576r6/!3{S(=N-ORQ/! 8 T *v(V1VQ +[:+5>I/(!3:hEJ5S!#8-(Q/!B8 T *'(+1VQ/*06/?ª5>L(+Q/!rE/"%(+"PT . "71Vx>!(V89LM:57,*'(+8h*06/./I/T (g.<57:H(h(+5P(Q/!BEJ!=8*':+!=E57IJ(./I/(g.<57:H(#l_85P(Q<"4(g*'( :+!="71VQ/!=8`(Q/!E/!=8H(*06 "4(+*'576">E EJ:!#88=N]jZ7!3:+@-8 T *'(+1VQ +4:57IJ(!=:_1="%6gAC!,-5JEJ!3$0!=E">8R"9~7I !3I/!7l T Q/!3:+!p. ">1Vx7!(+8`LM:+5>,EJ*'dy!3:+!36^( 5 T 8 135>,-.:f(Q !98 *v(V1VQ/*06/?. :5J1!#88*06/?h(*0,-!h"%6 Eo57IJ(. IJ($'*06/xyNORQ/!3:+!9,-"[@bAC!i,h">6^@o*06 135>,-*'6 ?g$0*'6/xJ8(5b"8 *'(+1VQ|lC(+Q/!3:+! ,h"[@rAC!g"o6SI/,iA6/6 !=1e(+*'576 8pLM57:!="71VQD$0*06/xylz">6 ED(Q !3:+!h,-"[@BAL. ">1Vx7!(+8*'6ª!#">1VQªT 1576/6/!=1(*05>6 (+5DAC!q8!3:+Z>!=E|NGORQ/!#8H!b. "71Vx>!(V89,-"[@G15>,-.C!(+!LM57:-(Q/!o8+"%,-!b5>IJ(+./IJ(;$0*'6 xCN ORQ/!b,h"%6 6/!3:h*06 T Q *01VQG(Q/!q~^I/!=I/!=EG. "71Vx>!(V8 ">:!98H!=$'!#1e(!#EbLM5>:(Q !X(+:+">6 8H,-*288*05>6o5>6r(Q/!i$'*06/xo*28fx^6 5 6q">8$'*06/xo5>:(:V"4;1i81VQ/!#EJI/$0*'6 ?EJ*2813*'. $'*06/!>NORQ/!981VQ !=EJI/$0*06/?EJ*28+1*'& ./$0*06/!"4(]!="71VQi8 T *v(V1VQi8!3$0!=1e(V8 T Q/*21VQX. "71Vx>!((5f(+:+">6 8H,-*'(T 6 !{S(]A^@iEJ*08+1:+*0,9*06 "%(*06/?.<">1Vx>!3(+8A "78H!#E5>6X(Q/!=*': T 5S:+!=~^I/*0:!=,-!36^(+8=N
A M E 0 E
O:+"%;1?7!(V8RA/I/:V8U(+*'!=:"%6 EA/I/:V8U(+*'!=:"4La(+!3:*'(. ">8+8H!#8s(Q/:+5>I/?7Q!#">1VQ8 *'(+1VQ|l<"%6 E*v(,h"[@;6 59$05>6 ?>!3:8+"4(+*08HLM@;*'(+885>I/:V1!p1VQ ">:+"71e& (+!3:+*'m#"4(*05>6«NzORQ *08*28RAC!=13">I 8!>lS(Q !~7I !3I/*06/?;"4(!#">1VQb8 T *'(+1VQQ ">8"-A I/T 6 1VQ/*06/?-!dy!=1(5>6(Q/!.<">1Vx>!3(+8_5%Lz"h8H!#88*05>6|N n 5>:!3{J">,-./$'!7l<*'L`";135>6/6/!#1e(+*'576q8"%(*28UW !#8XÁ D JÄ"%((Q !X8H57I/:V1!>l (Q/!=6q*'(+8 57:+8H(13"78H!p(+:+"%;11VQ "%:V">1(!=:*0m="%(*05>6 UI 8U(fA:+! (+Q/!*'(Qb8 T *v(V1VQgAC!=157,-!=8pÁ D JÄel T Q/!3:+! "%6 E T *08s(+Q/!p$'5J13">$CE/!3$2"[@9AC5>I 6 E;LM57:`(+Q/!1576/6/!=1(*05>6 "%(_(+Q/! w(Qq8 T *'(+1VQ|N Çi»C±yµ3¶4»<É)ÉY·)±¸Æ· =µ=»<¶[µ=·)»<±s½;ORQ/!;:+5>$0!h5%LR(Q !h(:V"4;1;EJ*28H(5>:(*05>6PQ ">6 EJ$0*'6 ?q*08(Q/!=6P(5q,-5JEJ*'LM@D(Q/!;*06/./I/(X(:V"4;1-!=*v(+Q/!3:iA^@ :+!=135>6 8H(:+I 1e(+*'6 ?9*'((5h*'(+85>:+*'?7*'6 ">$|8H57I/:V1!p1VQ "%:V">1(!3:+*28U(+*01=8s57:AS@EJ!=:*0ZS*'6/?9(+Q/!6/! T (+:+"%h1p1VQ ">:+"71e(+!3:+*'m#"4(*05>6"4((+Q/!!36^(:V"%6<1! (+5p(Q/!8 T *'(+1VQh">8+8HI ,9*06/?p(+Q/! T 57:+8H(`13"78H!R,iI/$v(+*'. $'!3{S*06/?!3:+@8 T *v(V1VQ9AS@:+!=135>6 8H(:+I 1(*06/?(+Q/!R(:V"4;1_5%Lk"p1576/6/!=1(*05>69(5p*'(+8j85>I :+13!_1VQ ">:+"71e(+!3:+*'m#"4(*05>6«N«u$0$/6/576J& T 5>:+x^&135>6 8!3:+ZS*'6 ? EJ*28+1*0./$'*06/!#8./:+5>.C578!=E;*06(Q/!$0*'(!3:V"4(+I/:+!fI<8H!f(Q *08R(+!=1VQ/6 *0~^I/!7NjORQ/!3@g8!3.<"%:V"4(!f(+Q/!8H!=:Z7!3:_*'6^(+5-( T 5h157,-.<576/!36^(+8 Î Nu :+"%(!15767(+:57$'$0!3:# (15>6^(+:57$08_(+Q/!EJ*28U(+5>:(*05>6g576b!=">1VQb1576/6/!#1e(*05>6I 8*'6 ?9:+!3?7I/$2"4(57:+8_"%6<E">$'$05J13"%(!=8_A ">6 E T *2ES(Q(+5-(Q/!=,N Ã/Nu 81VQ/!#EJI/$0!3:# (5>:VEJ!3:R(+:+">6 8H,-*288*05>6g5>L.<">1Vx>!3(+8_5>6bEJ*'dC!=:!=6^(15>6 6/!=1(*05>6 8">6 Eg. :54ZS*2EJ!p54Z>!3:R1576/6/!#1e(*05>6oEJ!=$0"[@hAC5>I 6 E/8=N u 8H!=:ZS*21!iE/*08+1*0./$0*'6/!9Q/!=$'. 8*28H57$0"%(! T !3$0$'&cAC!3Q "[Z7!=Eb?7I "%:V"%6^(!=!=E(+:+"%h1i8H57I/:V1!=8LM:57,*'$0$v&AC!3Q "[Z7!=Eq85>I/:V1!#83lC6/!3( T 57:x$'5^">E I<1e(I<"4(*05>6"%6 EFANKORQ/!*0$0$v&A6/*06/?D!=~^I/*0./,-!36^(9,h"[@K8!36 EF. ">1Vx7!(V8(+5r(+Q/! 8 *v(V1VQF"4(9"oQ/*0?>Q/!=:i:V"4(+!h(Q/!=6FEJ!#1$2"%:+!=EkNqORQ/!6/!( 5>:+xr$057"7)E I 1(I "%(*05>6K,h"[@P13"%I<8H!;Q *'?7Q/!3:i*'6 8H(+">6^(+"%6 !35>I<8X"%:+:+*'Z4"%$`:+"%(! !=TZ>!36PLM:+5>,Â"r85>I :+13!>l T Q/*01VQFQ ">8i8"%(*28UW !#ED(Q/!g(:V"4;T 1;135>6 8H(:V"%*06^(i"4((+Q/!g!=6^(:V"%6 13!;5%L(+Q/!g6/!3( T 57:xyNbw6ª(+Q/!1=">8!;5%LAC!=8H( !3dC57:H((:V"4;1%lk8*'6 13!X(+Q/!i(:V"4;1*28f6/5%(1576 8U(+:+">*'6 !=E(Q !3@q13">6rZ7!3:+@ T !3$0$]13"%I<8H!915>6 ?>!=8H(*05>6q">6 ErE/*08:I .J((+Q/!98!3:+ZS*013!(+5g(+Q/! T !3$0$v&AC!3Q "[Z7!=E;?7I "%:V"%6^(+!3!=E;(:V"4;1p8H57I/:V1!=8=N $ %
$
$ %
$
%
A M H M4
4@SC E
E ME C E 4
n 5>:j8I/./.C5>:(*06/?pA1576SZ>!36^(+*'576 "%$S8H!=:ZS*21!EJ*2813*'. $'*06/!=8`8HI 1VQ-">8]nzÌ_n]57:]:57I/6 Ei:57A/*'6-8!3:+Z^*21!#8z"%:+!R8IJ;1*0!36^(#N ¬5 T !=Z>!3:#l>.C!3:_1576/6/!=1(*05>6;.C!3:LM5>:+,h"%6 13!?>I<"%:V"%6^(!=!=8]6/!=!=Eh,-57:!!=$0">A<57:+"%(!8!3:+ZS*013!EJ*2813*'. $'*06/!=8=N]uÀ8!3:+ZS*013!EJ*2813*'./$0*06/!1="%6;AC! Ã=
Version 2 CSE, IIT Kharagpur
Eligible Time computation
Active Msgs
1
D M U X
Hold Queue
2 n−1
MUX
Departing msg
n
n*'?7I/:! Î-. j:+5J1!=8+8*'6/?9*06b"-¿5>6J&}B57:x^&HÌs5>6 8!3:+ZS*'6 ?iS!3:+ZS*013! ! *2813*'. $'*06/!
13$0"788*vW8p!3*'(Q !3: T 5>:+x7&w1576 8!3:+Z^*06/?;57:p6/5>6J& T 5>:+x7&w1576 8!3:+Z^*06/?:+x^&135>6 8!3:+ZS*'6/?EJ*08+1*0./$0*'6 !>l"b8!3:+Z>!=:f*28p6/!=Z>!3:*2EJ$0! T"%LaQ/(!3!=: 69(Q/Q/!=*01V:!Qo*2"-8j"p. "7. 1V"7x>1V!3x>(R!(zAC!=(+1355>8H,-!=6 !=Ek8N!3$0w*'6-?7*'"pA/$06 !p5>(6J5h& T AC57!:8x^!3&w:+1Z^57*26 18H!#!=Ek:N`ZS*0uº6/?8!3EJ:+*2Z>8+1!=*0:./*0$'*086/">!7$'l>$05!="71V!=QiEg.<(">5;1Vx>8!3!36 (]E*08j5>"76 8$'8@g*0?>(6/Q/!#!Ei. ">"7691Vx>!=!3$'*0(+?>8 *0A/*0$'Q/*'(U*21V@Qo(+*'"%,-:+!f!>lS!="f$'*0?>(*0*0A/,-$0!! ">6 EK*'(9T *2896/!3Z7!3:-*2EJ$'!b">8i$05>6/?P">8X(Q/!=:!b"%:+!g!=$'*0?>*0A/$0!.<">1Vx>!3(+8X(5P8H!=6 EkNKuT ,9576/?B(Q/!b./:+5>.C578!=EK8!3:+ZS*013!EJT *28+1*0./$'*06/!#83l ZS*':(I ">$ 13$'5J1Vxyl }n T l^ Ì_n T l !!3$2"[@^& ! ! "%:+! T 5>:+x^&135>6 8!3:+ZS*'6/? .J&w"%6 EJ& 6 5 6 8!3:+ZS*'6/?-EJ*2813*'. $'*06/!>N O5B. :54ZS*2EJ!!=6 ES&c(5>&c!=6 E T 5Sª?7I "%:V"%6^(!=!=8X(5P*06 EJ*0Z^*2EJI ">$1576/6/!=1(*05>6 8=l`:+!=">$_(*0,9!q8!3:+ZS*013!E/*08+1*0./$0*'6/!#8-6/!3!#EK(+5ª8HI/. ./$'@ 85>$0IJ(*05>6<8_LM5>:#.C!3:15>6 6/!=1(*05>6A "%6 E T *0ES(+Qo"%6 EEJ!3$2"[@g">$'$05J13"4(+*'576*06o"-8H*06/?>$0!8 T *'(+1VQ«N (h./:+54ZS*0EJ!#8X$05J13">$_.C!3:LM5>:+,h"%6 13!?7I "%:V"%6^(+!3!=8(5ª"D15>6 6/!=1(*05>6G"%(-"P8 T *v(V1VQ|NFORQ/!=:!b"%:+!!=8+8H!=67(+*0">$'$0@D(Q/:+!3!o">././:+57">1VQ !=8(+5 A ">6 E T *2ES(Qo">6 EbEJ!3$2"[@;"%$0$'5J1="4(*05>6(5hEJ*'dy!3:+!36^(1576/6/!=1(*05>6 8R*06o"-8H*06/?>$0!8 T *'(+1VQ« Î N®°²ÉMµ=·)ÉYÅ C<ÅSÉpÊ|¶4¯/¼F·Y±¸ µ=¶4¯Jµ=ÅS¸<Ë]½g(X*28I 8!=EPAC5%(+Qª*'6^(57.J&">6 ES& 6 5o"%6 Eª¬ 8!3:+Z^*21!;E/*08+1*0./$0*'6/!#83No¾«!(XI 8i1576J& 8H*2EJ!=:5>6 !$'!=Z>!=$«LM:V"%,-*06/?hW :V8U(#Nw6q576/!$0!3Z7!3$LM:+">,9*06/? lC$05S1="%$(*0,-!i"4{J*28*28E/*'ZS*2EJ!=Eo*06^(5gW/{J!=Eo*06^(!3:+Z4"%$28 Opl1="%$0$'!#Eª"LM:+">,9!7Nou$'(Q/57I/?>QK135>6SZ>!=6/*'!=6^(=lLM:+">,9!#85>LE/*vdy!3:+!36^(X6/5JEJ!#86/!=!=EP6/5>(XAC!8@^6<1VQ/:576/*0m3!=E|N R"%6<E T *0EJ(Qª*28 "%$0$'5J1="4(!#EP(5B!="71VQF1576/6/!=1(*05>6">89"r1!=:H(V"%*06KLM:V">1(*05>6K5>L(Q/!LM:V"%,-!;(+*',-!>l Q/*21VQFAC5>I/6 E 8X(+Q/!b"[Z>!3:V"%?7!h:+"%(!5%L(+Q/! (:V"4;1-5%L"q135>6/6 !=1e(+*'576|l T Q/!3:+!-(Q !"[Z>!=:+">?>*06/?*'6^(!=:Z4">$`*28XOpN !*28"7EJZ4"%6^(+">?>T !h5%L576/!;$0!3Z>!=$jLM:V"%,-*06/?o*08(Q/!g(:V">EJ!3&c5>d A:V"%6SI/$2"%:+*v(U@p5%LyA ">6 E T *2ES(Qh"%$0$05S1="4(+*'5769">6 Ei(Q/!EJ!=$0"[@XA<57I/6 EkN]ORQ/!#8H!RLY"71e(57:+8]">:!_*06^Z7!3:V8H!=$'@X./:57.<57:H(+*'576 "%$cN O«554Z>!=:+135>,-!(Q *08f,XI $v(+*'./$0!iLM:+">,9!-8*'m=!X*28*06^(:+5JEJI 1!#EkN _IJ(f*06B(Q/!#8H!981VQ/!=,-!9">$085;(+Q/!3:+!i">:!98H5,-">6S@o./:57A/$0!3,h8"78 $'5 T !3:I/(*0$'*0m="%(*05>6 85%L]A ">6 E T *2ES(Q|Nu6/5>(Q/!=:fEJ*28+">EJZ4"%6^(V"%?>!p5>L]LM:+">,9*06/?h(+!=1VQ/6 *0~^I/!*28*v(V8*06/!;1*0!36<1@b*'6oQ<"%6 EJ$0*06/?;(+Q/! 1576/6/!=1(*05>6 T *'(QoA/I/:V8H(U@;(:V"4;1>N _IJ(LM:V"%,-*06/?h8U(+:+"%(!3?7@g*28!="78H@g(5h*0,-./$'!=,-!36^("%6<ELY">8H(!36/57I/?>Q(5hAC!I 8!=Eo"%(Q/*0?>Q 8H.C!3!#E;(+:+">6 8,9*28+8H*05>6:+"%(!#83N Ã/N »<¶[µ=ÅSÆ p¶4·Y»<¶[·YµVË h²ÅS²ÅC½_(R*28RI 8!=Eg(5i(5-*0,9. $'!=,9!=6^(EJ@S6 "%,-*21./:+*05>:+*v(U@;8+1VQ/!=E/I/$'!=:+8R8I 1VQb">8R ! ! I 8!=E*'6bEJ!3$2"[@^& ! !À">6 E U*v((!3:&w ! !À"%6<Eh"%$28H5pI 8!=E-*06hZS*':(I ">$ 1$05J1Vxyl>}n T l^ Ì_n T N7(sEJ5S!=8]6 5%(`Q "[Z7!_(Q/!">6S@X5%Ly(+Q/!8Q/5>:(+135>,-*'6 ?78 5%LRLM:V"%,-*'6 ?q8U(+:+"%(!3?7*'!#83Nb¬5 T !3Z7!3:#l«*'(i8IJdC!=:+8LM:57, "bQ *'?7QKEJ!3?7:!=!h5%L157,9. $'!3{S*'(U@>Nbw6 8!3:(*05>6ª*06^(5q"q85>:(!#ED./:*05>:+*'(U@ ~^I/!3I/!p*28"%6q\9ÁM$05>?-¿Ä./:57A/$0!3,bl T Q/*21VQ1="%6bA1=1!3./(+"%A $'@g8$05 T LM5>:Q/*0?>Qo8.:+*v(U@P81VQ !=EJI/$0!3:V8=NB¾|!=Z>!=$08X5%L(Q !nzÌ_nzK~7I !3I/!#8 157::+!=8.<576 E(5;. :*05>:+*v(U@$0!3Z>!=$08=N`"71VQq1576/6/!=1(*05>6o*28"788*0?>6/!#E";./:*05>:+*'(U@">6 Eo"%$0$.<">1Vx>!3(+8RLM:+5>, (+Q "4(p15>6 6/!=1(*05>6q"%:+! *'6<8H!=:H(+!=E;*06^(59(Q !nÌ_n]g~^I/!=I/!p5%L(Q "%(./:*05>:+*'(U@h$'!=Z>!3$cDN 5oI/$'(*0./$0!15>6 6/!=1(*05>6 8R13">6AC!">8+8H*0?>6 !=Eh(+59(Q/!8+"%,-!f./:*05>:+*'(U@ $'!=Z>!=$)N ]">1Vx7!(+8`"%:+!81VQ !=EJI/$0!=E;*'6nÌ_n]-5>:VEJ!=:jLM:+5>,(Q/!Q/*0?>Q/!#8U(&c./:+*05>:+*v(U@i6/5>6J&!3,-.J(U@h~^I/!=I/!LM57:`(+:+">6 8H,-*288*05>6|NORQ/!=8! 81VQ !3,-!p*08RI 8!=E*06(Q/!ÌR ÍEJ*2813*'. $'*06/!>N ORQ/!R5>6/$0@X:+!=8H(:+*21e(*05>6i*'6-I 8*06/?,XI/$'(*0$0!3Z>!=$/nÌ_n]9~^I/!3I/!RLM57:j8U(V"4(+*01R./:+*05>:+*v(U@8+1VQ/!=E/I/$'!=:+8z*28z(+Q "4(](+Q/!6SI/,XAC!3:]5>LyEJ*'dy!3:+!36^( EJ!3$2"[@bA<57I/6 EBZ4"%$0I/!=8(Q<"4(13">6BAC!-./:54ZS*2EJ!=Eo(5(Q/!-1576/6/!#1e(*05>6<8f">:!9AC5>I/6 E/!=EBA^@b(+Q/!-6SI/,XAC!3:p5%L_./:+*'57:*'(U@b$'!=Z>!3$28f5%L (Q/!8@J8U(+!3,bN ORQ/!=:!">:!f!=8+8H!=6^(*2"%$0$'@h( T 59(U@S.
Ã:
Version 2 CSE, IIT Kharagpur
»<¶ Çi»C± #Å^G¶ C|·)±¸U· =´7· zÉY·)±ÅC½hw6 T 5>:+xB1576 8!3:+Z^*06/?q8+1VQ/!=E/I/$'*06/?q8+1VQ/!3,-!#83l(Q/!8H!=:Z7!3:*286 !3Z>!=:*2EJ$'!g*vL(+Q/!3:+!;*28 E/"4(V"i(5-A6J& T 5>:+x-135>6 8!3:+ZS*'6 ?9EJ*28+1*0./$'*06/!7lJ!=">1VQ. ">1Vx7!(R*08"788*0?>6/!#EklS!3*'(Q/!=:!{S& ./$0*013*v(+$'@7lJ5>:R*',-./$0*21*'($0@>l ">6g!3$0*0?>*0A/*'$0*'(U@h(*0,-!>NjORQ/!p8H!=:Z7!3:_*0E/$'!#8ÁM6/5>(_(+:+">6 8,9*'(H(+*'6 ?-">6S@;E/"4(V"7Ä T Q/!366/5-E/"4(V"i*28_!3$0*'?7*'A $'!7N } Q/!3(Q/!=:i"q8!3:+ZS*013!;EJ*2813*'./$0*06/!;*28 5>:+xB1576 8!3:+Z^*06/?o57:6/5>6/& 5>:+xr1576 8!3:+Z^*06/?q"%dC!#1e(+8XA/IJdy!3:i:!#~7I *':+!3,-!36^(V83lzEJ!3$2"[@B">6 E EJ!=$0"[@ U*'(H(+!3:#NG}D5>:+xK1576 8!3:+Z^*06/?DEJ*08+1*0T ./$0*'6 !=896/!3!#EF$0!=8+89A/IJdy!3:;">T 6 EG1="%I 8!b8HQ/57:H(+!3:-EJ!3$2"[@ªA/IJ(;1="%6/6/5>(hA<57I/6 EEJ!3$2"[@ U*v((!=: (+*'?7Q7(+$'@7NORQ/!i5>./.C578*v(+!*28(+:I/!LM5>:6 5>6J& T 57:x1576 8H!=:ZS*06/?;EJ*2813*'. $'*06/!=8=_(Q/!=@b6/!3!#Eo";$2"%:+?>!3:A IJdC!=:=lk1="%I 8!$05>6/?7!3:EJ!=$0"[@7l A/I/( 1="%6AC5>I/6<EXEJ!=$0"[@ U*v((!=:(+*'?7Q^($0@>NzORQ/!jLM57$'$05 T *'6 ?"%:+!`"LM! T 13:*'(!=:*2"R(5 UI EJ?7!`(+Q/!_8I/*'(+">A/*'$0*'(U@f5>L ". ">:H(+*013I/$2"%:8!3:+ZS*013!sEJ*28+1*0./$'*06/!7N } Q/!3(Q/!=:z*v(]*28z:!#~7I *':+!=E(5f./:54ZS*2EJ!R8U(V"4(*28H(*213"%$S57:zE/!(!=:,-*06/*28U(+*01s?>I ">:+">6^(!3!#83NORQ/!R./:57..C!3:(*0!=8(+Q "4(`">:!R5>La(!36-?7I "%:V"%6^(!=!=Ei"%:+!sI/T . .6-$0578+8 :V"4(+!>lS(Q ! T 57:+8H(H&w13"78H!A "%6 E T *0ES(+Q|l/(+Q/!I/./.C!3:A<57I/6 E/8R576b~^I/!=I/*06/?hEJ!3$2"[@>l/">6 EbEJ!3$2"[@ U*'(H(!=:=N`J5>,-!81VQ !3,-!=8R576/$'@g?>I ">:+">67(+!3! 576/!i57:f85>,-!i5%Lj(+Q/!=8!i. :57.,-./:+!3Q !36 8*'Z7!i">6 "%$0@J8H*285>L`Z4"%:+*'57I 8(+:+"%;1iEJ*28+1*0./$'*06/!#89ÁYA<5>(Q T 57:xo1576 8!3:+Z^*06/?g">6 E 6/576 T 5>:+xg135>6 8!3:+ZS*'6/?SÄ`">6 Eg(Q/!=*'::+!3$2"4(+*'Z7!f135>,-. ">:*28H5761="%6A6 8!3:+ZS*'6 ?iEJ*2813*'. $'*06/!=8=l ">6 E8I/A 8!=~^I/!=6^($0@ T !EJ*2813I 8+8"XLM! T 6/576J& T 57:x^& 135>6 8!3:+ZS*'6/?-8!3:+Z^T *21!pEJ*2T813*'. $'*06/!=8=N E
d
) 4 K LBE
E ME C E B
w6(Q *088I/A 8!=1(*05>6|l T !EJ*2813I 88"iLM! T *0,-.<57:H(V"%6^( T 57:x;135>6 8!3:+ZS*'6 ?98!3:+ZS*013!fEJ*28+1*0./$'*06/!#83N ÅS·)¸<Èyµ#Å^Æ Ê«¯/·Y¶ k²ÅS²·)±¸ # Ê %&4½]}n T 8 :;< Q "78!3Z75>$0Z>!=ErLM:+5>, n$0I/*2Eªn "%*0: T I/!=I/*06/?KÁYnzn T Äl">$085bx^6 5 T 6P"78 ]">1Vx7!( 6 !=6/!3:V"%$0*'m=!=E `:5J13!=8+8H57:iSQ ">:*06/?GÁ 6 _/ÄeNzw6Gnzn T (Q/!=:!*08-"D8H!=. "%:V"4(+!gnUn\~^I/!=I/!;LM57:-!=">1VQG15>6 6/!=1(*05>6F8Q "%:+*06/?q(+Q/! 8+"%,-!g$0*06/xyN !I/:+*06/?B">6^@D(+*',-!b*'6^(+!3:+Z[">$ Q !36K(+Q/!3:+!b"%:+!;!{/">1($0@K¿6 5>6J&!3,-.J(U@ª~^I/!3I !=8=l](Q/!b8!3:+Z>!3:98H!=:Z7!=8(Q/!b¿.<">1Vx^& !3(+8-"4(9(Q/!Q/!#">Eª5>L(Q/!o~^I/!=I/!=898H*0,XI $v(V"%T 6/!=5>I 8$'@7l]!="71VQF"4(9(Q/!:V"4(!5%L Î +4¿(QF5>L(Q !$0*'6 xK8H.C!3!#EkNKnzn T "%$0$05 T 8iEJ*'dy!3:+!36^( 135>6/6/!#1e(+*'576 8f(5bQ "[Z7!-E/*vdy!3:+!36^(8H!=:ZS*21!h8Q "%:+!=8=N9u nzn T *281VQ "%:V">1(!=:*0m3!#EoAS@r¿.<5^8H*'(*0Z>!-:+!=">$]6^I ,XAC!3:V8 %D 9l«!#">1VQ 135>:+:!#8H.C5>6 E/*'6/?p(+55>6 !~^I/!3I/!7N]u_(s"%6S@i(*0,9!(Q/!f8H!=:ZS*21!:V"4(+!LM5>:_"6/5>6/&c!=,9./(U@9~^I/!=I/!*<*08`!{/">1($0@Á
Ä T Q/!3:+! pÁ Äf*28(Q/!h8!(p5%L`6 5>6J&!3,-.J(U@q~^I/!=I/!=8p"%6<EDÌ *28(Q/!-$0*'6 xq8H.C!3!#EkNiORQ/!=:!3LM5>:+!>lknzn T 8!3:+Z>!#8.<">1Vx>!3(+8*'6D6/576J&c!=,-.J(U@o~7I !3I/!#8 "713157:+E/*'6/?(5b(+Q/!3*0:8!3:+Z^*21!h8Q "%:+!=8=Nhnzn T *08*0,-./:V">1e(+*01="%$j"78p*v(X"788I/,-!=8f(+Q "4((+Q/!;8H!=:Z7!3:13">6ª8H!=:Z7!9">$'$j135>6/6/!#1e(+*'576 8 *'(Q 6/576J&!3,-.J(U@b~7I !3I/!#88*',iI/$v(V"%6/!=5>I 8$0@"%6<Eb(Q "%((Q !(:V"4;1*28*06JW 6 *v(+!3$0@bE/*'ZS*28H*0A/$0!>Nw6q"h,-57:!:+!=">$'*28H(*21p. ">1Vx7!(8@J8U(+!3,bl T 576/$'@ 576/!15>6 6/!=1(*05>6h13">6i:+!=13!3*0Z>!8H!=:ZS*21!"4(j"f(+*',-!"%6<E9">6i!=6^(*0:!. "71Vx>!3(z,iI 8H(zAC!8!3:+Z>!#EAC!LM5>:+!"%6 5%(Q !3:]. "71Vx>!(j1="%69A!#EkN
4j
Rd
S K LBE
E ME C E 4
¿5>6J& T 75 :x;135>6 8!3:+ZS*'6 ?9EJ*28+1*0./$'*06/!#8 T !=:!p6/5>(R?7*'Z7!36bEJI/!*0,-.<57:H(V"%6 13!f!#"%:+$'*0!3:RAC!=1="%I 8!p5%L( T 5-,h"%*06:+!="78H576 8=N E j:+!3ZS*05>I 8$'@(Q/!,h" U5>:j.C!3:LM5>:+,h"%6 13!*'6 E/*013!=8 T !3:+!R(Q !"[Z>!=:+">?>!EJ!3$2"[@X5>L|"%$0$/(Q !. ">1Vx7!(V8j"%6 E9(+Q/!"[Z7!3:V"%?>!s(Q :57I/?>Q/. IJ( 5%L(Q/!8!3:+Z>!3:#N} *v(+Qb"96/576J& T 57:xh1576 8!3:+Z^*06/?9EJ*08+1*0./$0*'6 !>l "9. "71Vx>!(R,h"[@hA!3:_!3Z7!36 T Q/!36(Q !8H!=:Z7!3: *08R*2EJ$0!>NjORQ/*28,h"[@;*06 1:+!="78H!(Q !"[Z>!3:V"%?7!EJ!=$0"[@h5>L(+Q/!. "71Vx>!(V8R"%6 EbEJ!#1:+!=">8!(Q/!"[Z7!3:V"%?>!(Q/:+5>I ?>Q/./I/(R5>L(+Q/!8!3:+Z>!3:#N E T I/!3I *'6/?K">6 "%$0@J8H*28h85PLY"%:g"788I/,-!=E5>6 $'@"ª8H*06/?>$0!q8!3:+Z>!3:h!=6SZ^*0:+5>6/,-!36^(#N ORQ/!o.C5%(+!36^(*2"%$f">EJZ4"%6^(V"%?>!#8-5%Lp6/5>6/& T 5>:+x 1576 8H!=:ZS*06/?oEJ*2813*'./$0*06/!=8X*'6K6 !( 5>:+x>!=EB!36SZS*0:576/,-!36^( !3:+!h6/!3Z7!3::+!=">$'*0m3!#EPw6ª?>I ">:+">67(+!3!#EB.C!3:LM5>:+,h"%6 13!;8H!=:ZS*21!7l«(+Q/! ,-5>:+!*',-.C5>:(+"%6^(.C!3:LM5>:+,h"%6 13!T *'6<EJ!{b*08(Q/!i!36 EJ&)(+5%&!3T 6 EbEJ!=$0"[@A<57I/6 Eo:V"4(+Q/!3:(+Q "%6b(+Q/!i"[Z7!3:V"%?7!fEJ!=$0"[@7NRw6q">E/EJ*'(*05>6«l EJ!3$2"[@X6 !3!=E 8](5AC!AC5>I 6 EJ!=E-*06;"6/!3( 57:xS*06/?p!36SZS*':+5>6 ,9!=6^(j:+"%(Q/!=:](Q ">6 UI 8H(s*06;"8H*06/?>$0!6/5JEJ!7N]ORQ/!3:+!LM57:!7l4(Q/!"%AC54Z>! :!#">85>6 8`LM5>:6 5%(I 8*'6 ?96 5>6J& T 57:x;135>6 T 8!3:+ZS*'6 ?9EJ*28+1*0./$'*06/!#8EJ5h6/5%(Q/57$0Eb">6^@h,-57:!7N Ã,
Version 2 CSE, IIT Kharagpur
w 6(Q/!pLM57$'$05 T *06/? l T !EJ*08+1I<88"iLM! T *0,9.C5>:(+">6^(6/5>6J& T 5>:+x7&w1576 8!3:+Z^*06/?8!3:+ZS*013!pE/*08+1*0./$0*'6/!#83N |·Mµ=µ=Å^¶ f¯J¶4ÉY·)Å =µ%U²Å U¯Jµ#Å<½ORQ !7*v((!=:H&w ! ! 8 Ã$ < . :54ZS*2EJ!=8EJ!3$2"[@^& U*'(H(+!3:fA<57I/6 E/8=NuLa(!=:";. "71Vx>!3(Q "78AC!3!=6B8!3:+Z>!=Eo"%( !#">1VQr8!3:+Z>!=:=ly";W,-.EJ$0*06/!9">6 Eo(+Q/!-">1e(+I "%$W 6 *08Q/*06/?g(+*',-!7N uG:!=?>I/$2"4(+5>:«"%(«(+Q/!`!=67(+:+">6 1!s5%LJ(+Q/!`6/!3{S(z8!3:+Z>!=:|Q/5>$2E/8«(Q/!_. "71Vx>!(«LM5>:|(+Q/*28.C!3:+*05SEA:+!`*'(*28«,h"7EJ!`!=$'*0?>*0A/$0!j(5A
Delay Bound PreAhead
Switch i−1
Arrival
Departure
Deadline
Holding Switch i
Delay Bound
Arrival
Eligible
Deadline
n *0?>I :!Ã* ]">1Vx>!3(J!3:+Z^*21!p*06 >*'(H(+!3:& ! ! 7*v((!=:H&p ! !*28i*'$0$'I<8U(+:+"%(!=EP*06Gn*0? NPÃ*/l Q/*21VQF8Q/5 8(+Q/!./:57?>:+!=8+8p5%L"r. ">1Vx7!((+Q/:57I/?>QK( 5r"7E H">13!36^(98!3:+Z>!=:+8=Now6 (+Q/!bW :V8U(g8!3:+Z>!=:=l](+Q/!o. "71Vx>!(h?75%(;8H!=:Z7!=E j:+!=T uQ !=">E8!=T 1576 E/8-AC!LM57:!b*'(+8;EJ!#">EJ$0*06/!>NÀS5*0A/$0!(5A6/$0@"%La(!=: j:+!=uQ/!="7Eb8H!#15>6<E/83NJ*'6 13!(+Q/!3:+!*28"g135>6 8H(+">6^(EJ!3$2"[@AC!( T !3!=6b(Q/!i!3$0*'?7*'A *'$0*v(U@(+*',-!=85%L](+Q/! . "71Vx>!3("%(( T 5h"7E H">13!36^(8H!=:Z7!3:V83l^(Q !. ">1Vx7!(8H(:+!="%,13"%6AC!./:+54Z^*2EJ!#E"-EJ!=$0"[@ U*'(H(+!3:A<57I/6 EkN`u88I/,-*06/?-(Q/!=:!*286/5-:+!3?7IJ& $2"4(+5>:j"4(z(+Q/!EJ!=8H(*06 "%(*05>6-Q/578H(=l%(Q/!!=6 ES&c(5%&!36<EiEJ!=$0"[@ U*v((!3:`A<57I/6 E9*08](Q/!8+"%,-!">8(+Q/!$'5J1="%$/EJ!=$0"[@AC5>I 6 E-"4(z(Q/!$0"78U(j8!3:+Z>!3:#N µ=» V¯/±Æ »«½p^(57.J&">6 ES& 6 5;EJ*2813*'./$0*06/%! 8 ( < *28A<">8!=Eb5>6o,iI/$'(*0$'!=Z>!3$«LM:+">,-*'6/?8U(+:+"%(!3?7@>NRn*':V8U( !E/!=8+1:+*'AC!(Q *08fEJ*2813*'./$0*06/! I 8*06/?i576/!$0!3Z7!3$CLM:V"%,-*'6 ? lJ"%6 Eh(Q/!=6 T !!3{S(!36<E;*'(s(+5i,iI/$v(+*v&$0!3Z>!=$CLM:+">,9*06/? l7(Q/!(*0,-!p"%{J*08s*08REJ*0ZS*0E/!=E *06^(5bLM:V"%,-!=8=l T Q *01VQK">:!-.C!3:+*'5JE/8X5%L8H57,9!;135>6 8H(+">6^($'!=6/?%(+QKOpN^(+5>.J&w"%6 EJ& 6 5qEJ!3W 6/!#8EJ!3.<"%:(*06/?q"%6 Eª">::+*0Z^*06/?LM:V"%,-!=8pLM57: !#">1VQ$'*06/xyNsu_(!#">1VQb8 T *'(+1VQ|l/(Q/!X">::+*0Z^*06/?iLM:+">,-!5%Lz!=">1VQ*06 157,9*06/?-$0*'6/x*28,h"%./.C!=E(5-(+Q/!EJ!=. "%:(*06/?-LM:V"%,-!p5%L(Q/!57IJ(. IJ( $0*'6 x;AS@h*'6^(:+5JEJI 13*'6/?-"-1576 8U(V"%6^(EJ!3$2"[@ E/l T Q/!=:! * & E N]u13135>:VEJ*06/?X(+5X(+Q/!^(57.J&w"%6 ES& 6 5-EJ*08+1*0./$0*'6 !>lS(Q !(+:+">6 8,9*28+8H*05>6 5>L_". ">1Vx7!((+Q "4(Q "78p"%:+:*0Z>!#Eo5>6D"%6S@o$'*06/xq$jE/I/:*06/?b";LM:V"%,-!iL_8Q/5>I $0EB"%$ T "[@J8A6/!#ErI/6^(+*'$z(+Q/!-A*06/6/*06/?5>L`(+Q/! 6/!3{S(LM:+">,9!7lS(QSI 8R(+Q/!8!3:+Z>!3:_:+!3,h"%*06 8R*2EJ$'!I 67(+*'$|(Q/!=6!=Z>!=6*'L(+Q/!3:+!"%:+!f. ">1Vx7!(+8~^I/!=I/!=EgLM5>:R(+:+">6 8,9*28+8H*05>6|N ORQ/!fLM:V"%,-*06/?h8U(+:+"%(!3?7@h*'6^(+:5JEJI 13!=8_(+Q/!./:+5>A/$0!3, 5>L135>I/./$0*06/?-AI/6 Eb">6 EgA<"%6 E *2ES(+Qb">$'$05J13"%(*05>6?>:V"%6SIJ& $2"%:+*v(U@7N_ORQ !XEJ!3$2"[@g5>Lj"%6S@.<">1Vx>!3("4(";8*06/?>$0!8 T *'(+1VQo*28AC5>I 6 EJ!=EqA^@gT ( T 5-LM:V"%,-!(+*',-!#83NO5;:!#EJI 13!pT (Q/!9EJ!3$2"[@>l "g8H,h"%$0$0!3:O *28EJ!=8*0:!#EkN]¬5 !3Z>!=:=lJ8*'6<1!O*28"%$28H59I 8!=Eg(5h8.6 E *2ES(Qo">$'$05J13"4(+*'576g?7:+">6^I $0">:*'(U@>Nu8+8HI/,-*06/?h" W/{J!#Eb. ">1Vx7!(8*'T m=! zlJ(Q/!i,-*'6/*0,XI ,?7:+">6^I $0">:*'(U@h5%L]A ">6 E T *2ES(Qq">$'$05J13"4(+*'576b*08 J+4T OpN/O5;Q "[Z7!p,957:! 6 E *2ES(Q«l^57:_8,h"%$0$'!=:sA<"%6 E *2ES(+Q"%$0$05S1="4(+*'576h?>:V"%6SI/$2"%:+*v(U@7l7"$2"%:+?>!=:`O *28`. :!3LM!3:+:!#EkN(R*28_13$'!#"%:`(Q "%(_$05 EJ!3$2"[@9A<57I/6 Eg">6 E W 6 !?>T :V"%6SI/$2"%:+*v(U@-5%LA "%6<E T *0EJ(T Qq"%$0$05S1="4(+*'57613">6/6/5>(RAC!">1VQ *'!=Z>!=E8*',iI/$v(V"%6/!=5>I 8$0@h*'6o"iLM:+">,-*'6/?h8H(:V"4(+!3?>@gT $'*0x>!^(+5>.J&w"%6 EJ& 6 5
T2 Frame T1 Frame
n*'?7I/:+!à Π]O T 95 ¾«!3Z>!=$|n/:V"%,-*06/? T *v(+Q Ã.
V
Version 2 CSE, IIT Kharagpur
O5?7!(">:57I/6 Ep(+Q/*28135>I/. $'*06/?. :57A/$'!=, ,XI/$'(*'&c$0!3Z7!3$7LM:+">,-*'6/?*08I 8!=E|Nw6(+Q/*283l4(+Q/!s(*0,9!R"4{J*28«*28EJ*'ZS*2EJ!=EX*'6^(+5f"Q/*'!=:+">:+1VQ *01="%$ LM:V"%,-*06/?8U(+:I 1(I/:+!8Q/5 T 6i*06hn*'?:`"f6-$0!3Z>!=$JLM:V"%,-*'6 ? T *'(Q9LM:V"%,-!8*'m=!=8]O Î l0N0N'l^OR6-">6 E-OR, Î ;p,bN OR,°LM5>:`, Î l/N0l 6J& Î l#. "71Vx>!(V8k5>6"$'!=Z>!3$7.1576/6/!=1(*05>66/!=!=Ef(+55>A 8!3:+Z>!z(+Q/!s^(+5>.J&w"%6<ES& 6 5:I/$0! T *'(QLM:V"%,-!`8*'m=!`OR.|l[*cN !7N'l[$0!3Z>!=$>.. "71Vx>!3(+8 T Q/*21VQ ">::+*'Z7!=Ei"4(j"%695>IJ(+./IJ(j$0*'6 xiEJI/:+*06/?"fOR.9LM:V"%,-! T *'$0$/6/5>(]A,-!R!3$0*0?>*0A/$'!RLM57:z(:V"%6 8,-*08+8*'576XI/6^(*0$J(+Q/!8U(V"%:(]5%L<6 !{S(`OR.XLM:V"%,-!7N u$085 l :( 5g. ">1Vx7!(+8 *v(+QBEJ*'dy!3:+!36^(LM:V"%,-!i8*0m3!=8=lC(Q/!i. ">1Vx7!( *'(QD"g8,h"%$0$'!=:LM:V"%,-!i8*'m=!XQ "78";6/5>6J&./:+!3!=,9./(*0Z>!X. :*'& 57:*'(U@q54Z>!=:f(Q/!;T .<">1Vx>!3( T *v(+QPT "b$2"%:+?>!=:fLM:+">,9!h8*'m=!>N;} *'(Qª,iI/$'(*'&)LM:V"%,-T !g^(+5>.J&w"%6 EJ& 6 5 I/6<E/8_(5h85>,-!f1VQ<"%6/6/!=$08RAS@h./I/(H(*06/?-(+Q/!3, *06LM:+">,-!=8 T *v(+Q"-8,h"%$0$'!=:sLM:V"%,-!(*0,-!>l ">6 E;(+5h"%$0$'5J13"%(!fA "%6<E T *0EJ(Q T *v(+QW<6/! ?7:+">6^I $0">:*'(U@b(5b5%(+Q/!3:i1VQ "%6/6 !3$28pA^@B./IJ((*06/?b(Q/!=, *06P$'!=Z>!=$08 T *'(QK"b$2"%:+?>!=:LM:V"%,-!9(*0,-!>N¬5 T !3Z>!=:=ly(+Q/!g135>I/./$0*06/?bA6 EoA ">6 E T *2ES(QD"%$0$'5J13"%(*05>6o?7:+">6^I $0">:*'(U@8H(*0$'$z!3{S*28H(+8 T *v(+Q/*'6B!="71VQoLM:+">,-!>Npu 8+1VQ/!3,-!X*28f./:+5>.C578!=E(5">E/Er"8!3. ">:+"%(! 8Q "%. *'6/?-,-!=1VQ<"%6/*28H, "4((+Q/!6/!( 5>:+x;!=67(+:@g.<57*'6^(LM5>:6/!( 5>:+xJ8 *'(QbLM:V"%,-*06/?-A ">8!=EEJ*2813*'. $'*06/!=8=N`} *'(Q(+:+"%h18Q ">./*'6 ?-"%( (+Q/!!=67(+:+">6 1!R(+5(Q !6/!3( T 57:xyl>*'(`T *28`.C578+8*'A/$0!(+5,XI/$'(*0./$0!{hT 8H!=Z>!=:+">$ T 1576/6/!=1(*05>6 8`5>6;"8*06/?>$0!8H$05%(s5%L«"pLM:V"%,-!>l>(Q/!=:!3LM5>:+!"[Z>57*0E (+Q/!./:+5>A/$0!3, 5>Lz135>I/. $'*06/?-A,-!p8*0m3!"%6<EgA ">6 E T *2ES(Qo">$'$05J13"4(+*'576?7:+">6SI/$0">:*'(U@>N ¯Jµ=Å eÇi»C±yµ3¶4»CÉYÉYÅSÆ µ#¯Jµ=·)´ p¶4·)» ¶4·MµVË]½`ORQ !_. :!=Z^*05>I<8H$0@EJ*08+1I<88!=Ei8H!=:ZS*21!&wEJ*2813*'. $'*06/!=8 T !3:+!s!=*v(+Q/!3:zA "78H!#E5>6-85>:(!=E./:*05>:+*'(U@ ~^I/!=I/!R,9!#1VQ "%6 *08, ÁM!7N ? N ? N]^(+5>.J&w"%6 EJ& 6 5SÄeNJ5>:(!=EX./:+*'57:*'(U@8H!=:ZS*21!3&EJ*28+1*0./$'*06/!#8">:!R157,9. $'!3{ ">6 EoEJ*'h13I/$'((+5;*',-./$0!3,-!=67("%6<ELM:+">,9*06/?g8H(:V"4(+!3?7@8IJdC!=:LM:+5>,(Q !iEJ!=.6 Eo?7:+">6^I $0">:H& *'(U@o5%L`A<"%6 E T *2ES(+Q|NiO5?7!("%:+5>I/6<Eb(Q/!#8H!9./:+5>A/$0!3,h8=lkm3Q ">6/?">6 Ern !3:+:+">:* 8 Ã =;< lk./:+5>.C578!=T Er"4(!3&UÌs576^(:+5>$0$'!#Eq^(+"%(*21e& j:+*'57:*'(U@ T Q/!=:!=*'6(Q !pLMI/6 1e(+*'576b5%Lz:+"%(!15767(+:57$CLM:57,EJ!3$2"[@g135>6^(:+5>$yQ "78RAI ./$'!#Eg*06(Q/!E/!=8*'?765>L8!3:+Z>!3:#N
Regulator 1
Regulated Traffic
Priority level
Regulator 2
1
input
output
n Regulator h
Scheduler
Rate Controller
n *0?>I :!Ã>Ã/]"4(+!iÌs5>6^(:+5>$0$'!#E^(V"4(+*01 `:*05>:+*v(U@ u88Q/5 6o*06Cly"gÌR À8!3:+Z>!=:Q "78( 5157,-.<576/!36^(+8=";:V"4(+!&w15>6^(+:57$'$0!3:">6 Eq"g8H(+"%(*21./:+*05>:+*v(U@81VQ/!#EJI/$0!3:#NpÌs576 1!=.J& (+I "%$0$'@7l/"X:V"4T (+!f135>6^(:+5>$0$0!3:s135>6 8*28U(V8s5>L"98H!3(R5>TL«:+!3?>I $0"%(5>:V8_15>:+:+!=8.<576 EJ*06/?(59!="71VQg5>L|(Q/!135>6/6/!#1e(+*'576 8s(:V"[Z>!3:V8*'6/?(Q/!8!3:+Z>!3:# !#">1VQª:+!3?>I $0"%(5>:X*08i:!#8H.C5>6<8H*0A/$0!hLM5>:-8HQ<"%./*06/?o(+Q/!g*06/./IJ(9(:V"4;1h5>L(Q/!b157::+!=8.C5>6 EJ*06/?q135>6/6/!#1e(+*'576ª*'6^(5r(Q/!EJ!=8*0:!#EP(:V"4;1 . "%(H(+!3:+6|N .C5>6P"%:+:*0Z4"%$5%Ls!#">1VQq.<">1Vx>!3(=lk"%6B!3$0*'?7*'A *'$0*v(U@b(+*',-!9*08p1="%$21I/$2"4(+!=Er">6 Er"788*0?>6/!#Eb(5(Q/!9. "71Vx>!(pAS@(Q/!-:+!3?>I $0"%(5>:#N ORQ/!. ">1Vx7!(X*289Q/!3$2Eª*06K(+Q/!g:+!3?7I/$0"%(57:(*0$'$R*'(+8i!3$0*'?7*'A *'$0*v(U@D(+*',-!A:+!gAC!3*06/?rQ ">6 EJ!#Eª(5r(Q/!81VQ !=EJI/$0!3:iLM5>:X(:V"%6 8,-*08+8*'576|N ORQ/!8H(+"%(*21. :*05>:+*v(U@;8+1VQ/!#EJI/$0!3:V8s. :54ZS*2EJ!?7I "%:V"%6^(+!3!=8s5>6bEJ!=$0"[@;">6 EE/!3$2"[@7& U*'(H(!=:A<57I/6 EkNjORQ !p8+1VQ/!#EJI/$0!3:*28R*',-./$0!3,-!36^(+!=EA^@ ",XI/$'(*0$0!3Z>!=$]nÌ_n]q~^I/!=I/!>l Q/*21VQB8!3:+Z>!#8(+Q/!-. ">1Vx7!(+8">1=15>:VEJ*06/?;(+5*'(+8f./:+*05>:+*v(U@b*cN !7NpW :+8H(p. ">1Vx7!(*06q(+Q/!-Q/*0?>Q/!#8U(f./:*05>:+*'(U@ 6/576J&!3,-.J(U@g~^I/!=I/!>NjORQ/!=:!">T:!f( T 5X([email protected]!=85>L:+!3?7I/$0"%(57:+8=
V*
Version 2 CSE, IIT Kharagpur
"4(+!& U*v((!=:ÁY#SÄ_:!=?>I/$2"4(+5>:#l T Q/*01VQb1576^(:+5>$28s:V"4(+!& U*v((!=:A^@. "%:(*2"%$0$0@h:!#15>6<8U(+:I 1(*06/?i(Q/!p(+:+"%h1>N E !!=$0"[@^& U*v((!=:bÁ ! SÄ9:+!3?>I $0"%(5>:#l T Q/*21VQÍ15>6^(+:57$08-EJ!=$0"[@^& U*v((!3:hAS@ªLMI $'$0@F:+!=135>6 8H(:+I 1e(+*'6 ?q(Q !b(:V"4;1%NÍ}D!b"788I/,-!(Q "%( (Q/!;ÌR º8+"4(+*08HLM@q(+Q/!qÁ 3,-*'6|l 3f"[Z>!>l«HÄ1VQ "%:V">1(!=:*0m="%(*05>6|NhORQ/!qÁ 3,-*'6«l 3f"[Z>!7l|HÄ#o:+!3?7I/$2"4(57:p!36 8I/:+!=8f(Q<"4((+Q/! 5>IJ(+./IJ(;5>L(Q !o:!=?>I/$2"4(+5>:-8"%(*28ULM@ª(+Q/!KÁ 3,-*'6|l3f"[Z>!>lsHÄi(:V"4;1,-5SE/!3$cl T Q/*0$0!(+Q/! ! ª:!=?>I/$2"4(+5>:9!36 8I/:+!=89(+Q "4(h(+Q/! 5>IJ(+./IJ((+:+"%h1f5>L(+Q/!:!=?>I/$2"4(+5>:R*28!{/">1($0@h(Q !X8">,-!p"78_(Q/!57IJ(. IJ((:V"4;1f5%L(Q !:!=?>I/$2"4(+5>:"4((+Q/!./:+!3ZS*'57I 88!3:+Z>!3:#N ORQSI 83lJ*'L«(+Q/!p(:V"4;1p8+"4(*28HW !=8s(Q !;Á 3,-*06|l 3f"[Z>!>lSHÄR1VQ ">:+"71e(+!3:+*'m#"4(*05>6;"%(6/!( T 5>:+xh!36^(:V"%6<1!>lSAC5%(+Q([email protected]!=8R5>L:+!3?>I $0"%(5>:V8 T1VQ *'"%$0$z:V">!36 1(8!=I/::+*0!Xm="%(+(Q *05>"46|(fN (Q !957IJ(. IJ(f5>L`(+Q/!i:+!3?7I/$2"4(57:=l T Q/*21VQr*28f(Q/!9*06/./IJ(p(5(Q !-8+1VQ/!#EJI/$0!3:#l T *0$0$j8"%(*28ULM@(Q !-8+"%,-!i(:V"4;1 ORQ/!i81VQ/!#EJI/$0!3:*06q";8!3:+Z>!=:ÌR I 8!=8"h6 5>6J&./:+!3!3,-.J(+*'Z7!8U(V"4(+*01. :*05>:+*v(U@.<57$'*21@yC*v(f"%$ "[@J88!3$0!=1e(V8(+Q/!X. "71Vx>!3("4((+Q/! Q/!#">E-5>L|Q/*'?7Q/!=8H(s. :*05>:+*v(U@9~^I/!3I/!(Q "%(s*28j6/5>(s!=,9./(U@>N]ORQ/!f K81VQ !=EJI/$0!3:sQ ">8s"6SI/,iA:+*v(U@i$'!=Z>!=$08 T *v(+Q;!="71VQh./:*05>:+*'(U@ $0!3Z7!3$ 135>:+:!#8H.C5>6 E/*'6/?(5"E/!3$2"[@A<57I/6 EkN]s">1VQ-15>6 6/!=1(*05>6-*08`">8+8H*0?>6/!#E(+5"p./:+*'57:*'(U@$0!3Z>!=$ EJI/:+*06/?1576/6/!=1(*05>69!=8H(+">A/$'*28Q/,-!36^( (+*',-!>N 5qI/$v(+*'. $'!135>6/6/!#1e(+*'576 813">6AC!">8+8H*0?>6/!#Eh(+5i(+Q/!8+"%,-!p./:*05>:+*'(U@h$'!=Z>!3$clJ"%6 E"%$0$k. "71Vx>!(V8_5>6(Q/!135>6/6/!#1e(+*'576 8R">8+8H5J1*2"4(+!=E T *'(Qo"9./:+*'57:*'(U@;$0!3Z>!=$|"%:+!f">./.C!36 EJ!#E(5-(Q !!36 E5%L(Q/!~^I/!=I/!pLM5>:R(+Q "4(./:+*05>:+*v(U@;$0!3Z7!3$cN ORQ/!i81VQ/!#EJI/$0!3:*06q";8!3:+Z>!=:ÌR I 8!=8"h6 5>6J&./:+!3!3,-.J(+*'Z7!8U(V"4(+*01. :*05>:+*v(U@.<57$'*21@yC*v(f"%$ "[@J88!3$0!=1e(V8(+Q/!X. "71Vx>!3("4((+Q/! Q/!#">E-5>L|Q/*'?7Q/!=8H(s. :*05>:+*v(U@9~^I/!3I/!(Q "%(s*28j6/5>(s!=,9./(U@>N]ORQ/!f K81VQ !=EJI/$0!3:sQ ">8s"6SI/,iA:+*v(U@i$'!=Z>!=$08 T *v(+Q;!="71VQh./:*05>:+*'(U@ $0!3Z7!3$ 135>:+:!#8H.C5>6 E/*'6/?(5"E/!3$2"[@A<57I/6 EkN]s">1VQ-15>6 6/!=1(*05>6-*08`">8+8H*0?>6/!#E(+5"p./:+*'57:*'(U@$0!3Z>!=$ EJI/:+*06/?1576/6/!=1(*05>69!=8H(+">A/$'*28Q/,-!36^( (+*',-!>N 5qI/$v(+*'. $'!135>6/6/!#1e(+*'576 813">6AC!">8+8H*0?>6/!#Eh(+5i(+Q/!8+"%,-!p./:*05>:+*'(U@h$'!=Z>!3$clJ"%6 E"%$0$k. "71Vx>!(V8_5>6(Q/!135>6/6/!#1e(+*'576 8R">8+8H5J1*2"4(+!=E T *'(Qo"9./:+*'57:*'(U@;$0!3Z>!=$|"%:+!f">./.C!36 EJ!#E(5-(Q !!36 E5%L(Q/!~^I/!=I/!pLM5>:R(+Q "4(./:+*05>:+*v(U@;$0!3Z7!3$cN ÌR *28"bA$'?75>:+*v(+Q/,t8*'6 13!h*v(*28!#">8@o(5o*0,-./$'!=,-!36^(i"%6<EB*28EJ!=Z>57*0EB5%L./:+5>A/$0!3,h8fLY"71!=EDAS@r5>(Q/!=: 8+1VQ/!=E/I/$'!=:+8=N o w6^(!=:6 !(f`6/?>*06/!=!3:+*'6/?;O">8xbn/5>:V1!ÁMU`On]Ä ./:+5>.C578!=Eo8!3Z7!3:V"%$|,-5JEJ!3$28LM5>:. :54ZS*2EJ*'6 ? T 5^b"788I/:V"%6 13!=8_(5w6^(!3:+6/!3(H&A ">8!=E ">././$0*01="4(*05>6<83N-ORQ/!=8!-,-5SE/!3$28"%:+!91="%$0$'!#E 7 O/1 &f5>: #%"$L
31C"L'&eN;ORQ/!-,-5JEJ!3$28p:!#~^I/*':+!i(Q "%((Q/!;135>6/6/!#1e(+*'576 8 :+!=~^I/!#8U(+*'6/? T 5S;,iI 8U(LM57$'$05 T 13!3:(+">*'6b./:+5J1!=E/I/:!#8s(5;"[Z4"%*0$y(Q/! T 5^yN/ORQ/!=:!">:!f(Q :!=!,-" U5>: T 5S;,-5JEJ!3$28R(+Q "4(Q "[Z7!pA.C578!=E|NORQ/!#8H!">:!w6^(+!3?>:V"4(+!=E-S!3:+ZS*013!=8ÁYw6^(VS!=:Z/Äel !*vdy!3:+!36^(*2"4(+!=E;S!=:ZS*21!#8Á!*vd|S!=:Z/Ä]">6 E-$0"78U(+$'@ 5oI/$'(*'& `:5>(5J157$/¾«">A!=,9!=6^(p576Bw6^(eS!3:+Z T Q/*0$'! 5 `¾r*28". ">1Vx7!(H&cLM5>: T "%:VEJ*'6 ?g81VQ !3,-!-Q "[ZS*'6/?(+Q/! "7EJT Z4"%6^(+">?>!=8_5>LAC5%(Qbw6^(VJ!3:+Zg"%6 E !*vd|S!=:ZyN E
;j
4
A
HJ KL EMN
w6^(!=?>:V"4(+!=EqS!=:ZS*21!=8iÁMw6^(VJ!3:+ZJÄBo5 5JEJ!3$
*'6<1$0I EJ!=8( 5h(U@S.L`8H!=:ZS*21!=8(+"%:+?>!3(!#E(5 "%:VE:+!=">$v&c(*0,-!(:V"4;1>_?7I "%:V"%6^(+!3!=E >" 6 E./:!#EJ*21e(*0Z>!8!3:+ZS*013!>Nj(*06^(!=?>:V"4(!#8_(Q/!#8H!8!3:+ZS*013!=8 T T *'(Qq135>6^(:+5>$0$'!#Eg$0*06/x8Q ">:*06/? l/">6 T E*v(*08E/!=8*'?76/!=E(5 T 5>:+x T !3$0$ T *'(Q ,iI/$v(+*01=">8H(">8 T !=$'$">8I/6/*213">8H((+:+"%h1>Nw6^(+8!3:+Z:+!=~^I/*0!3:V8!{J./$0*21*'(:+!=85>I/:V1!p:+!=8!3:+Z["%(*05>6(5gA6/!7l T Q *01VQo*06o(I :6o:+!=~^I/*0:!#8 5 T &w8.IJ(+!3:V83N ORQ/!w6^(+!3:+6/!(jQ "78z(5AC!I 8!=E-"78j"157,9,-576i./$2"4(LM5>:+,°LM57:jA<5>(Qh:+!=">$v&c(*0,-!R">6 E96/5>6/&c:+!=">$v&c(*0,-!s(+:+"%;1"%6 Ei(QSI 8`./:+!=1$0I EJ!#8 (+Q/!6/!3!#E(5;EJ!#8H*0?>6b"-. ">:+">$'$0!3$k*06JLM:V">8H(:+I 1e(+I/:!fLM57::!#"%$'&)(+*',-!p(:V"4;1>N 8!5%Lz!{J*08H(*06/?hw6^(!=:6 !(H&$2"[@>!3:R./:+5%(+5J15>$jÁY!>N ? N0l/ sÄsLM57: :+!=">$v&c(*0,-!E/"%(+"i*08s./:+5>.C578!=E;85X(+Q "4(R!=135>6/57,X@95%L135>,-,XI 6/*01="4(+*'576"%6<Eh*'6^(+!3:+5>.C!3:V"%A/*0$'*'(U@-A6/&cw6^(VJ!3:+Z 6/!3( T 57:xJ8j1="%6;AC!f:!#"%$0*'m=!=EkNzORQ/!3:+!8Q/5>I $0EhAC!p"8H*06/?7$'!f8H!=:ZS*21!,-5JEJ!3$CA/IJ(R. "71Vx>!(_81VQ/!#EJI/$0*'6 ?i"%6<Eh">EJ,-*288*'576g1576^(:+5>$ ,-!#1VQJ& ">6/*08,1="%6bZ4"%:+@>N
"!$#%&'!)(**,+-.#/0 1 2 $3 # $+%#454,6 78#9 :;#1< =#/0>3 #?=$@ <#?=$ < %>*%# % <1:* A .@ #+6B # C#9 .
%> % 6D <" 45#2# "#/0>3 # C#9E . 2 F
V/Î
Version 2 CSE, IIT Kharagpur
w6^(VJ!3:+Zo*',-./$0!3,-!36^(V"4(*05>6BQ ">8LM57I/:*',-.C5>:(+">67(157,-.<576/!36^(+8=(+Q/!h8H*0?>6<"%$0*'6/?./:+5%(+5S135>$RÁY sÄlk(Q !-"7EJ,-*08+8*'576r15767(+:57$ :+5>IJ(+*'6 !>ls(Q/!r13$0"788*'W !3:h"%6<EF(+Q/!q. "71Vx>!3(h8+1VQ/!#EJI/$0!3:#NuLa(!=:;(+Q/!o:!#8H57I/:V1!:!#8H!=:Z4"4(+*'576">6 EÍ13">$'$"7EJ,-*08+8H*05>6Í./:+5J1!#88!=8-"%:+! 135>,-./$0!(!7l T Q/!=6"9:+5>IJ(+!3::+!=1!=*'Z7!=8R"9. ">1Vx7!(#lS(Q/!13$0"788*vW8+8*vW<1="4(+*'576"%6<Eg*06 8!3:(+8_(Q !. ">1Vx7!(*'6o"-8.8!=E576b(Q/!X13$0"788*'W<13"%(*05>6:!#8HI/$'(=N_ORQ/!. "71Vx>!3(8+1VQ/!#EJI/$0!3: T *0$'$|(Q/!=6q81VQ/!#EJI/$0!(Q !. ">1Vx7!(">1=157:+EJ*06/?7$'@h(+5h,-!3!(*v(V8 T 5S;:+!=~^I/*0:!=,-!36^(+8=N n*0? N Î7Î 8Q/5 83lCQ/5 (Q !=8!i157,-.<576/!36^(+8,-*'?7Q^(W/(f*'6^(5"%6q :57IJ(!=:(Q<"4(pQ ">8A:V"4(+!=E 8!3:+ZS*013!=8=N«ORQ/!_:57T IJ(!=:Q T "78( T 5A/:5^">EpLMI 6 1e(+*'576 "%$JEJ*0ZS*08*'576 8=k(Q/!_LM57: T "%:VEJ*06/?. "%(QXAC!3$05 T (Q !RE/5>I/A/$0!_Q/5>:+*'m=5>6^(+">$>$0*'6 !>l>">6 E(+Q/! A "71VxS?>:+5>I/6 E15JEJ!"%AC54Z>!f(+Q/!$'*06/!7N`ORQ/!pLM5>: T "%:VEJ*'6 ?i. "%(Q5%L(Q/!:+5>I/(!3:*28!3{S!#1IJ(+!=ELM5>:!=Z>!=:@;.<">1Vx>!3(R">6 E,XI 8H((Q !3:+!LM5>:+! AC!Q/*0?>Q/$0@;5>./(*0,9*0m3!#EkN]w6 EJ!=!=Ekl *'6b,-578H(157,9,-!=:+13*0">$C:+5>I/(!3:V8=l^*'(*28*',-./$0!3,-!=67(+!=E*06Q<"%:VE T ">:!7N ORQ/!gLM5>: ">:+E/*'6/?r. "4(+QK*08-EJ*0ZS*0E/!=Eª*06^(5B(Q/:+!3!8H!#1e(*05>6<83h*06/./IJ(hEJ:+*'Z7!3:#l]w6^(!3:+6/!3(XLM5>: "%:VEJ!3:#l">6 EK57IJ(. IJ(-E/:*0Z>!=:=NDORQ/! w6^(!=:6 !(_LM5>: T T ">:+EJ!=:s*06^(!=:./:+!(V8j(+Q/!p FQ !=">E/!3:#Nzn 5>:R!="71VQ;. "71Vx>!(#lJ"%6gw6^(+!3:+6/!(RLM5>: T "%:VEJ!3:sT !{J!=13IJ(!#8_"98I/*v(+!&wEJ!3.C!36<EJ!36^(1$2">8H& 8*vW8+8!=8(Q/!h. "71Vx>!3(p">6 Eq*'(+813$0"788(5(+Q/!;"%./. :57./:*2"4(+!X57IJ(./I/(E/:*0Z>!=:=N9u13$0"788*'W !3:p,XI<8U(AC!9AC5%(+QB?7!36/!=:+">$ ">6 E!;1*0!36^(=Njn 5>:!3;1*0!36 13@>l "-157,-,9576,-!#1VQ "%6/*28,8Q/5>I/$2EA(Qb:+!=85>I/:V1!p1$2">8+8H*'W<1="4(*05>6b"%6<Eg:+5>IJ(+!p$'5S5>xSI/.«N ORQ/!57IJ(. IJ(EJ:+*'Z7!3:R*',-./$0!3,-!=67(V8R(Q !. ">1Vx7!(81VQ !=EJI/$0!3:#N ORQ/!A ">1VxS?7:57I/6 E-15JEJ!*08R8*',-./$0@-$'5^">EJ!#Eh*'6^(+5X:+5>IJ(+!3:`,-!=,957:@h">6 Eh!{J!#1IJ(+!=EhAS@h"?7!36/!=:+">$v&./I/:+.<5^8H!Ì NSORQ/!=8!A<">1Vx^& ?7:57I/6 Eh:+5>IJ(+*'6 !=8R1:+!="%(!E "4(+"98H(:+I 1e(+I/:!#8s(Q "%(135>6^(:+5>$<(Q !LM57: T "%:VEJ*06/?X. "%(Q|N]ORQ/!p:+5>IJ(+*'6 ?i"%?7!36^(R*',-./$0!3,-!36^(V8_"i. ">:H(+*013I/$0">: :+5>IJ(+*'6 ?. :5>(5J157$j"%6 EDA/I/*0$2E/8"b:+5>IJ(+*'6/?oE/"%(+">A ">8!>N;ORQ/!h:+!=8!3:+Z4"4(+*'576B8!(I .K"%?>!=6^(p*0,-./$0!3,-!36^(+8(Q/!h./:+5%(+5J15>$]I<8H!#Er(+5q8H!3( I/.B:!#8H57I/:V1!X:+!=8!3:+Z4"4(+*'576 83NfL_"7EJ,-*08+8*'576r15767(+:57$?7*'Z7!=8(Q/!hS\ -LM5>:";6 ! :+!=~^I/!#8U(#lk"%././:+5>. :*2"4(+!X1VQ "%6 ?>!=8f"%:+!X,h"7EJ!X(+5 (+Q/!i13$0"788*vW6 Eb. "71Vx>!(f81VQ/!#EJI/$0!3:fE/"4(V"%A "78H!(+5;*0,9. $'!=,9!=6^((+Q/!iEJ!#8H*0:+!=E T T 5^kN!=:@:57IJ(!=:8I/./.C5>:(+8">6r"%?7!36^( LM57:_6 !( T 5>:+xh,-">6 "%?7!3,-!36^(#NORQ/*28"%?7!36^(R,XI 8H(A1Vx7!(81VQ !=EJI/$0!3:E/"%(+">A ">8!=8`(5h8!(I/. 135>6^(:+5>$0$'!#E$'*06/x8Q ">:*06/?;"%6<Eg(+5g8!("7EJ,-*08+8H*05>6o135>6^(:+5>$k.C5>$0*013*'!#83NRORQ/!*0,-./$0!3,-!36^(+"%(*05>6bLM:V"%,-! T 5>:+xhLM57:"-Q/578H(*28?7!36/!=:+">$'$0@ 8*',-*0$0">:p(5b(+Q "4(LM57:"b:57IJ(!=:=l T *'(QD(+Q/!;">E/E/*v(+*'576D5>LR">././$0*01="4(+*'576 83Nh"%(Q/!=:(Q<"%6DA:+*0?>*06 "4(+!=8 ">6 Eo(+!3:+,9*06 "%(!=8*06B"%6B"%././$0*213"4(+*'576|Nu6D"%././$0*213"4(+*'576q6/!=!=EJ*06/?b";:+!="%$'&c(*0,9! T 5^LM57:f%" 5 T ,iI 8U(85>,-!3Q/5 T *06SZ>5>x7!X"$'5J13">$ :+!=8!3:+Z4"4(*05>68H!3(I/.o">?>!36^(#N u88U(V"4(!#E!="%:+$0*'!=:_w6^(eS!3:+Z;Q "78RA6/!#E;(+5h./:54ZS*2EJ!( T 59(U@S.:"%. ./$'*213"%(*05>6 8R:+!=~^I/*0:+*'6/?iW/{J!=EbEJ!=$0"[@hAC5>I 6 E E j:+!=EJ*21e(+*'Z7!S!3:+ZS*013!LM5>:`">././$0*01="4(+*'576 8]:+!=~^I/*0:*06/?./:+5>A ">A/*0$'*28U(+*01E/!3$2"[@XAC5>I/6 E|NzORQ !*0,9. $'!=,9!=6^(+"4(+*'576 8]5>LC(+Q/!?7I "%:V"%6^(+!3!=E 8H!=:ZS*21!"%6<E9(Q/!. :!#EJ*01(*0Z>!8!3:+ZS*013!R">:!E/!W 6/!#E-*'6-(+Q/!?7I "%:V"%6^(!=!=Ei8H!=:ZS*21!nzÌ 8 1Î V < "%6 E9(+Q/!135>6^(:+5>$0$'!#EX$057"7E-8H!=:ZS*21! nÌ 8 à V;< l/:!#8H.C!=1(*0Z>!=$'@7N ORQ/!pw6^(VJ!3:+Zg"%:V1VQ/*'(!=1(I/:+!f:!=./:!#8H!=6^(+8_"XLMI 6 E/"%,-!=67(V"%$«1VQ<"%6/?7!(+5i(+Q/!pw6^(!3:+6/!3("%:V1VQ/*v(+!=1(I/:+!A IJ(*v(*28RA6S@ ./:+5>A $'!=,-8=l T Q/*21VQ,h">x>!=8R*'(Z>!=:@;E/*v;1I $v((+5hEJ!3./$054@>N`J5>,-!p5%L(Q/!p*0,9.C5>:(+">6^(./:57A/$0!3,h8"%:+!(+Q/!pLM5>$0$05 T *'6/?< T E ORQ/!i">,-5>I/6^(5>Ls8U(V"4(+!X*06JLM5>:+,h"4(*05>6o*06 13:!#">8!=8. :57.<57:H(+*'576 "%$0$'@ T *v(+Qq(+Q/!X6SI/,iADL 5 T 83NfORQ/*28./$2">13!=8f";QSI/?7!X8U(+5>:& "%?7!_">6 E./:+5J1!#88*'6 ?54Z7!3:+Q/!="7E5>6i(Q/!R:+5>IJ(+!3:V83NORQ/!3:+!LM57:!7l[(Q/*28]"%:V1VQ/*'(!#1e(I :!REJ5S!=86/5>(`81="%$0! T !3$0$J*'6i(Q !_w6^(+!3:+6/!(j157:!7 E ORQ/!9:!#~7I *':+!3,-!36^(f5>6r:+5>I/(!3:V8*08fQ/*0?>Q|Niu$0$:+5>I/(!3:V8,XI 8H(f*0,-./$0!3,-!36^( zl|">EJ,-*288*'576r1576^(:+5>$cNl 5rn 1$2">8+8H*'W<13"%(*05>6 "%6 E. "71Vx>!(8+1VQ/!=E/I/$'*06/?< E A/*2~^I/*'(5>I<8_E/!3./$054@S,9!=6^(_*28_:!#~7I *':+!=E-LM57:R?>I ">:+">67(+!3!#E;8H!=:ZS*21!7Nw6 13:!=,-!36^(+">$yE/!3./$054@S,9!=6^(_5>LzÌs5>6^(:+5>$0$0!=ES&w¾|5^">E;S!=:ZS*21! *08R.C578+8*'A/$0!fA^@EJ!3./$054@S*'6 ?hÌs5767(+:57$'$0!=EJ&¾«57">ES!3:+ZS*013!f">6 E GLMI/6 1(*05>6 ">$'*'(U@g"%(_(+Q/!AC5%(H(+$'!=6/!=1Vxg6/5JEJ!=8R5>L"9EJ5>,h"%*06 "%6 Eg(I 6/6/!3$0*06/?-(Q/! Í,-!=8+8+"%?>!#8_54Z>!3:_5%(+Q/!3:.<"%:(R5>L(+Q/!EJ57,-">*'6«N VÃ
Version 2 CSE, IIT Kharagpur
;j
4
E K E A
$H K LBE MN
O5h54Z>!=:+135>,-!(+Q/!$0*',-*'(+"%(*05>6 85>Lw6^(eS!3:+Zyl/U`OnF./:57.<5^8H!#E !*'dC!=:!=67(+*0"%(!#EqS!3:+ZS*013!=8Á !*'dkS!=:Z/Ä 8 Î ( < l Q/*01VQb*288*',-./$0!3:">6 E -, 5>:+!X8+13">$0">A/$'!7N !*vd|S!=:Zb:+!=EJ!3W 6/!=8(Q/!9 jZ $gOs@S.: jZ = O:+"%;19Ìs$2">8+8 _T @^(!i"78EJ*'dy!3:+!36^(*2"4(+!=E 8!3:+ZS*013!Á!p/Ä]WLC(+Q/!W8 !fÌs5SE/!.<57*'6^(#l Q/*21VQ Q/!=6;,h"%:+x>!=E-EJ*'dy!3:+!36^($0@i*06 EJ*213"%(!#8 (+Q/!A8R.C!3:&cQ/57.AC!3Q<"[Z^*05>:57: `¬ Ä_!#">1VQ:57IJ(!=:_*28:+!=~^I/*0:!#Eh(+5;T "%././$0@hT (+59*06 EJ*0ZS*0E/I "%$|.<">1Vx>!3(+8=N ORQ/!*'6/LM5>:+,-"%(*05>6ª:+!=~^I/*0:!#EPAS@B(+Q/!gA IJdC!=:i,h">6 "%?7!3,-!36^(i">6 EK8+1VQ/!=EJI $'*06/?q,-!=1VQ<"%6/*28H,h8i*08i13">::+*'!#E *v(+Q/*06K(Q !g. "71Vx>!(#N ORQ/!=:!3LM5>:+!>l/EJ*'dy!3:+!36^(*2"4(+!=Eb8H!=:ZS*21!#8EJ5h6/5%(:+!=~^I/*0:+!p8.C!=1*2"%$8H*0?>6 ">$'*06/?-./:+5%(+5S135>$28_(5;135>6^(:+5>$y(+Q/!,-!=1VQ ">6/T*08,h8R(Q<"4("%:+!pI 8!=E (+5B8!3$0!=1e(-EJ*'dC!=:!=67(i(:+!="%(,-!36^(XLM57:X(+Q/!*'6 E/*'ZS*2EJI "%$_. "71Vx>!(V83NªÌs5>6 8!=~^I/!=6^($0@>l(Q/!b"%,-57I/6^(X5%L8H(+"%(!*'6JLM57:,h"%(*05>6|l T Q/*21VQK*28 :+!=~^I/*0:!#EB(5qAC!g,h"%*06^(+">*'6/!#ED.6 EP6/5%(i./:57.<57:H(+*'576 "%$j(5o(+Q/! 6SI/,iA:R*',-./:+54Z>!=,-!36^(_54Z7!3:Rw6^(VS!=:ZyN u 1I<8U(+5>,-!3:,iI 8U(Q "[Z7!8H!=:ZS*21!f$'!=Z>!3$|">?>:+!3!=,9!=6^(pÁcJ¾«ufÄ *v(+Q*'(+8RH G*06b5>:VEJ!3:_(+59:+!=13!3*0Z>! !*'d|S!3:+ZyN`u6oJ¾«uº8.C!=1*'W !#8 (+Q/!;1$2">8+8p5%L8H!=:ZS*21!-8HI ./.<57:H(+!=EP"%6<Eq(+Q/!;"%,-5>I 67(5>L`(+:+"%h1hT ">$'$05 T !=Eq*06P!="71VQD13$0"788=Nhu6KJ¾«u 1="%6PAC!;8U(V"4(*2195>:EJ@S6 ">,-*01>N ^(V"4(+*01J¾u8">:!f6/!3?75%(+*0"%(!=Eg5>6b"9:!=?>I/$2"%:#l7!7N ?lSA ">8*283N`ÌsI 8H(57,9!=:+8 T *'(Q !@^6<"%,-*01J¾u8R,iI 8U(I<8H!p" 8*'?76 "%$0*06/?i. :5>(5J157$)lJ!7N ? :8!3:+Z^*21!#8_5>6bEJ!3,h"%6<EkN
;j
4
4@ 4
M E BADC
C
)
E HJ KL MSEF
M @B
8 $ = < *08f157,9.C578!=Eb5>Lj"h6SI/,XAC!3:5%LzLMI/6 1(*05>6 ">$!=$'!=,9!=6^(+8=l<6 ">,-!3$0@. "71Vx>!3(1$2">8+8H*'&
ORQ/! !*'dC!=:!=6^(*2"4(!#ErS!=:ZS*21!=8"%:V1VQ/*'(!=1(I/:+! W !=:+8=lS(:V"4;1p1576 EJ*'(*05>6/!=:+8">6 E..LM5>: T "%:VEJ*'6 ?iAC!3Q "[ZS*05>:V8pÁ `¬ ÄeN/ORQ/!#8H!">:!pEJ!=8+1:+*0A½ ]">1Vx7!(;1$2">8+8*vW<1="4(+*'576G*28h6/57:,h"%$0$0@FEJ5>6 !q"4(h(Q !q!=EJ?7!o5%Lf(Q/! !fÍEJ57,h"%*06AS@G. ">1Vx7!(g1$2">8+8*vW !=:+8=l T_!3Q/Q<*21V"[QGZ^*085>!3:-$0!=u1(h?7?>. :+">!31V?^x7"4!((+!D8iÁ A R"7u8H!#Ä-EK13$05>"76F88(*'W Q/!3!b:#l1576^Q/(!3*21V6^Q(-85%!3Lf$0!=. 1">(+1V89x7. !(i"71VQ x>!=!">(VE/89!3A :V83">NK8!=EGO T 5>5r6F(U(@SQ/.C! !=89!p5%LfÌs15J$2">EJ8+! 8Hz*'W 5>!3*0:V6^89(9"%57:+6/!$'@713lsI/">::+6 !3EK6^(+(+$'Q/@ª! EJ5o!3W I/6/$'!=(E|*'&gn*0(+!3Q/$2E ! Á 5qn]Ä1$2">8+8*vW !=:=l T Q *01VQo.C!3:LM5>:+,h8R(Q/!i8H!=T $'!#1e(*05>6bA "78H!#E5>6(Q/!i15>,iA/*06 "4(+*'5765>L]5>6/!57:,-5>:+!fQ !=">E/!3:W !=$0E 83lC8HI 1VQo"788H57I/:V1! "7E/EJ:+!=8+83lJEJ!#8U(+*'6 "%(*05>6o">E EJ:!#88=l^(U@S.Lz8!3:+ZS*013!AS@^(!7l/./:+5%(5J135>$28s !il 85>I/:V1!f.C5>:(6^I ,XAC!3:"%6<EEJ!#8U(+*'6<"4(*05>6b.C5>:(6^I ,XAC!3:#N s¶4¯ K´ÇX»C±Æ·Yµ=·Y»C±Å7¶ 7½oO«:V"4;1g135>6 E/*v(+*'576/!3:V8LM57:, (+Q/!,-5^8U(-ZS*v(V"%$R. "%:(i5>L"rE/*vdy!3:+!36^(*2"4(+!=EG8H!=:ZS*21!=8X6/!( 5>:+xyNDORQ !3*0: ?757"%$]*28f(5q">././$0@B135>6 EJ*'(*05>6 *'6/?LMI/6<1e(*05>6<85>6B(Q !;./:+!3ZS*'57I 8$'@q13$0"788*vW1Vx7!(V8f"713135>:VEJ*'6 ?(+5o"b./:!#EJ!W<6/!=EPTO:+"%h1;Ìs$2">8+8 S.C!=13*vWC13"4(+*'576b*'6oJ¾«uXN u (:V"4;1p1576 EJ*'(*05>6/!=:1576 8H*28H(+8R5%Lz5>6 !f57:,-5>:+!5>L(+Q/!pLM5>$0$'5 T *06/?-157,9.C5>6 !36^(+8= 5o!3(!=:=]uºEJ!=Z^*21! T Q *01VQ,-!=">8I/:+!=8s(Q !p(!3,-.C5>:V"%$k./:+5>.C!3:(*0!=8R5>Lz"i(+:+"%h1p8H(:+!=">,8H!=$'!#1e(+!=EA^@"h1$2">8+8H*'W !3:#N 5q">:x7!3:#uºE/!3ZS*013!f(Q "%(8H!3(+8R(+Q/! !foÌs5JEJ! z5>*067(R*06b"9. "71Vx>!3(RA<">8!=E5>6 T !=$'$'&E/!W 6/!#Eg:+I/$0!=8=N SQ<"%.C!3:#`u°EJ!=Z^*21!p(+Q "4(E/!3$2"[@S8. ">1Vx7!(+8 T *'(Q *'6q"9(+:+"%h18H(:+!=">, (5;1="%I 8!p(Q !X8U(+:!#"%, (+5;1576JLM5>:+, (+5;8H57,9!E/!W 6/!#E(:V"4;1 ./:+5%W<$'!hÁ)J!3!XS!#1e& V N = ÄN !:57./.C!3: + z5>$0*21!3:#uºE/!3ZS*013!f(Q "%(EJ*08+13">:+E 8R. ">1Vx7!(+8_A "78H!#Eg5768.C!=1*'W !#E:+I/$0!=8ÁcS!3!XS!#1%N V N = ÄeN Å7¶ ;o» iÅSȯ C|·)» Q ¶ # 4; &4½«u s¬ *08f"gE/!=8+1:+*'.J(+*'576o5%L](+Q/!X!3{^(+!3:+6 "%$0$0@57A 8!3:+Z[">A/$0!pLM5>: ">:+EJ*06/?hAC!3Q "[ZS*05>:5%L`";EJ*'dy!3:& !=67(+*0"%(!#Eq8H!=:ZS*21!#86/5JEJ!>ly"%. ./$'*0!=Eo(5"g15>$0$0!=1e(+*'576o5%Lj. "71Vx>!3(+8 T *'(Qr(Q/!98">,9!!frÌs5JEJ! z5>*06^(T (Q "%(f">:!13:5^88*'6 ?;";$0*'6/x*06r" . ">:H(+*013I/$2"%:EJ*0:!#1e(+*'576DÁ)13"%$0$0!=EbEJ*'dC!=:!=67(+*0"%(!#E8!3:+ZS*013!=8_AC!3Q "[ZS*05>:"%?7?>:+!3?^"4(![ÄeNz`"71VQ8!3:+ZS*013!p13$0"788R*28"7885J1*2"4(!#E T *'(Qq" `¬ fN s¬ R8">:!9EJ!W<6/!=EB*'6r(!=:,h8f5%L`AC!3Q<"[Z^*05>:p1VQ ">:+"71e(!=:*28H(*2138:+!3$0!3Z4"%6^(f(5b8H!=:ZS*21!i./:54ZS*28H*05>6 *'6/?h.C5>$0*21*0!=8=l|"%6 Er6/5%(p*'6r(!=:,h8f5%L . ">:H(+*013I/$2"%:]*0,9. $'!=,9!=6^(+"4(+*'576 8=N s¬ R8],h"[@i">$085pAI :+13!_. :*05>:+*v(U@X:!=$0"%(*0Z>!_(55>(Q/!=: `¬ _8=l>57: *06g(+!3:+,h8s5>L|(Q !3*0::!=$0"%(*0Z>!57A 8!3:+Z[">A/$0!(:V"4;1f1VQ "%:V">1(!=:*28U(+*01=83N]ÌsI/:+:!=67(+$'@-(+Q/!3:+!p"%:+!(+Q/:!=!. :57.<5^8H!#E `¬ _8s(+Q "4("%:+!A :*0! @ EJ!#813:*0AC!=EAI/$v(Á !fsÄ `¬ G*28`(Q/!f15>,-,-5>6«l7AC!=8H(H&!dy5>:(jLM5>: T "%:VEJ*'6 ?"[Z[">*'$2"%A $'!*06;(+5SE "[@C© 8]w6^(!=:6 !(=Nz F. ">1Vx7!(+8j,-">:x7!=E LM5>:`(Q/*28R8H!=:ZS*21!">:!f8H!=67(_*'6^(+5i"6 !( T 5>:+x T *'(Q/57IJ(_"7EJQ/!=:*06/?(+5i">6^@9. ">:H(+*013I/$0">:`:+I/$0!=8_"%6 E-(+Q/!f6/!( T 5>:+x T *0$0$CEJ!=$'*0Z>!=:_"78 ,h"%6S@;5%L(Q/!#8H!.<">1Vx>!3(+8R">8R.C578+8*'A/$0!"%6 Eb"788H5S5>6b">8_.C578+8H*0A/$0!A/IJ( T *'(Q/57IJ("%6S@;?7I "%:V"%6^(+!3!=8=N E u8+8HI :!#E;n/57: T "%:VEJ*06/?gÁYun]Ä s¬ Í*28R"X,-!=">6 8sLM5>:R"X. :54ZS*2EJ!3:_EJ*vdy!3:+!36^(+*0"%(!=E8!3:+Z^*21!#8`EJ57,h"%*06;(595%dy!3:EJ*'dy!3:+!36^(_$0!3Z7!3$28 5%LLM5>: T ">:+EJ*06/?-">8+8HI :+">6 1!#8jLM57: G.<">1Vx>!3(+8R:+!=13!3*0Z>!=E;LM:57,"h1I<8U(+5>,-!3:EJ*'dy!3:+!36^(*2"4(+!=E8H!=:ZS*21!=8REJ57,h"%*06|N
V/V
Version 2 CSE, IIT Kharagpur
ORQ/!j{J.: "%:VEJ*'6 ?KÁY`n]Ä `¬ *28-"qQ/*0?>QF./:*05>:+*'(U@BAC!3Q "[ZS*05>:9"%6 EF*089EJ!W<6/!=EG">89"oLM5>: "%:VEJ*'6 ?b(:+!="4(+,-!36^( LM5>:"-. ">:H(+*013I/$2"%:EJ*'dC!=T :!=6^(*2"4(!#Eb8H!=:ZS*21!=8">?>?7:!=?7"4(+! T Q !3:+!(+Q/!XEJ!=. "%:(I :!p:V"4(!5>L(+Q/!X">?>?>:+!3?^"4(+!>© T8`. "71Vx>!3(+8_LM:+5>,">6S@ !fS&135>,-./$0*0">67(-6/5JEJ!,XI 8H(-!=~^I "%$R57:i!3{J13!3!#EF"D15>6/W ?>I/:V"%A $'!:+"%(!>NKORQ !sn (:V"4;18Q/57I/$0EFA$'$05J13"4(+!=EP(+Q/*28-:+"%(! *'6<EJ!3.C!36 E/!36^($0@g5>L«(Q !*'6^(!=6 8*v(U@5%L">6S@;5%(+Q/!3:R(+:+"%h1p"%(H(!=,-.J(*06/?-(5-(+:+">6 8*v(R(Q !6/5JEJ!>N § E !=">$v&c(*0,-!r157,-,XI/6/*213"%(*05>6 :+!=~^I/*0:!=,-!36^(+8h5>LX"%./. $'*213"%(*05>6 8"%:+!o!{J./:+!=8+8H!#EÍ*'6 (+!3:+,h8;5%LX13!3:(+">*'6~^I ">$'*'(U@G5>L8H!=:ZS*21! Á T 5S/Ä. ">:+">,-!(!=:+8=Npu :+!=">$v&c(*0,-!X./:+5%(+5S135>$?>I ">:+">6^(!3!#8R(Q ! T 5Sb:+!=~^I/*0:!=,9!=6^(5%Ls">6B">././$0*01="4(*05>6«lC576 1!i*v(">1=1!=.J(+8f" 1576/6/!=1(*05>6:!#~^I/!=8H(=N E !=">$v&c(*0,-!157,9,iI/6/*213"%(*05>69./:5>(5J157$08]">$'$05 T A<5>(Q-6/5>6/&c:+!=">$v&c(*0,-!R">6 E-:+!="%$'&c(*0,9!R,-!=8+8+"%?>!#8(5AC!Q ">6 EJ$0!=E9*'6-(+Q/!8+"%,-! LM:+">,-! T 5>:+xCN E w6g(+Q/!w6^(!=:6/!3(!36SZS*':+5>6 ,9!=6^(=lS5>6/$0@85%La(:+!=">$v&c(*0,-!p135>,-,XI 6/*01="4(+*'576*288HI ./.<57:H(+!=EkN Î N^(+"%(! T Q !(Q !3:9@>5>Iª135>6 8*0E/!3:(+Q/!hLM57$'$05 T *'6 ?r8U(V"4(+!3,-!36^(+8(5qAC! 5>:iÊy¹ 2 XN >I<8U(+*vLM@P@>57I/:X">6 8 T !3:X*'6K!#">1VQ 13"78H!7N ÁY"^Ä^(+:!#"%,-*06/?h15>,-./:+!=8+8!=E;ZS*2EJ!35-(+:+">6 8,9*28+8H*05>6*08">6!3{/"%,-./$0!f5>L:+!=">$v&c(*0,-! RÁYZ4"%:+*0">A/$'!pA/*'(:V"4(![Ä`(:V"4;1%N ÁMA<ÄORQ/!rZ^*0:(I ">$(*0,-!q./:+5%(5J135>$*28;"%6 !3{/"%,-./$0!o5%L"ªA<57I/6 EJ!#E ">1=1!=8+89(U@S.1313!=8+8 6/!3( T 57:xyN ÁY1=Äw6À"PAC5>I 6 EJ!=EÀ">1313!=8+8-(57x>!=6:+*06/?K./:+5%(+5S135>$I<8H*06/?ª!3*'(Q !3:;(+Q/!r. :57.<57:H(+*'576 "%$57:;(Q !q$'5J1="%$(+:+">6 8,9*28+8H*05>6(*0,-! ">$'$05J13"4(+*'5768+1VQ/!=,9!#83lS(+Q/!8I/,h8R5%L(Q/!8@S6 1VQ/:+5>6/57I 8`A<"%6 E T *2ES(+Q 8 !=~^I ">$08 Î N ÁYE Ä 6 EJ!3:6/5>:+,h"%$y:!#"%$'&)(+*',-!f(:V"4;1p1576 EJ*'(*05>6 8=lS(Q !,-"%{J*',iI/,EJ!=$0"[@g8IJdy!3:+!=EAS@;(Q !fQ *'?7Q/!=8H(./:+*'57:*'(U@h. ">1Vx7!(V8_"%( "h8 *v(V1VQ Q/!36o"9,XI/$'(*'&$'!=Z>!3$nUnz\°~^I/!=I/!&A "78H!#E8!3:+ZS*013!pE/*08+1*0./$0*'6/!*28EJ!=./$054@>!=E T 5>I/$2EgAC!$05 T !=:15>,-. ">:!#E;(+5 (+Q/!T 13"78H! T T Q/!=6b"iLM:V"%,-*06/?%&A ">8!=E8H!=:ZS*21!pEJ*2813*'./$0*06/!*08EJ!3./$054@>!#EkN ÁM!#Ä!#"%$'&)(+*',-!135>,-./IJ(+!3:157,-,XI/6/*213"%(*05>6*08R!#88!36^(+*0">$'$0@g157,-,XI/6/*213"%(*05>6b"4(Q/*0?>QoE/"%(+"9:+"%(!#83N ÁaL+Ä 6 EJ!3:b6/57:,h">$(+:+"%h1B1576 EJ*'(*05>6 8=l"G./:+*'57:*'(U@~^I/!=I/!&A "78H!#E8H!=:ZS*21!DEJ*08+1*0./$0*'6 ! T 5>I/$2E *06 1I :$0!=8+8./:+5S13!=8+8H*06/? 54Z7!3:+Q/!="7E/8s"%("-8 T *'(+1VQo157,-. "%:+!=E;(5h"-,XI/$'(*'&$'!=Z>!3$|nUnz\º~^I/!3I !&A ">8!=E5>6/!7N ÁM?SÄ;w6D(Q !hZ^*0:(I ">$v&c(*0,-!h./:5>(5J157$)l8HI/. .<5^8H!9(Q<"4((Q !hQ/*'?7Q/!=8H(./:+*'57:*'(U@o. "71Vx>!(p(+Q "4(X"b6/5JEJ!-6/!=!=E/8(5b(:V"%6<8H,-*'("%( 85>,-!*06 8U(V"%6^(5>L(+*',-!*28,bNORQ/!36LM57:!;13*'!=67( 5>:+xS*'6 ?95>Lz(Q/!. :5>(5J157$)l E/I/:*06/?h./:+*05>:+*v(U@g">:A *v(+:+"%(*05>6b*'6^(+!3:+Z[">$ (+Q/!6/5JEJ!8Q/5>I $0E T "%*'(LM5>:à H>(+*',-!I/6 *v(V8T A:+!8U(V"%:(*06/?9(:V"%6 8,-*08+8*'576|NÁ 9*28R(Q/!X./:57. "%?^"4(+*'576EJ!=$0"[@;*06 (+Q/!6/!( T 5>:+xyN Ä ÁMQ<ÄORQ/!h135>I/6^(+E/5 T 6r./:+5%(+5S135>$]8Q/5>I/$2E T 57:xo8I 1313!=8+8ULMI/$0$0@q*':+:+!=8.!95%L T Q/!(+Q/!3:p(+Q/!-./:+*'57:*'(U@q"%:+A/*'(:V"4(*05>6q(:V"%6 8H& ,-*288*'576 8h8H(+"%:( T *v(+Q!=*v(+Q/!3:-(+Q/!o,h8HA5>:h$28AG!=6 EF5>L(+Q/!o./:+*'57:*'(U@ªZ4"%$0I/!>l_">8-$05>6/?ª">8-">$'$6/5JEJ!#8h"%?7:!=!576F(+Q/! 135>6SZ>!=67(+*'576|N ÁY*2Ä`Z>!36 T Q/!=6o"-?>$05>A ">$k./:*05>:+*'(U@7&A "78H!#E;,-!=8+8">?>!(:V"%6 8,-*08+8*'576*288I/./.C5>:(!=EAS@"-:+!=">$v&c(*0,-!157,9,iI/6/*213"%(*05>66/!(& T 5>:+xylS45qu ÁM:V"4(+!p,9576/5%(+5>6/*21p"%$0?>57:*'(Q/,;Äs81VQ !=EJI/$0*06/?-5%Lz:!#"%$'&)(+*',-!p,-!=8+8">?>!=8_*28R*'6 !dy!=1e(+*'Z7!>N Á Än 5>:(+:+">6 8H,-*'(H(+*'6/? R :+!=">$v&c(*0,-!-(:V"4;1h"%,-576/?(+">8xJ8p54Z>!=:"o¾«u¿Xl"o1="%$0!36 E/">:H&A "78H!#Eq:+!=8!3:+Z["%(*05>6B./:5>(5J157$ T Á 6 5>I/$2Á EÍfÄR@S*'*2!=8_$0E(Q/Q/!*'?7?7I Q/!3"%::V"%66^(!=!Á . Ä-:57(+A Q "%"%A/6À*0$0*v!3(U*'@;(Q/"%!=(:IJ"ª(*0$'?7*0m=$'57"%A (*0"%5>$6 ./:*0Ä 5>:+*'(U@7&A "78H!#Ekls57:"ªAC5>I 6 EJ!=EÀ">1313!=8+8-(U@S.$cN ÁYxJÄw6P,XI $v(+*'./$0!hAC5>I/6 E/*'6/?q"[Z7!3:V"%?7!X:V"4(!h1VQ ">:+"71e(+!3:+*'m#"4(*05>6r5%LRA/I/:V8U(U@o(+:+"%;1%lk(+Q/!;$2"%:+?>!3:f*28p(Q/!;"[Z7!3:V"%?7*'6/?*'6^(+!3:+Z[">$ (+Q/!$'5 T !3:R*28R(Q !:+"%(! T *v(+Q T Q/*01VQ(Q !8H57I/:+13!p*08RAC5>I/6<EkN E
V$
Version 2 CSE, IIT Kharagpur
ÁY$2ÄORQ/!-Á ;D 7Äj,-5JEJ!3$CLM57:s:+!=">$v&c(*0,-!(:V"4;113"%6A1e(+5>:+*'$0@9I 8H!#EhLM57:s:+!=85>I/:V1!:!#8H!=:Z4"4(+*'576-(5i./:54ZS*2EJ! T 5S;?7I "%:V"%6^(!=!LM57:157,9. :!#88!=E"%I EJ*05h"%6 EZS*2EJ!35h8*'?76 "%$283N ÁYw6r(+Q/!Á D Ä,-5SE/!3$z(Q !i,-*06/*',iI/, *06^(!3:V"%:+:+*'Z4"%$«(*0,-!9AC!( T !3!=6r. "71Vx>!3(+8*08fAC5>I/6 E/!=EBA6 E(Q/!$2"%:+?>!#8U(R. ">1Vx7!(8H*0m3!*28RAC5>I/6 E/!=Eb"%AC54Z>!fAS@S,h"4{ Ä ÁY,hÄORQ/!,h"4{J*',iI/, EJ!3$2"[@h8HI/dC!=:!#E-A^@-. "71Vx>!3(+8jI 6 EJ!3:R",iI/$'(*0$'!=Z>!3$ynÌ_n]h~^I/!=I/!A<">8!=E;8!3:+ZS*013!EJ*2813*'./$0*06/! T 5>I/$2EhAC! $05 T !=:_(Q ">6(+Q "4(*06o"iLM:+">,9*06/?>&cA "78H!#Eg8!3:+ZS*013!fEJ*28+1*0./$'*06/!I/6<EJ!3:8*0,9*0$2"%:R(:V"4;1p1576 EJ*'(*05>6 8=N ÁM6<Äw6"%6S@-./:+"71e(+*01="%$C:!#"%$'&)(+*',-!135>,-,XI 6/*01="4(+*'576;./:+5%(5J135>$cl T !f1="%6;!3{J.I ">:+">67(+!3!. :57A "%A/*0$0*v(U@oÁ 6 _Ä](+5 AC!1$0578!_(5*fLM5>:]I/(*0$'*0m="%(*05>6-$'5 T !3:z(+Q "%69(+Q/!uZ7!3:V"%?>! _:!#"%xJEJ5 T 6 (*0$0*'m#"4(*05>6oÁ)u Ä]">6 E 6 T 57I/$2Ei">././:+57">1VQ Î ">8_(+Q/!IJ(+*'$0*'m#"4(+*'576*06 13:!#">8!=8_A576 Eu N ÁM5SÄ;Lk"13!3:(+">*'6i(57x>!36/&c. "788*06/?6/!3( T 57:xpQ "78]"1VQ<"%6/6/!=$/13">. ">13*v(U@5>L Î *0*/5oA . 83l#(+Q/!369(Q !_Us` , *^ÃJN (ÁM. :*05>:+*v(U@^&A ">8!=E ./:+5%(+5J15>$aÄ T 57I/$2E. :54ZS*2EJ!pQ/*'?7Q/!3:?7I "%:V"%6^(+!3!p./:+5>A ">A/*'$0*'(U@g157,9.<"%:+!=Eg(5hU`s , *7Ã/N $oÁa(+*',-!#E(5>x7!36./:+5%(5J135>$aÄs"%( Z7!3:+@;$'5 T 1VQ "%6 6/!3$kIJ(+*'$0*0m="4(+*'576 8=N ÁM.<ÄORQ/!135>I/6^(VEJ5 T 6:+!=">$v&c(*0,-!p?>$05>A ">$C. :*05>:+*v(U@;135>,-,XI 6/*01="4(+*'576./:+5%(+5J15>$|8Q/57I/$0E T 5>:+x;8HI 1=1!#88HLMI/$0$'@*':+:!#8H.C!=1(*0Z>!f5%L T"78RQ/$'!357(6/Q/?h!=:">(+8Q/"%!X$0$k. 6/:5J*05>EJ:+!#*v(U8@b"%"%?7:+:A/!=!*'(:V57"46g(+*'(+57Q/6!(+1:+57">6^6 Z78!3,96^*2(8+*08H5>*06«5>6 N 88U(V"%:( T *'(Qq!=*v(+Q/!3:(Q/!i,h8HAq57:$28HAr!36 Eo5>Lz(Q/!9./:+*'57:*'(U@gZ4"%$0I/!7l Á)~SÄ`Z>!36 T Q/!=6o"-?>$05>A ">$k./:*05>:+*'(U@7&A "78H!#E;,-!=8+8">?>!(:V"%6 8,-*08+8*'576*288I/./.C5>:(!=EAS@"-:+!=">$v&c(*0,-!157,9,iI/6/*213"%(*05>66/!(& T 5>:+xylS45qu ÁM:V"4(+!p,9576/5%(+5>6/*21p"%$0?>57:*'(Q/,;Äs81VQ !=EJI/$0*06/?-5%Lz:!#"%$'&)(+*',-!p,-!=8+8">?>!=8_*28R6/5%(Z7!3:+@h!dy!=1(*0Z>!>N Ã/N#!@S6 ">,-*011VQ "%6/?7!=8z(+5(+Q/!:+!=8!3:+Z>!#E9:!#8H57I/:+13!=8]*28_"%6h*0,9.C5>:(+">6^(_EJ*28U(+*'6 ?>I/*28HQ *'6/?91VQ "%:V">1(!=:*28U(+*01R5>Lk(Q/!f K./:+5%(+5S135>$cN 8*'6 ?oLM5>I/:X5>:W!;8!36^(!=6 1!#8!{J./$2"%*06ªQ/5 T º./:+5%(5J135>$j*28X1="%. ">A/$'!g5%LEJ@S6 "%,-*213">$'$0@B1VQ ">6/?>*06/?b(+Q/!g:+!=8!3:+Z4"4(*05>6 8U(V"4(+I 8R5%Lz"h15>6 6/!=1(*05>6bEJI/:+*'6/?9(+Q/!$'*'LM!p(*0,-!5%L(Q/!135>6/6 !=1e(+*'576|N V Nw6K"%6ªUs` , *^ÃJN $o6/!( T 5>:+xyl«*'L b*08(Q/!8HQ 5>:(!=8H(XEJ!#">EJ$0*'6 !;5%L">$'$s,9!#88+"%?7!=8p:+!=~^I/*0:!#ED(5qAC!;(+:+">6 8,9*'(H(+!=EP54Z7!3:(+Q/! 6/!( T 5>:+xylS*0EJ!=6^(*'LM@;(Q !./:5^8R"%6 Eb1576 8R5%L,h"%xS*'6 ?-OOzO !=~^I ">$y(5 ÁY1=Ä ÁYE<Äà ÁY"^Ä ÁMA<Ä $ 6^(!3{S(`5%L|"iÌsQ/!=,-*01="%$ ,h">6^I/LY">1e(+I/:+*'6/?i15>,-. ">6S@(Q<"4( T *28Q/!=8j(5X">IJ(57,-"%(!*'(+8`./:+5S13!=8+8 15767(+:57$k"%././$0*213"4(+*'576| ÁY"^Ä;} Q "%(_. :57A/$'!=,h8s,-*0?>Q^("%:+*08!*'L"%6"4(H(+!3,-.J(*28s,h"7EJ!(+5X*0,-./$'!=,-!36^(R(Q/!p1VQ/!3,-*213">$C. $0">67(1576^(:+5>$<85%La( T "%:+!I 8*06/? (+Q/!](+Q/!3:+6/!(¾u¿°"[Z4"%*0$2"%A/$0!*06(Q/!pLY"71e(+5>:[email protected] ÁMA<Ĭ5 T 13">6o"i?7$'57A "%$y./:+*05>:+*v(U@h./:+5%(+5J15>$kAC!8I/./.C5>:(!=E*06b"-¾u¿ T *'(Qq157$'$0*28H*05>6J&A "78H!#E;">1=1!=8+8 F ÁY1=ÄL45qu 8+1VQ/!#EJI/$0*'6/?i5%L«5>L|. ">1Vx7!(V8`*28j(+5iAC!p8HI/. .<57:H(+!=Ekl T Q "%(s*28`(+Q/!,h"%{S*0,XI , 1VQ "%6/6 !3$CIJ(*0$'*0m="%(*05>6g(Q "%(_13">6gAC! "71VQ/*'!=Z>!#(E F ÁYE Ä} Q "%("%:+!f(Q/!,h"%*065>A 8H(+"71$0!=8_(5-!3h13*'!=6^(*',-./$0!3,-!36^(V"4(*05>6b5>LB5qu *06(Q/*288!(I/9. F (/NÌs5>6 8*2EJ!3:(Q/!iI 8H!i5%L](+*',-!=Eo(5>x7!36q. :5>(5J157$`ÁMUs` , *7ÃJN $^Ä*'6o(+Q/!LM57$'$05 T *06/?g8*v(+I "4(+*'576|N}D!XQ "[Z7!LM5>I :6/5JEJ!#8*06q(+Q/! 8H@J8H(!=,NORQ/!b:!#"%$'&)(+*',-!:!#~^I/*':+!3,-!=67(h*28i(Q "%(;6/5JEJ! AA/$'!(+5B(+:+">6 8,9*'(hI/.J(+5 pA *v(V8-54Z>!3:9!="71VQF.C!3:+*'5JEG5%L EJI/:V"4(+*'576 ,9*0$0$'*aS!=135>6 E 83l Q/!3:+! "%6 E "%:+!?>*0Z>!=6*06o(+Q/!(V"%A/$0!XAC!3$05 Nu8+8HI ,9!X(Q "%((+Q/!X./:+5>.<"%?7"%(*05>6(*0,-!X*28 6/!3?7$'*0?>*0A/$0!15>,-. ">:!#Eh(+5-OOT zO "%6 E(+Q "4((+Q/!6/!( T 5>:+xhA ">6 E T *2ES(Qb*28 Î 5oT A/.<83N ¿5JEJ! 6 Î Î */* pA Î *9,h8H!#1 6<à /à */* pA Î (4,h8!=1 6 V (/*/* pA Î */*%,h8!=1 ÁY"^ÄÌsQ/5S5^8H!8I/*v(V"%A/$0!OOzO ÁM(+"%:+?>!3(R(5>x7!36:5>(+"%(*05>6(*0,9![ÄeN ÁMA<Ä} Q "%(*08(Q/!,h"4{J*0,XI/, (*0,9!pLM57: T Q/*21VQb"9:+!=">$v&c(*0,-!f,-!#88+"%?7!,h"[@g8IJdy!3:*06^Z7!3:V8H*05>96 F ÁY1=Ä57AJ(+">*'6ª8I/*v(V"%A/$0!-Z4"%$0I/!=85>L ÁM(5>(+"%$`6^I ,XAC!3:5%LRA/*'(+8p(+Q "4(X1="%6DA6 EB6 V 54Z7!3:R!3Z7!3:+@;1@J1$0!>N ÄiI/6 EJ!=:./:+5>.C5>:(*05>6 ">$C">6 E$'5J13">$|"%$0$'5J1="4(*05>681VQ !3,-!=8=N
V(
Version 2 CSE, IIT Kharagpur
ÁYE Ä !!(+!3:+,9*06/!-(+Q/! T 5>:V8U(13"78H!9(*0,-!=8AS@ T Q/*01VQD6 Î 135>,-./$0!(!#8f(:V"%6 8,-*v((*06/? Î *0* pAB5%LR:!#"%$'&)(+*',-!-,-!=8+8">?>!9I/6 EJ!=: !#">1VQ5%L(Q/!p( T 5iA<"%6 E T *2ES(+Qb">$'$05J13"%(*05>6b81VQ/!=,-!=8=N ÁM!#Ä !!(+!3:+,9*06/!(+Q/! T 5>:V8U(`1=">8!_(*0,9!A^@ T Q/*21VQ-6 Î 157,-./$'!3(!#8z(:V"%6 8,-*v((*06/? Î *0* pA95%Lk6/576J&c:+!=">$v&c(*0,-!R,9!#88+"%?7!RI/6 EJ!=: !#">1VQ5%L(Q/!p( T 5iA<"%6 E T *2ES(+Qb">$'$05J13"%(*05>6b81VQ/!=,-!=8=N = NÌs5>6 8*2EJ!3:"-13">$'!=6 E/"%:&A ">8!=Eg:!#8H!=:Z4"4(+*'576g./:+5%(+5J15>$C(+5-(:V"%6 8,-*v(:+!="%$'&c(*0,9!p,-!=8+8+"%?>!#8_54Z>!3:R"h157$'$0*28H*05>6J&A "78H!#Eh6/!( T 5>:+xy ÁY"^Ägj{S. $0">*'6qQ 5 T (+:+">6 8,9*28+8H*05>6o5>Ls">8@S6 1VQ/:+5>6/57I 8,-!=8+8">?>!#8AS@6 5SE/!=8f13"%6rA6/57I 8,-!#88+"%?7!=8 Q "[Z7!p./:57A "%A *'$0*08H(*21f"%:+:*0Z4"%$C(*0,-!=8">6 EbEJ5-6/5%(Q "[Z7!f">[email protected]!=13*vW*'6 T *'(QK. :57.85>6 *'6/?(+Q/!;([email protected]!=85>L(:V"4;138LM5>: T Q *01VQF"r13"%$0!36<E/"%:&cA<">8!=EB./:5>(5J157$ T 5>I/$2EP.C!3:LM5>:+, 8+"4(+*08HLY">1(5>:+*0$'@;">6 E(Q/!p([email protected]!=8_LM5>: T Q *01VQb*'( T *'$0$|6/5>(=N : NORQ/!A ">6 E T *2ES(Qg5%L«"./:+*05>:+*v(U@^&A ">8!=EX(57x>!36h:+*06/?6/!3( T 57:xÁMU`s , *^ÃJN (>Ä*28 Î */*/5qA/. 8=Nu88I/,-!(Q<"4(`(+Q/!. :57. "%?^"4(*05>6 (*0,-!B5>L(Q/!D6/!( T 5>:+x*08 Î *K,9*0$0$'*aS!=135>6 E 83N !!(!=:,-*06/!B(Q/!BLM:+"71e(+*'5765%LA ">6 E T *2ES(Q T "78U(+!=EE/I/:*06/?G!3Z>!=:@LM:V"%,-! (:V"%6 8,-*08+8*'576|l T Q !36;(+Q/!fLM:+">,-!f8*'m=!*28Ã _. 8pÁDp*0$05 _@^(!#8`.C!3:8!=135>6 E Ä 6 E/!3: T Q "%(R135>6 EJ*'(*05>6<8 T 5>I/$2Eh(+Q/! T "78U(+!=E A "%6<E T *0EJ(QbA$v&c(*0,-!p135>,-,XI 6/*01="4(+*'576 8R*'6b. "71Vx>!3(H&w8 T *'(+1VQ/!#Eg6 !( T 5>:+xS8=N u8+8HI ,9!9(+Q "4("1!3:(+">*'6D:+!="%$'&c(*0,9!-"%. ./$'*213"%(*05>6B:!#1!3*0Z>!#8pE/"4(V""%(f(+Q/!-:+"%(!95%L Î */5qA/. 8=N9ORQ/! T 5So?>I<"%:V"%6^(!=!(5(+Q/! "%./. $'*213"%(*05>6.L]/Ã *%,;S!=1>N`Ìs5>,-./IJ(+!p(Q/!A/I/dC!=::!#~^I/*':+!3,-!=67("4((+Q/!:+!=1!=*'Z7!3:#N . NÌs5>6 8*2EJ!3:(Q/!iI 8H!i5%L](+*',-!=Eo(5>x7!36q. :5>(5J157$`ÁMUs` , *7ÃJN $^Ä*'6o(+Q/!LM57$'$05 T *06/?g8*v(+I "4(+*'576|N}D!XQ "[Z7!LM5>I :6/5JEJ!#8*06q(+Q/! 8H@J8H(!=,NzORQ/!:+!=">$v&c(*0,-!_:+!=~^I/*0:+!3,-!36^(]*08](Q "%(j6/5JEJ)! AC!"%A $'!_(5p(+:+">6 8,9*'(jI/.J(+5 A/*'(+8`54Z>!3:z!#">1VQ9.LyE/I/:+"%(*05>6 ,-*0$'$0*aS!=135>6 E/8=l T Q/!=:! ">6 E ">:!f?>*0Z>!=6*06(Q/!p(V"%A/$0!AC!3$05 T N ¿5SE/! Î Î */l */*0* $ (/*/l */*0* 1Î = . */l */*0* 1Î = . */l */*0* ÌsQ/5S578!8I/*'(+"%A $'!OOzO°Áa(V"%:+?>!3(s(+5>x>!=6g:+5%(V"4(*05>6;(*0,9![ÄR"%6 Eg5>AJ(V"%*068I/*'(+"%A $'!fZ4"%$0I/!=8R5>L Áa(+5%(+">$y6^I ,XAC!3:5%LA/*v(V8_(Q "%( 13">6gAC!(+:+">6 8,9*'(H(+!=EgA^@g6/5JEJ! 54Z>!3:_!3Z7!3:+@;1@J1$0!>N Äiu8+8HI/,-!f(Q<"4(R(Q/!p./:+5>.<"%?7"%(*05>6-(+*',-!p*08R6 !3?>$0*0?>*0A/$'!p157,-. "%:+!=E-(+5 OOzOÀ"%6<Eg(+Q "4((+Q/!8@S8H(!=, A ">6 E T *2ES(Qb*28 Î 5oA . 83N Î */NRL@>5>IK">:!;135>6 8H(:V"%*06/!#ED(5qI 8!g">6ª!{J*08H(*06/?rj(Q/!=:6 !(9¾u¿LM57:i"bLY"71e(+5>:+@D">IJ(57,-"%(*05>6ª"%. ./$'*213"%(*05>6|l T Q "%(i"%:+!h(+Q/! EJ*'dC!=:!=67(R./:+5%(+5S135>$28](+Q "4(R@>57Ig13">6gI 8!(+5i8I/./.C5>:(R135>,-,XI 6/*01="4(+*'6/?i:!#"%$'&)(+*',-!(+">8xJ 8 F} Q *01VQ5%L|(+Q/!f">$v(+!3:+6 "4(+*'Z7!=8`(Q "%( @>57IgQ "[Z7!f*2EJ!=67(+*vW57Ig(+Q/*'6 x T 5>I/$2E T 5>:+xhAC!=8H( F 6 *0Z>!p@75>I/:R:+!=">85>6 *'6/?^83N Î7Î NÌs5>6 8*2EJ!3:9" Î */5oA/.<8(57x>!=6J&c:+*06/?q6/!3( T 57:xP5>.C!3:V"4(+*'6 ?qI/6 EJ!=:9(Q/!./:+*'57:*'(U@^&cA "78H!#ED./:5>(5J157$fÁYU`s , *^ÃJN (>ÄeNPn/57:X(+Q/*28 6/!( T 5>:+xyl`(+Q/! T "%$0xK(+*',-!r*28gÃP,;S!#1q"%6<EF(+Q/!qLM:V"%,-!o$0!36/?>(Q *28 Î *7Ã$ _@^(!#83N !!3(!=:,-*06/!o(Q !qLM:V">1e(+*'576Í5%L T "78U(+!=E A "%6<E T *0EJ(QgEJI !(+5(Q ! T "%*'(j(*0,-!:+!=~^I/*0:+!=E9LM5>:s(Q !(+5>x>!=6-(5i:!3(I/:+6h(5X(Q/!(:V"%6<8H,-*'(H(*06/?i6/5JEJ!"%La(!3:s(:V"%6<8H,-*288*'576h5%L "9LM:+">,-!*08157,9. $'!3(!>Nu_((+Q/!X?7*'Z7!36bA ">6 E T *2ES(Q T 5>I/$2Eo"hAC5>I/6<EJ!=Eo"7131!#88./:5>(5J157$|.C!3:LM5>:+,AC!(H(+!3: Fª]{J./$2"%*06b@>57I/: "%6 8 T !3:#N Î ÃJNÌs5>6 8*2EJ!3:" Î */5oA/.<8p(57x>!36P:+*'6 ?6 !( T 5>:+xCNORQ/! T "%$0xo(*0,-!;*08 Î ,;S!=1>NORQ/!-LM:V"%,-!;8*'m=!h*08 ( Î ÃgAS@^(!#83N !!3(!=:,-*06/! (Q/!,h"4{J*',iI/, (*0,9!LM5>: T Q/*21VQF"o,-!=8+8">?>!h,h"[@PI/6 EJ!=:?75o./:+*'57:*'(U@B*06SZ>!=:+8*'576PI/6 EJ!=:iUs` , *^ÃJN $q"%6 EKU`` , *7Ã/N ( ./:+5%(5J135>$283N Î-V NÁY"^Ä;UEJ!=6^(*'LM@-"%(s$0!="78U(s( T 5LY"71e(+5>:V8 T Q/*21VQg15767(+:*0A/IJ(+!(+5XEJ!3$2"[@ U*v((!3:R*06;:+!="%$'&c(*0,9!15>,-,iI/6/*213"4(+*'576 8`">6 E-!{J./$2"%*06;Q/5 T (+Q/!3@13"%I<8H! U*'(H(!=:=N ÁMA<Ä} Q "%(f*28(Q/!-EJ*'dC!=:!=6 1!iA6o(+*',-!-"%6 Er:!#8H.C5>6<8H!(+*',-!95%Ls";(+"78Hx Fw6 T Q "%(p13*':V1I ,-8H(+">6 1!#81="%6 (+Q/!3@A
V/=
Version 2 CSE, IIT Kharagpur
Î $ NÌs5>6 8*2EJ!3:(Q/!iI 8H!i5%L](+*',-!=Eo(5>x7!36q. :5>(5J157$`ÁMUs` , *7ÃJN $^Ä*'6o(+Q/!LM57$'$05 T *06/?g8*v(+I "4(+*'576|N}D!XQ "[Z7!LM5>I :6/5JEJ!#8*06q(+Q/! 8H@J8H(!=,NzORQ/!:+!=">$v&c(*0,-!_:+!=~^I/*0:+!3,-!36^(]*08](Q "%(j6/5JEJ)! AC!"%A $'!_(5p(+:+">6 8,9*'(jI/.J(+5 A/*'(+8`54Z>!3:z!#">1VQ9.LyE/I/:+"%(*05>6 z,-*0$'$0*28H!#15>6<E/83l T Q !3:+! ]"%6 E ]"%:+!f?7*'Z7!36*'6(+Q/!p(+">A/$'!pAC!3$05 T N ¿5JEJ! *06 s@^(+!=8 *06,-*0$'$0*S!#1576 E/8 $ Î* (/* Î* Î* .* /à * Î *0* ÌsQ/5S578!8I/*'(+"%A $'!OOzO°Áa(V"%:+?>!3(s(+5>x>!=6g:+5%(V"4(*05>6;(*0,9![ÄR"%6 Eg5>AJ(V"%*068I/*'(+"%A $'!fZ4"%$0I/!=8R5>L Áa(+5%(+">$y6^I ,XAC!3:5%LA/*v(V8_(Q "%( 13">6;A6 8H,-*'(H(+!=E;AS@-6/5JEJ! 54Z>!=:`!=Z>!3:+@h1@J1$0!>N Äiu8+8HI/,-!(Q "%(s(+Q/!f./:57. "%?^"4(+*'576-(*0,9!p*28 Î ,-*'$0$0*2S!#1p"%6 E-(+Q "4(R(+Q/! A "%6<E T *0EJ(Qb5%L(Q/!6/!3( T 57:xh*28 Î */5oA/.<83N Î (JNu Á D SÄ(:V"4;11VQ ">:+"71e(+!3:+*'m#"4(*05>65%Lj"h1!=:H(V"%*06o. ">1Vx7!(8 T *v(V1VQ/!=E:+!=">$v&c(*0,-!(:V"4;1p*281VQ ">:+"71e(!=:*0m3!#EgAS@"h.1Vx>!3(+8j">6 Eh"[Z>!=:+">?>!s(:V"4;1R:V"4(!iÁ JÄz5%L Î *p.<">1Vx>!3(+8].C!3:_8H!#1576 EkNzORQ/!. "71Vx>!(`8*0m3!*28 ( Î ÃfAS@7(+!=8=Nu88I/,-*06/? (Q "%((Q !g. "71Vx>!(V8I/6 E/!3:+?>5r"o,h"%{S*0,XI , ~^I/!=I/*'6 ?rEJ!3$2"[@D5%SL (*>,;S!=1h"%(i!="71VQP5%L(Q !8 T *v(V1VQ/!=8=l T Q<"4( T 5>I $0EPAC!;(+Q/! (:V"4;1p1VQ "%:V">1(!=:*0m="%(*05>6g"%La(!3:R(+Q/! Î *%(Qb8 T *'(+1VQ5>6(+Q/!:57IJ(!7N Î-= NÌs5>6 8*2EJ!3:9" Î */5oA/.<8(57x>!=6J&c:+*06/?q6/!3( T 57:xP5>.C!3:V"4(+*'6 ?qI/6 EJ!=:9(Q/!./:+*'57:*'(U@^&cA "78H!#ED./:5>(5J157$fÁYU`s , *^ÃJN (>ÄeNPn/57:X(+Q/*28 6/!( T 5>:+xyl`(+Q/! T "%$0xK(+*',-!r*28gÃP,;S!#1q"%6<EF(+Q/!qLM:V"%,-!o$0!36/?>(Q *28 Î *7à $ _@^(!#83N !!3(!=:,-*06/!o(Q !qLM:V">1e(+*'576Í5%L T "78U(+!=E A "%6<E T *0EJ(QgEJI !(+5(Q ! T "%*'(j(*0,-!:+!=~^I/*0:+!=E9LM5>:s(Q !(+5>x>!=6-(5i:!3(I/:+6h(5X(Q/!(:V"%6<8H,-*'(H(*06/?i6/5JEJ!"%La(!3:s(:V"%6<8H,-*288*'576h5%L "9LM:+">,-!*08157,9. $'!3(!>Nu_((+Q/!X?7*'Z7!36bA ">6 E T *2ES(Q T 5>I/$2Eo"hAC5>I/6<EJ!=Eo"7131!#88./:5>(5J157$|.C!3:LM5>:+,AC!(H(+!3: Fª]{J./$2"%*06b@>57I/: "%6 8 T !3:#N Î : NÌs5>6 8*2EJ!3:" Î */5oA/.<8p(57x>!36P:+*'6 ?6 !( T 5>:+xCNORQ/! T "%$0xo(*0,-!;*08 Î ,;S!=1>NORQ/!-LM:V"%,-!;8*'m=!h*08 ( Î ÃgAS@^(!#83N !!3(!=:,-*06/! (Q/!,h"4{J*',iI/, (*0,9!LM5>: T Q/*21VQF"o,-!=8+8">?>!h,h"[@PI/6 EJ!=:?75o./:+*'57:*'(U@B*06SZ>!=:+8*'576PI/6 EJ!=:iUs` , *^ÃJN $q"%6 EKU`` , *7Ã/N ( ./:+5%(5J135>$283N Î-, NÌs5>6 8*2EJ!3:(Q/!iI 8H!i5%L](+*',-!=Eo(5>x7!36q. :5>(5J157$`ÁMUs` , *7ÃJN $^Ä*'6o(+Q/!LM57$'$05 T *06/?g8*v(+I "4(+*'576|N}D!XQ "[Z7!LM5>I :6/5JEJ!#8*06q(+Q/! 8H@J8H(!=,NzORQ/!:+!=">$v&c(*0,-!_:+!=~^I/*0:+!3,-!36^(]*08](Q "%(j6/5JEJ)! yAC!"%A $'!_(5p(+:+">6 8,9*'(jI/.J(+5 yA/*'(+8`54Z>!3:z!#">1VQ9.LyE/I/:+"%(*05>6 z,-*0$'$0*28H!#15>6<E/83l T Q !3:+! ]"%6 E ]"%:+!f?7*'Z7!36*'6(+Q/!p(+">A/$'!pAC!3$05 T N ¿5JEJ! *06 s@^(+!=8 *06,-*0$'$0*S!#1576 E/8 $ Î* (/* Î* Î* .* /à * Î *0* ÌsQ/5S578!8I/*'(+"%A $'!OOzO°Áa(V"%:+?>!3(s(+5>x>!=6g:+5%(V"4(*05>6;(*0,9![ÄR"%6 Eg5>AJ(V"%*068I/*'(+"%A $'!fZ4"%$0I/!=8R5>L Áa(+5%(+">$y6^I ,XAC!3:5%LA/*v(V8_(Q "%( 13">6;A6 8H,-*'(H(+!=E;AS@-6/5JEJ! 54Z>!=:`!=Z>!3:+@h1@J1$0!>N Äiu8+8HI/,-!(Q "%(s(+Q/!f./:57. "%?^"4(+*'576-(*0,9!p*28 Î ,-*'$0$0*2S!#1p"%6 E-(+Q "4(R(+Q/! A "%6<E T *0EJ(Qb5%L(Q/!6/!3( T 57:xh*28 Î */5oA/.<83N Î-. NR}B57I/$2EB*'(XAC!;">EJZS*28">A/$0!i(+5oI 8!;"%6ª](+Q/!3:+6/!(X¾u¿ *06ª"bQ "%:VEB:!#"%$'&)(+*',-!;"%. ./$'*213"%(*05>6P8HI<1VQP"78pLY">1(57:@r">IJ(57,h"4(*05>96 F >I<8U(+*vLM@;@75>I/:">6 8 T !=:=NzjZ4"%$0I "%(!f(Q/!. :5^8_">6 Eb1576 8R5%LI 8H*06/?;">6j(Q/!=:6/!3(H&A ">8!=Eg./:+5%(5J135>$k*06b8I 1VQb"%6b"%./. $'*213"%(*05>6|N Ã/*/NSI/?7?>!=8H(g"K8+1VQ/!3,-!b(+Q "4(b13"%6 Q !3$0. Q "%6 E/$'!r">.:V">EJ*21b,-!=8+8">?>!=8-*06"ª:+!=8!3:+Z4"4(*05>6ºÁ)13"%$0!36<E/"%:&cA<">8!=E Ä ./:+5%(5J135>$ T *v(+Q/5>I/(,-">xS*'6/?-,h" U57:1VQ "%6/?7!=8s(5-(+Q/!./:+5%(+5S135>$cN à ΠNRUEJ!36^(+*vLM@(Q/!LY">1e(+5>:V8 T Q/*21VQq15>6^(+:*0A/IJ(+!p(5gEJ!=$0"[@ U*v((!3:f*06o:!#"%$'&)(+*',-!157,9,iI/6/*213"%(*05>6 8=Nsu88I/,-!(Q<"4("h13!3:(+"%*06b:!#"%$'& (*0,-!9">././$0*01="4(*05>6r:!#1!3*0Z>!#8E/"%(+""4((Q/!9:+"%(!i5%L Î */5oA/.<83NORQ/! T 5^b?7I "%:V"%6^(+!3!(+5;(Q !9">././$0*01="4(*05>6B.,-./I/(!p(Q !A/IJdy!3::+!=~^I/*0:!=,-!36^(R"%((Q/!:+!=13!3*0Z>!=:=N
$ (%
$
%
V:
Version 2 CSE, IIT Kharagpur
Ã7ÃJN]{J./$2"%*06 T QS@(+:+"%h1_?7!(+8]E/*08H(57:H(+!=Ei*'6h"f,XI/$'(*28!3?>,-!=67(]6/!3( T 57:x">6 EiQ/5 T (+:+"%h1_:+!=8Q "%. *'6/?f*28]">1VQ/*0!3Z7!=EXLM5>:z./:+54Z^*2EJ*06/? T 5^;?>I ">:+">67(+!3!7N Ã V NÌs5>,-. ">:!(+Q/!p.6 1!5%L|U`s , *7ÃJN $./:+5%(+5J15>$ T *'(QgUs` , *7Ã/N (./:5>(5J157$ LM57:s:+!=">$v&c(*0,-!">././$0*01="4(*05>6<8s"%(_Q/*0?>Q«l ,-!=EJ*0I/,bl "%6<Eg$05 T A ">6 E T *2ES(Q<83N Ã $ N]{J./$2"%*06;I 8*'6 ?LM5>I :s57:`W Z7!f8!36^(+!36 13!=8=l7Q/5 T ?7$'57A "%$C./:+*'57:*'(U@-"%:+A/*v(+:+"%(*05>6;*28_">1VQ/*0!3Z7!=EhI 8*06/?XZS*0:H(+I "%$<(*0,-!f. :5>(5J157$)Nzu_( T Q/*21VQH \º$0"[@7!3: T 5>I/$2E8I 1VQo"9./:+5%(5J135>$y5>.C!3:V"4(+G! F Ã0(JNSI/./.C578!(Q "%( T !bQ "[Z7!g(+Q/:+!3!b.6 E, V (+5DAC!b(:V"%6<8H,-*'(H(!#EKLM:+5>,(Q/:+!3!q8H(+"%(*05>6 8h Î l /ÃJl">6 E V l:+!=8.6 ">6Ín ! !h6 !( T 5>:+xCN ¾|!3(;(Q/!BOOOÂÁM(5>x7!36Í:+5%(+"%(*05>6(*0,-!#Ä;A $'xD . (+*',h,-8H!!#1%AÎ8!=*>1B,hNK8H!#1=ORÄeQ/f!;Á (+:+7"> 6 Î 8HÃ4,-,h*2888!=*01>5>l 6ª (+ *',-Î (/!ª*%Á,h 8 !=,-1=Ä38Á!=1#ÄX@ ">6 Î (4Eª,h(+8HQ/!#!1%l .<!= : *05JÎ1EK= *>5%,hL8H(!#Q/1=!ÄeN ,-!!=8+!8(+">!3?>:+,-!=8*'6/Á ! (ÄXQ ">!b:!8@S">6 8X1VQ/LM5>:+5>$0$'6/5 57T I 8=8 A "%6<E T *0EJ(Q(Q "%(6/!3!#E/8_(5-AC! "%$0$'5J1="4(!#E;(+5h!="71VQ8H(+"%(*05>6LM 5>:8I 1313!=8+8ULMI/$y(+:+">6 8,9*28+8H*05>65%L(Q/!,-!=8+8+"%?>!#83N Ã = N]{J./$2"%*06q(+Q/!-*',-.C5>:(+"%6^(8Q/5>:(+135>,-*'6 ?785%L`(+Q/!hw6^(VS!=:Zq">:+1VQ *v(+!=1e(+I/:+!i*06D8I/./.C5>:(*06/?b:+!="%$'&c(*0,9!-157,-,XI/6/*213"%(*05>6|l|">6 E Q/5 T !*'dkS!=:Zg54Z>!3:V157,-!=8_*v(#N Ã : NÌs5>,-. ">:!(+Q/!p">EJZ4"%6^(V"%?>!#8j"%6<EgEJ*28"7EJZ4"%6^(+">?>!#8]5%L«I<8H*06/?i"X:*06/?i6/!( T 5>:+x9">6 E;"i15>$0$0*08*'576;A "78H!#Eh6/!( T 5>:+xiLM5>:_:!#"%$'&)(+*',-! 157,9,iI/6/*213"%(*05>6|N Ã , NR} Q "4(EJ5h@75>II/6 EJ!=:+8H(+">6 EA^@ T 5^g:57IJ(*06/? N]j{S. $0">*'6(Q/!E/*vdy!3:+!36^((U@S.57:*'(Q/,h8=N Ã . N]{J./$2"%*06 T Q "4(s">:!R(+Q/!EJ*'dy!3:+!36^( T 5^9135>6 8H(:V"%*06^(+8z(+Q "4(s">:!135>6 8*2EJ!3:+!=E-EJI/:+*06/? T 5^i:+5>IJ(+*'6/? *'69(+Q/!LM!#"4(I :!#8]5%L (Q/!#8H!135>6 8H(:V"%*06^(+8sA ">8!=Eg5>6 T Q/*01VQ(Q !p135>6 8H(:V"%*06^(+8R13">6gAC!1$2">8+8H*'W !#EkNz} Q "4("%:+!(Q/!p*0,9. $'*213"%(*05>6 8R5>L«(Q !=8!LM!#"4(+I/:!#8 5>6(Q/!:+5>I/(*06/?h"%$0?>5>:+*'(Q/,h8 F V */NR} Q "4(EJ5@>5>IrI/6 EJ!=:+8H(+">6 EqAS@ T 5^b:+5>I/(*06/? F 6 *0Z>!98H57,9!9!{/">,9. $'!#85>L`">E/EJ*'(*0Z>!7lk,XI/$'(*0./$0*01="4(+*'Z7!>lk"%6 EB1576 13"[Z7!X1576J& 8U(+:+">*'6^(V8(+Q "4(X">:!96/57:,h"%$0$0@r1576 8H*2EJ!=:!#Eq*06 T 5Sq:+5>I/(*06/?o81VQ/!=,-!=8=N-j{J./$0">*'6BQ/5 T (+Q/!=8!-LM!="%(I/:+!=8">:!-1576 8*0EJ!=:!#Er*06 T 5^;:57IJ(*06/?-./:+5%(5J135>$283N V Î N]{J./$2"%*06g(+Q/!XEJ*'dy!3:+!36 13!A6 E.<57$'*21*06/? 8H(j!{S(!=6 8H*05>6<8z(55^8H.JLUN ." 6 #QA"'^. a# O/#%"$O\&"$#/06 (!G "$0 % "$0%6 Eb.<57$'*21*06/?h./:+5%(+5J15>$|">6 E A/:+*'! @gEJ!#813:*0A6|N V ÃJNR} Q "4(*08"h135>6^(:+5>$0$0!3:"%:+!="96/!3( T 57:xBÁcÌ_u¿fÄ F9]{J./$2"%*06o"h:+!="%$'&c(*0,9!135>,-,XI/6 *01="4(*05>6b./:+5%(+5J15>$|(Q "%(13">6AC!I 8!=Eb*06o" Ì_u¿XN > ]£b¤ 8 Î < u8HQ 5>x;u?^"%: T ">$0"iu:VE/">8Ìs*0$'*06/?7*':+5>?7$'I|l/SI 6/?h¾|!3!7N]!=">$v&c(*0,-!p135>,-,XI 6/*01="4(+*'576| X5O`# LO !" CO% *'&1T 33T F, !" ;! *1 !6I
`T F,P#%"'^=#N O4l 7
`">!6S"I &'"%
:+^.@ -1Î ,.0. : #N "'^ # O' &'C
3 ,!" 8 Ã < JQ/*'?^"%6/?ÌsQ/!=6-">6 E p$0">:+"f¿">Q/:V8U(+!=ES(#N u6h54Z7!3:+Z^*0! T 5>Ly~^I ">$'*'(U@^&c5>La&8!3:+ZS*013!`:+5>IJ(+*'6 ?LM57:z(Q/!6 !{S(j?>!=6/!3:V"4(+*'576XQ/*0?>QJ&w8.:+xS8= `:5hA $'!=,-8f"%6<Eo8H57$'IJ(+*'576 8= N (!G "$0 /1 *#&&'7 "L# &' )&& *% # ON )&'C"' *b1 * -,f [Q/
3#% I *O/4l<¿54ZyN + !!#1%N -Î ././, N 8 V< !iN>}P"%*'(m=,h"%6gÌN ]">:H(+:*2EJ?>!yN !!=!3:+*'6/?<N !*08H(+">6 1!Z>!=1(57:],XI/$'(*213"78U(j:+5>IJ(+*'6 ?./:5>(5J157$)N !#"6$N1CG %"$0% "$0%
AQ & "$% a6 3#% R,!"LO'I a
`\1"&'
C^4lC¿54Z7!3,XAC!3: -Î ./,/, N 8 $ < uXN¬!3$0,X@ !XNzn ">:*06 ">1=1*j!3(=N"%$cN `:5>(5J157$]*'6<EJ!3.C!36 E/!36^(i,iI/$v(+*01=">8H(H&w8H.<"%:V8H!-,-5JEJ!rÁM. *',9&w8H,;Äe `:5>(5J157$)( N )+*+,-)/6 #%33QA"'^./ 9!!"'
! a3#% l 7I/6/! -Î ././, N 8 ( < kN N 6 5>$0!=8H(+">6/*cNFu8U(+5>.J&w"%6 EJ&c?75B~^I/!3I *'6/?BLM:V"%,-! T 5>:+xDLM5>:h1576/?>!#8U(+*'576K,h"%6 ">?>!3,-!=67(#N 0 & 212(43 5 a^&
(6 %( *# * &5X5"$L
31C"LN# O76K"LR 686 Z
#/O/1 Z *#\626;XlJ. "%?7!=8 ,:9C1Î , l/S!3.J(+!3,iA
V/,
Version 2 CSE, IIT Kharagpur
eN *06/*'5>(*28;¬NRJ"%$2"%,h" l !iN`!=!3Z>!#8h"%6 EÍOpNRSQ/!3I«N Ìs5>,-. ">:*28H576G5>Lf,iI/$'(*213">8H(;:+5>IJ(+*'6/?ª">$'?75>:+*v(+Q/,h89LM5>:hQ/*0?>QJ&w8.:+xS8=N aL *#%"'*6 R )+5:T 5*%l Î1./. $ N uXN!!3,-!=:+8RyN.p!=8Q "[Zi">6 EgyN/SQ !36/x7!3:#N|u6 ">$'@J8*08s"%6 E;8*0,XI/$2"4(+*'576;5%L«"LY"%*0:s~^I/!3I *'6/?9"%$0?>57:*'(Q/,bN 6K"LRO
AQ%&_F, X7 ! & 12 3 56 X5Z&'
l/. ">?>!#8 Î 9CÎ ÃJlJS!3./(!3,iA6 E CQ/!=6/? T N ^(V"4(*28H(*213"%$:!#"%$'&)(+*',-!o157,-,XI/6/*213"%(*05>6Í54Z>!=:h!(+Q/!3:+6/!(hLM57:;,h"%6SIJLY"71e(I :*06/? ">IJT (57,h"4(*05>6b8@S8H(!=,h83N 6K"$ LO
ZQ&7-, 45# R
aL %=$Q/^ # O7XH: *#%C *% & ^ \&'
9l . ">?>!=8 -Î . Ã 9 Ã *^ÃJl -Î ./.0. N ^"%,-!#8n_9N pI :5^8H!X">6 E p!3*'(Qr}ºNy578+83N % 31"(!G "$0%
AQ CX O/G MXK/"$R#:LJN z!="%:V85>6b`EJI 1="4(+*'576qu8*0" l /Ã */*^ÃJN -N 6 1N T !35>6«l7yN -N>SQ/*06;"%6 Ei}B57:xS,h"%6 6 N$v&c(*0,-!15>,-,iI/6/*213"4(+*'576i54Z7!3:z!(+Q/!3:+6/!3( T *v(+Q-"7E/"%./(*0Z>!_(:V"4;1 8,-5S5%(Q *'6/?<N 6K"$ RT,\4 5# R
fZ %=LQ%^c# O XH/ *# * & a^\&'
2 f:X 23 )+.'< 6/% #\&$
AQ/3% (T T=6 Xl^.<"%?>!#8 . * 9CÎ *0*/l V/Î 5q"[@h&_Ã 7I/6/!Ã *0*/* N ¿XKN 5q"%$2157$', ">6 EB}ºN CQ "%5:+Er:!#"%$'&)(+*',-!-157,9,iI/6/*213"%(*05>6r*06D,XI/$'(*0./$0!;">1313!=8+86 !( T 5>:+xS8=N "' # -,5L#% R
7 ^\&'31N&el ]57$)N . : ( 9yÎ * : l -Î ./. (/N
AQ & "$ 66K"LL% ! T0l 5q">:+1VQ 1Î ./. $ N kN<SQ/!=6/x>!=:ÌN ]"%:(:+*0EJ?7!">6 EbN 6 I/!=:*06|NjS.C!=1*'W<1="4(*05>6b5>L?7I "%:V"%6^(!=!=E;~^I ">$'*'(U@;5>Lz8!3:+ZS*013!>N ).)0:)7lyS!=.J(=N 1Î ./. : N iN zN p57,-.ÌN ]"78~^I ">$'!s"%6 E 6 N%ÌN z57$'@Sm=578=0N 5oI/$'(*213"78U(z:+5>IJ(+*'6/?LM5>:,XI/$'(*0,-!=EJ*2"p157,9,iI/6/*213"%(*05>6|!N X7 "$#% &1#/1C *% &N (N1CG %"$0
ZQ%l ]5>$cN Î Á)¿5 N V Äe à ,0=-9 à . Ã/l 7I/6/! 1Î .0./V N !3(=N ">$)N kN _$0">x>! !XN _$2">1V%x 5KNCÌ_"%:+$085>6«Nu6b">:+1VQ *v(+!=1e(+I/:+!LM57:EJ*vdy!3:+!36^(+*0"%(!=Eb8!3:+ZS*013!=8=N ) -"4l !!#1%N -Î ./.0, N ¾`N yQ "%6/?yN !!=!3:+*'6/? !XNk`8H(:+*06ryN|SQ/!36 x>!3:f"%6 E !XN y">./. "%$2"/N8HZS.|u 6/! T :!#8H57I/:+13!:!#8H!=:Z4"%(*05>6o./:+5%(+5S135>$c N (!G "$0 #1QA# 1
3lCJ!3.J(+!3,XAC!3: 1Î ./.0V N u6 EJ:+! T yN O"%6/!=6^A<"%I/,bN !"(!G "$0&eN j:+!36^(*21!p¬">$'$«5%Lw6<EJ*0" l 1Î .0. : ÁYORQ/*0:VEsEJ*v(+*'576<ÄeN ÌN ]!36/x4"4(+:+">,h"%6/*">6 EÍOpN_yNÌsQ/*0I/!3Q|N SI/./.C5>:(*06/?K:+!=">$v&c(*0,-!(:V"4;1b5>6Í!(+Q/!3:+6/!3(=N 6K"$ RT"4 5L#% R
7 ^\&'31N& a^\&'
il . "%?7!=8Ã , Ã 9 Ã ,/= l -Î ./. $6 EBÌsQ ">5%& >Io¬5>I|Nfu 8I/:Z7!3@5>6q,iI/$'(*213">8H(:+5>IJ(+*'6 ?g"%6 Eq*v(V8~^578!{S(!=6 8*'576|R./:57A/$0!3,h83ly"%$0?>57:*'(Q ,-8=l<">6 E . :5>(5J157$08=8N N1CG %"$0 #1QA# 1
l ]5>$cN Î $CÁY¿5:@à */*0*/N ¬I/6/?>& f*'6/?qOs@7">6ªÌsQ<"%5%& 7ID¬5>I _*'6ª}P"%6 ?q"%6 E `"%5>& 5q*'6FÌsQ/!=6|N T 5^8p!{S(!=6 8*'576B(+5r1A/(=N X7 "L# &1T % (!G "$0%
AQ>l 7I/$0@Ã *0*7ÃJN zN }P"%6/?;">6 E NkÌs:5 T 1:+5%La(#N T 5^8:+5>IJ(+*'6/?-LM57:8I/./.C5>:(*06/?;:+!=85>I/:V1!p:+!=8!3:+Z4"4(*05>6«N Z%"' #% -, %! *#%;X5"$#&(-, %( *# *I/$ zN/} Q/*'(!7Nj8HZS.o"%6<Eg*06^(!3?7:+"%(!#E8!3:+ZS*013!=8_*'6(+Q/!*'6^(+!3:+6/!(#juÀ(+IJ(57:*2"%$cN ( a *# * &el 5q"[@ 1Î .0. : N 6b5%L(Q !15>6^(+:57$'$0!=ES&$057">E;6/!( T 5>:+xh!3$0!3,-!36^(8!3:+ZS*013!>N ).)0.%lyS!=.J(=N 1Î ./. : N !iN ]!3:+,-"X¬N CQ "%6 ?X"%6 E !XNSn/!=::V"%:+*)N 6 I ">:+">6^(!3!=*'6 ?EJ!3$2"[@ U*'(H(+!3:_A<57I/6 E/8s*06;. ">1Vx7!(`8 T *v(V1VQ/*06/?X6/!3( T 57:xJ8= N 6?"$RO
ZQ& F,."' *%('3 56 #1 f
6 ("'4' #"$%
#%l . ">?>!#8 V ( 9 $ = l^u./:*0$ -Î ././Î N ¬XN yQ "%6/?:?7I "%:V"%6^(+!3!=E.C!3:LM5>:+,h"%6 13!8H!=:ZS*21!*06q. "71Vx>!(8 T *'(+1VQ/*06/?;6/!3( T 57:xJ8=N 6K"$ LO
ZQ&7-, 4 _l ]57$)N , (/Á Î *7Äl \f1e(57A6 E !XNyn/!=::V"%:+*cNs"%(!&w1576^(:+5>$«8H(+"%(*21e&./:*05>:+*'(U@g~^I/!3I/*06/?
ZQ&F, 121243 5.*%6 ;# ;"L# 1 )&1\6 Xpl . "%?7!=8Ã>Ã : 9 Ã V/= l 1Î .0./V N
8 =<
8 :;<
8 ,<
8 .<
8 Î1.< 8 Ã* < 8Ã Î < 8 Ã>Ã < 8 Ã V< 8 Ã$ < 8 Ã/( < 8 Ã =<
8Î Ã <
8 Î;:;< 8 Î1,<
8 Î>Î <
8Î ( < 8 Î1=<
8Î * <
8 Î1V< 8Î $ <
V/.
Version 2 CSE, IIT Kharagpur