Real Time System Iit Notes

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*;*

Version 2 CSE, IIT Kharagpur

Timing Constraints Performance Constraints

Delay

Deadline

RR SR SR

RR

Behaviorial Constraints

Duration Delay

RS

(

SS

Deadline

SS

Duration

RS

#+%&)* [$I"%((*
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bC C

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C ;C

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*

*

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I*

*.

Version 2 CSE, IIT Kharagpur

e1/set timer(20 ms)

s1

s2

* 2(

#+%&0 . G@ P ! @Q1*#%@?( V(W53O@A49"h]7#@0+ ".@AG[ @

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+ [ @i(E

!#:%(3* 0!$#&%< A8 000!^0"./0$#=.-G"%@c0L1DCQ/M=%-G32"32$#O@0@)(D1"%O@Q14]U=>?"%3 2o1O@ E E 2( =; ¢7R8¡v¤7=R2 ¡' 1;ª¤7}1¦1¦¤ ;ª 21¦;1 } 4 ;£¤8¡;-§k 1 ¤7=$2=¡v ¤7}£¦¦¤R-$ 1 <}¦1¦ ¢¡; ;}2¤8¡ FH>0I(=>?"%(6?!@232!$#$#3#@Y#+)E * EdqX@y#+)E * 6)(W P ,1*>)".1V"%(V(W@i"%(H1>0`A)9(W1V32#+%O1VI(432I".$#$O53'S?1*>0=(*C2(D1! !@Q1*(J1*>0+>*4]U"%<1V5@)3.4#+%O1wK (D19"_1=".@)31>0`1O4I( (*1J1.* #$O$#K(W5%@?30(!EHqr-K1*>)=@0!^Q1\32O+<1\32(J@).1V"%/0/?5".J]7O1*>)O@+*%O$#$OK(*@)30(S01>0!@f1>0`1O!\".$I". !^/)O(J"%@)3 1>0;(WC2(W1* !@Q1!9(\1*>0 > J]H".O1U".$#$O`V ± @2Ns>)Q8£ K (W1".1*;".@?3c"f6M!/0O@)+i(W&0@)3d#(,/)*232&)!3'E:qr-1>0:(*@)3d32O+<1`2&09( 6M-R*.* #$O$#Z(*@)30(S1*>0@1*>0`(*C2(D1!1"%@)(WO1(U11*>0¶> J]H".O1 ^1VO+<1I K (D19"_1*E 0

32I(&)((W53O@

second digit/ set timer (5 ms)

Await Next Digit

timer alarm/beeping first digit/ set timer (5 ms)

Await Second Digit

Await Caller On−hook

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*

Version 2 CSE, IIT Kharagpur

Await Second Digit first digit

dial tone / set timer (30 s)

Await First Digit

Idle

*-*£(,@L232!$Z.-[".@

O+&0*

A>

IK

timer alarm / idle tone

±

l FGC/M\%- V"32$#O@0@)(W1*9".#@1

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Await First Digit dial tone

handset lift / set timer (2 s)

* 2(

timer alarm / beeping

Await Dial Tone

O+&0* % ,@L232!$Z.-[".@L l

Await Receiver On−hook

FGC/M\%- V"32$#O@0@)(W1*9".#@1

$ 5$ 5"8Q < qX@ 5.E E E 0S=]>?"%3w@)(*#32*53 1*>0y-R%$#$O_]7#@0+v!^2"%/0$Oy.-:".@ l4l 1DC/?%-:@2N (W1*9".#@Q1( =; = 2; ¬¡ =R¥2} 2 - ¯;£¦1¦ § ¯;-2 ¡R }2¤7$ =$¢ 2 ¢2; ' 7¡v¢ 7R¥2; 2¢ ¯;£¦1¦--R=$ ¬¡; ;}2¤8¡<§ ; -=¡; 2¬}£¦1¦¯¡ 2-}< -2¤

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*;,

Version 2 CSE, IIT Kharagpur

Await First Digit ring−back tone

ring tone / set timer (2 s)

* (

#+%&0

timer alarm / terminate call

Await Ring−back Tone

Await Receiver On−hook

@i30!$%-".@

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Await Next Digit timer alarm

first digit / set timer (10 ms)

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#+%&0

2;

next digit / beeping

Await Next Event

Await Caller On−hook

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*

Version 2 CSE, IIT Kharagpur

Local Operator button release button press set alarm (15sec)

Await Event1 button release

Inter− national Operator

timer alarm

set alarm (15sec)

Await Event2

timer alarm

* (

#+%&)*

Dial Tone

button release dial tone Await Button Release

@i30!$%-K" V&0".1*#%@)"%$%@)(W1*9".#@Q1

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*

Version 2 CSE, IIT Kharagpur

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*

Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

absolute deadline of Ti(1) = Φ+d relative deadline of Ti(1) =d Φ

Φ+ d

Ti(1)

Ti(2) Φ+ pi

0 arrival of Ti(1)

deadline of Ti(1)

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Version 2 CSE, IIT Kharagpur

T2 T1

T4

T3

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Version 2 CSE, IIT Kharagpur

ei

Φ =2000 0

di

Φ

Φ + pi

Φ + 2*pi

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Version 2 CSE, IIT Kharagpur

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*

Version 2 CSE, IIT Kharagpur

Φ+ x= pi

M

M

Ti(1) Ti(2)

Ti(k−1)

Φ

Ti(k) Ti(k+1)

Ti(2k−1)

Φ

x

x

rCMi/S*6)#L y,j0I?6 K c:17+M)H}~(*)>$W| ,?.Gº » ¶b,/.I/$:@)76=I U( ,?.CM$ i time

)<,?13(DE,50I?6P1c:17+M)/Q |..S*DE)f&( ,5&&=(*)m.YC-7)fI5T)>,/13(kDd,j0I/617cO17+M)HCX. sQ*^(*)7$J[:Ta6I/D ,5$CM$ .4z)>1 &=CMI/$I?TrC-i Q# [OTaI/6K&=(*)f&=,/.YGE&=Ie6=)74z)>,5&CX9:)>$/&=C-1>,5+-+Mc C-$W)>,?13(Dd,j0I/6^17c:1+-)?Q . ¼ Ì ¾ z»'M

s¼KJ Ì ¾ bIj8m[?TaI/6F&( )b&3,?.GZº\»\&=I'( ,on/)CX9:)7$N&CX17,?+LI:1>1S*6=6)>$ 1)&C-De)<.UC-$)<,?13(dDd,j0I/6K1c:17+M)/[ = WD'SL.0&)>`NS ,5+ &I"L»¼.)7)rC-i Q J:Q #N¾Q OS V .0&=CA&=S:&C-$*iE&=(*C-.CM$lq:4*6 [ . ¼ Ì '¾ ! LE» L» . ! L» OIL[&(*)DE,50I?6e1c:1+-) 17I?$N&=,?CM$ .Z,5$sC-$N&)7i/6=,?+UDZS*+A&=CM4 +M)I5T L»Qy^(*CX.e,56=i?S*DE)7$N&'( I?+X9*.mTaI/6')>,/13(u&=,/.YGuC-$s&(*)k&=,/.YGu.Y)7& C-66=)>.4z)>1 &=CMn/)I?TCM&=.4*( ,?.)?Q^(*)>6)7TaI?6=)?[ . t¼ IF 7 EH97 7 o¾ Q

87 . &87)35 $

&

(

Kc:1+-CX1k.=13(*)>9:S +M)>6=.e,56=)n?)>6cu4zI?4*S +-,?6e,?$ 9t,56=) V )7C-$*i{)qO&)>$ .YC-n?)>+McuS .)>9CM$&(*)C-$ 9:S .Y&6=c?Qu|·+X,56=i?)kDE,50I?6=CA&0cuI?Tb,5+-+.Dd,5+-+ )>D V )>9*9:)<9{,?4*4*+-C-1>,j&=CMI/$ . V )>CM$*iDd,5$OS:T,/1 &S 6)<9_4*6=)>.)7$N&+-c_,56=) V ,?.)>9yI?${17c:1+-C-1E.=13(*)>9:S +M)>6=.>Q Kc:1+-C-1E.=13(*)>9:S +M)>6=.f,56=)e.C-De4 +M)/[ ) d17CM)>$N&>[/,?$ 9e,56=)K)<,?.cm&IH4*6=I?i/6=,?DQ|$E)q*,5DE4*+-)P,54*4 +MCX17,5&C-I?$e8P(*)76=)P,f17c:1+-C-1^.=13(*)>9:S +M)>6CX.$*I/6Dd,?+M+-cmS .)>9ZC-.,&)>DE4L)>6=,5&S*6=) 17I?$N&6=I?+-+M)>6>Qd| &=)7DE4L)>6=,5&S*6=)d1I/$/&=6I/+M+-)76H4z)76=CMI:9:CX17,?+M+-cy.=,5DE4*+-)>.f&=(*)E&)>De4z)763,j&=S*6=)dI5T,W6=IOI?D ,?$ 9{DE,?CM$N&3,5C-$ .HCA&e,j&p,W4*6=)>.)& nj,5+-S*)/QUOS 13(&)7DE4z)763,j&=S*6)p17I?$N&6=I?+-+-)763.K,?6)H)7D V )<9*9:)<9C-$&0cO4*C-1>,5+]17I?DE4*S:&=)76@17I?$N&6=I?+-+M)<9,5C-61I/$ 9:CM&C-I?$*)>6=.>Q Task Number

Frame Number

T3

F1

T1

F2

T3

F3

T4

F2

r CMi/S*6=) (*|$lq*,5DE4*+-)p:13(*)<9:S*+-)p, V +M)fTaI/6, Kc:17+MCX1p:13(*)<9:S*+-)76 | 1c:1+-C-1e.=13(*)>9:S +M)>6b6=)74z)>,j&3.,k4*6=)>1I/DE4*S:&)<9_.=13(*)>9:S +M)/Qf^(*)e4*6=)>17I?DE4*S:&=)>9_.=13(*)>9*S*+M)Z$*)7)<9*.&I V )E.0&=I?6=)>9WI/$*+McWTaI/6bI/$*) Fd75Z¹ST?¹7M ,?.9:CX.=1S .=.Y)<9kC-$yO)<15Q J*Q #LQ Ì Q2K,?13(&=,/.YGC-$W&( )H&=,?.Gk.)&P&=I V )'.=13(*)<9:S*+-)>96)>4L)<,j&=.C-9:)>$N&CX17,5+-+-cCM$l)>n?)>6cdDd,j0I/6 17cO17+M)/Q{^(*)Dd,j0I?6e1c:1+-)kCX.e9:CMnOCX9:)>9tCM$N&I{I?$*)I?6ZDeI/6)kDeC-$*I/6e17cO17+M)<.k¼h.Y)>)rCMiLQ N¾ QuU,?13(uDEC-$*I?6E1c:1+-)kCX.e,5+X.YIy1>,5+-+M)<9s, "3XFE7Qx#%$t&( )k)q*,?De4 +M).Y(*Ij8P$sC-$rC-i Q *[2&( )kDd,j0I/6Z1c:17+M)( ,?. V )>)7$9*CMnOCX9:)>9CM$N&IyTaI?S*6ZDECM$*I/6e17c:1+-)>.¼Ta63,5DE)>.3¾ Qx^(*)

Version 2 CSE, IIT Kharagpur

.=13(*)>9*S*+MC-$*i4zI?C-$N&=.bI5TF,d1c:1+-CX1p.13( )>9:S*+-)76bIO1>1S*6f,j&Ta63,5DE) V I?S $ 9*,56=C-)>.>Q^(*CX.DE)<,5$ .&( ,5&,E&=,/.YG17,?$_.0&3,56&b)q:)>17S:&C-$*idI/$*+Mc ,5&&=(*) V )7i?C-$*$*C-$*idI?T2,ZTa63,5DE)?Q ^(*)Ta63,5DE) V I?S*$L9*,56=CM)<.^,56=)9:)7; $*)>9&(*6=I?S i?(&=(*)fCM$N&)>66=S*4:&3.i?)7$ )763,j&)<9 V c,p4z)76=CMI:9:CX1b&C-De)>6>QFK,?13(d&3,?.GEC-.^,?.=.CMi/$*)>9E&=I 6=S*$xCM$xI?$*)EI/6fDEI/6)ZTa6=,?DE)>.>QZ^(*)d,?.=.CMi/$*DE)7$N&fI?TU&3,?.GO.&=ITa63,5DE)<.CX.m.Y&I?6=)>9yCM$s,y7¹WV =XR:Mk M7QE|$u)q*,5DE4*+-)E.13(*)<9:S*+-) &3, V +-)mC-.P.(*Ij8P$CM$ (*Q Major Cycle

Major Cycle

Minor cycle

r C-i?S*6=) * _,50I?6,5$L9lC-$*I/6 KcO17+M)<.^CM$l, Kc:1+-C-1p*13(*)>9:S +M)>6 ^(*)m.CM>)I?TJ&=(*)fTa6=,?De)f&=I V )HS .)>9 V c&(*)m.=13(*)>9:S +M)>6CX.P,5$C-De4zI?6&=,?$N&^9:)<.YC-i?$4 ,?6=,?De)7&)>6,?$ 9k$ )7)>9 .&I V )m13(*IN.Y)>$kn/)76=c 1>,56=)TaS*+-+Mc/Q| .Y)>+M)<1 &)<9Ta6=,?De)m.CM>)m.Y(*I/S*+X9.=,j&=C-.YTacd&=(*)HTaI?+-+MIj8PC-$*iZ&(*6=)7)p17I?$ .Y&63,5C-$N&=.>Q Ì Q Á±Á xÇT ZÊz±²>´\² QEÁ²>³ RÁT± SGB ^(*CX.d1I/$ .Y&63,5C-$/&eC-.EC-DE4LIN.Y)<9t&=I{DEC-$*C-DeC-7)&=(*)W$NS D V )76dI5Tf1I?$N&=)qO&.Y8PCM&=13(*)<. I:171S 66=CM$ iW9*S*6C-$*i&=,/.YG{)q:)>17S:&C-I?$JQ^(*)k.C-De4 +M)<.0&pC-$N&)76=4*6=)&3,j&C-I?$uI?TK&=(*C-.Z1I/$ .0&=6=,?CM$N&mCX.H&( ,5&Z,&=,/.YG{CM$L.0&3,5$ 17)dD'S .Y& 1I/De4 +M)7&)6=S*$*$*C-$*iZ8PCA&=(*CM$kCA&3.K,/..CMi/$*)>9eTa63,5DE)/Q b$*+-)>.=.U,m&3,?.Ge17I?DE4*+-)&=)>.K8PCA&=(*CM$kCA&3.K,?+M+-I:17,j&=)>9ETa63,5DE)/[?&=(*)&3,?.GZDEC-i?(N& ( ,on?)k&I V )_.YS .4z)7$ 9:)<9,?$ 96)<.0&3,56&)>9CM$~,{+-,5&)>6ETa6=,?De)/Qv^( C-.E8I?S*+X96)<`/S CM6=),x1I/$N&)qO&.8PCA&313(C-$On?I?+-nOCM$ ix.I?DE) 4*6=IO17)>.=.YC-$*ieIjn?)>6(*)<,?9\Q2IE,on/I?CX9S*$ $*)>17)>.=.,?6ck17I?$N&)7qO&P.8PCM&=13(*)<.7[O&=(*)p.Y)>+M)<1 &=)>9Ta6=,?DE)H.C-7)m.Y( I?S*+X9 V )m+X,56=i?)>6K&=( ,5$&=(*) )q:)>17S:&C-I?$u&=CMDE)I?T)>,/13({&3,?.G[2.IW&(L,j&Z8P( )7$t,W&3,?.Gx.Y&=,?6Y&3.p,j&Z,lTa6=,?De) V I/S*$ 9*,?6cxCA&e.Y(*I/S*+X9 V ), V +-)d&I{1I?DE4*+-)&=) 8PCA&=(*C-$y&=(*).,?DE)'Ta63,5DE)?QEr*I/6Dd,?+M+-c?[]8)d17,?${.Y&=,j&=)e&(*CX.p1I/$ .Y&63,5C-$/&m,?.> 1 ¼ &o» j¾

·8P(*)76=)) &<»^CX.f&( )e)7q:)>1S*&C-I?$ &C-DE)>.KI5T\&( )I?T\&=,?.GEº\»0[:,5$ 9kr{CX.K&(*)bTa6=,?DE).CM>)?Q I?&)&=( ,j&&( C-.1I/$ .0&=6=,?CM$N&UC-DE4LIN.Y)<.K,'+MIj8)76@ V I/S*$ 9EI?$Ta6=,?De).YC-7)/[ ChQ )?Q2&=(*)HTa63,5DE)m.YC-7)mrtDZS .Y&$*I5& V )p.YDd,5+-+-)76^&(L,5$ 1 ¼ &o» o¾ Q J*Q Á±Á Á ?*²>ÁÊz± Ê 3¬K*ÉÀh´ QJÁ /E´ B ^(*CX.1I/$ .Y&63,5C-$/&d6=)>`NS*C-6)<.Z&( ,5&&(*)l$OS*D V )>6dI5TH)7$N&6=C-)>.EC-$&=(*)y.=13(*)>9*S*+M)&3, V +-) .Y( I?S*+X9 V )fDEC-$*C-D'S*D C-$kI/6=9*)76K&IeDeC-$*C-DECM>)&=(*)H.0&=I?63,5i?)6)<`NS*CM6=)7DE)>$/&I5T]&=(*)m.13( )>9:S*+-)&3, V +-)?QFg)7DE)7D V )>6K&=( ,j&P1c:17+MCX1 .13( )>9:S*+-)763.p,?6)SL.Y)<9sCM$.YDd,5+-+)7D V )>9 9:)>9t,?4*4*+-C-1>,j&=CMI/$ .p8PCM&(n?)76=c{.Dd,5+-+.Y&I/6=,?i?)1>,54 ,/1CM&0c?Q{OIL[&(*CX.Z17I?$ .Y&63,5C-$N&'CX. CMDE4zI?6&=,?$/&b&Id&=(*)Z17I?DEDE)7631CX,5+.S 1>1)>.=.I?TF,d4*6=IO9*S 1 &,5&C-I?$_I?T&(*)Z$NS D V )76bI?TF)7$N&6=C-)>.^&=I V )Z.Y&I?6=)>9WC-$l&=(*) .13( )>9:S*+-)H&=, V +-)p17,5$ V )',?13( CM)>n?)>98P(*)>$W&(*)pDEC-$*I?61c:1+-)p.`NS ,?6)>+Mc9:CMnOCX9:)>.P&(*)pDd,50I?61c:17+M)/QK}~(*)>$W&(*)mDEC-$*I?61c:1+-) .`NS ,?6)>+Mcl9:C-nOC-9*)>.f&( )eDd,50I?6m1c:1+-)?[]&(*)EDd,j0I/6H17c:1+-)e17I?$N&=,?CM$ .H,?${C-$N&)7i/6=,?+2$NS D V )76mI5TKDeC-$*I/6p1c:1+-)>.E¼a$ ITa63,?1&C-I?$ ,?+ DECM$*I/6F1c:1+-)>.3¾ Q $ +M)<..2&=(*)DEC-$*I?6U17c:1+-)^.=`NS ,56=)7+-c'9:C-nOC-9*)>.2&=(*)Dd,j0I/6F1c:1+-)?[N.0&=I?6=CM$*if&=(*).13( )>9:S*+-)^TaI?6UI?$*)^Dd,j0I/6F1c:1+-) 8KI/S*+X9$ I5& V )'.S 1C-)7$N&>[,?.^&=(*)'.=13(*)>9*S*+M)<.C-$W&(*)'DE,50I?6b17c:1+-)p8KI/S*+X9$ I5&b6=)74z)>,5&,5$ 9&=(*C-.8I?S*+X9DE,?G?)H&=(*)'.CM>)pI5T &(*)p.=13(*)<9:S*+-)&3, V +-)H+-,?6i/)?Q2}x)p17,5$TaI?6=D'S +-,5&)f&(*CX.17I?$ .Y&63,5C-$N&^,/.7 f1

f2

f3

f4

f4n

f4n+1

f4n+2

f4n+3

.

#%$sI5&=(*)76Z8KI/6=9*.>[CAT^&( ) L IOI?6'I5T 5r«)<`/SL,5+X. 5rK[J&(*)>$s&( )Dd,j0I?6Z1c:1+-)8I?S*+X9s1I/$/&3,5C-$t,5$sC-$N&)7i/6=,?+F$OS*D V )76ZI5T Ta6=,?DE)>.>Q

Q Q]*²>Á® 3*³5²<ÁÊz±wÊ 3P¬*®>¯Ã´N ÅÀhÁ±´EB ^(*CX.&(*C-6=91I/$ .Y&63,5C-$/&^I?$kTa6=,?DE)H.C-7)fC-.^$*)<1)<..=,56=ce&IEDE)7)&^&=(*)f&=,?.G9:)<,?9:+-CM$ )>.>Q ^(*CX.17I?$ .Y&63,5C-$N&CMDE4zI/.)>.b&( ,5& V )&08)7)7$_&(*)E,56=6C-nj,5+]I?TU,d&3,?.G,?$ 9lCM&=.f9:)>,/9:+MC-$*)/[L&=(*)76=)pDZS .0&f)q:CX.0&H,j&+-)>,/.0&fI?$*)pTaS*+M+ Ta6=,?DE)?QP^(*CX.17I?$ .Y&63,5C-$N&C-.b$*)>17)>.=.,?6c.YC-$ 1)Z,E&=,/.YGW.Y( I?S*+X9W$*I5&DeCX.=.bCM&=.9:)>,/9:+MC-$*)/[ V )>1>,5S .) V ck&=(*)p&=CMDE)ZCA&17I?S*+X9 V ) &=,?G?)7$kS*4TaI/6^.=13(*)<9:S*+-CM$*iL[N&(*)H9:)>,/9:+-CM$*)f8^,?.KCMDEDECM$ )7$N&>Q KI/$ .YCX9:)>6U&=(*C-.>F,m&3,?.G17,?$I?$*+-c V )b&3,5G?)>$kS*4kTaI?6P.=13(*)>9:S +MC-$*i ,j&&=(*)b.Y&=,56&UI?T\,fTa63,5DE)/Q#T V )&08)7)7$E&=(*)b,?66=CMnj,?+ ,5$ 9E17I?DE4*+-)&C-I?$dI?T],f&=,?.G'$ I5&U)>n?)7$dI/$*)^Ta63,5DE)P)q:CX.0&3.7[O,m.YCM&SL,j&C-I?$,/. .Y( Ij8P$CM$WrCMiLQ DEC-i?(N&P,56=C-.)?Q#%$k&=(*CX.P17,?.)?[N&=(*)f&=,?.G,56=6=CMn/)>.U,Z+-CA&&+-)p,jT&)>6&(*)HGN&(kTa6=,?De)H( ,/.^.0&3,56&)>9]QFR V nOC-I?S .+McECM& 17,?$d$*I5& V )b&=,?G?)7$kS*4dTaI?6^.=13(*)>9:S +MC-$*i'C-$d&=(*)GN&=(dTa6=,?DE),5$L917,?$I?$*+-c V )b&=,?G?)7$kS*4kC-$d&( )e¼G Ì ¾&=(dTa6=,?DE)?+Q S:&>[N&( )7$ CA&Dd,oc V )m&=IOId+-,5&)H&IdDE)>)&bCM&=.9*)>,?9*+MC-$*)p.CM$ 17)H&(*)')q:)>17S:&C-I?$&C-DE)pI5T,e&=,/.YG17,?$ V )mS*4:&=Id&( )p.YC-7)mI?T,ZTaS*+-+]Ta63,5DE)/Q ^(*CX.HDeC-i?(N&m6=)>.S*+A&pC-${&(*)E&3,?.G_DEC-.=.YC-$*iWCM&=.p9:)<,?9:+-C-$*)d.YC-$ 1)E&=(*)E&=,/.YGyDeC-i?(N&p1I/DE4*+M)7&)dI/$*+Mc{,j&H&(*)d)>$ 9xI5TH¼a'G Ì ¾%&( ÌË

Version 2 CSE, IIT Kharagpur

Task arrival Deadline ∆t

t

0

kF

d

(k+1)F

(k+2)F

rCMi/S*6) U:,j&=C-.YT,?1&C-I?$I5T,e,?.G )>,/9:+MC-$*)

∆t

Task arrival

t

Deadline

d

(k+1)F

0

kF

(k+2)F

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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Context Switching Time

Foreground Back ground 01

51 52

Foreground Back Foreground ground

100

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time in milli Secs

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

Priority

Priority

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(1,0)

Number of tasks

r C-i?S*6=) Ì?Ì |13(*CM)>nj, V +-) P&=CM+-CM<,j&=CMI/$8PCM&(&=(*) S*D V )>6I5T2,/.YG:.^S*$L9:)76g y| ] 2À´ B ]µ K(*)>13G8P(*)&=(*)76b&(*)pTaI?+-+MIj8PC-$*i.)&I5T4z)76=CMI:9:CX1m6=)>,?+A@B&C-DE)H&=,?.G:.PCX..13( )>9:S*+X, V +M)mS*$L9:)76fg _| I/$_,ES*$*C-4*6I?@ 17)>.=.YI/6>º F . ¼ & F . J5Ë*[ F . Ì Ë?ËN¾ [:º H . ¼ & H6. ?Ë*[ H . Ì (5ËN¾ [OOº N . ¼ &N . ?Ë*[ EN . J5Ë?ËN¾ Q S:&=CM+-CM<,j&=CMI/$W,/13(*C-)7n?)<9k9:S )H&IE&( )H&(*6=)7)Hi?C-n?)>$k&3,?.G:.7Q QJÊLÀhÇJ²<ÁÊz±Uµ ])7&S .; 63.0&b17I?DE4*S:&=)H&(*)H&=I5&=,?+ N J5Ë /Ë /Ë . Ë » . Ë/Ë Ì (?Ë J?Ë?Ë Ì » F ^(*CX.C-.^+-)>.=.K&( ,?$ Ì [O&(*)>6)7TaI?6=)&( )f$ )>1)<..=,56=cd1I/$ 9:CM&C-I?$TaI/6P.13(*)<9:S*+X, V C-+-CA&0cdI?TJ&( )&3,?.G:.KCX.^.,5&CX.0;L)>9\Q Ij813(*)>13GOC-$*i'TaI/6 &=(*)m.YS 17CM)>$ 1ck17I?$ 9*CA&=CMI/$][O&(*)f&3,?.Gk.Y)7&CX.P.=13(*)>9:S +-, V +M)fS*$ 9*)76g _|ÄCM'T JCMSW,5$L9 ,ocN+X,5$L9 .1I/$ 9:CM&C-I?$i?C-n?)>$ V ckq:4*69\Q K(*)>13GOC-$*ifTaI?6F.=,j&=C-.YT,?1&C-I?$eI5TzFq:4*6>6Q J:Q Ì Ë [j&(*)^Dd,jq:C-D'S*D ,?13(*C-)7nj, V +M)S:&=CM+-CM<,j&=CMI/$eCX.2i?C-n?)>$ V c LK¼ J Ì ¾ . Ë * ^(*N )Z&I?&=,?+S*&C-+MC->,5&C-I?$y(L,?.f,5+-6)<,?9:c V )>)7${TaI?S*$L9l&I V )eË Q Q bIj8 .S V .Y&CM&S:&=CM$*i&( )>.)ZC-$_&=(*) ]C-S{,5$L9 J,ocO+X,5$ )9 .16=CA&=)76=CMI/$] z» 3¼ J Ì ¾[*8K)Hi/)&Ë vË **Q FqO» 4 T6>F Q J:Q Ì Ëu8P(* CX13(wC-.,s.YS 17CM)>$/&1I?$L9:CA&=CMI/$wTaI?6kg _| .=13(*)>9:S +-, V CM+-CM&0cCX.k.=,j&CX.Y; )>9\QÄ^(*)>6)7TaI?6=)?[K&(*)l&3,?.G.)&kCX.kg _| .=13(*)>9*S*+-, V +-)?Q ] 2À´ B Jµ K(*)>13G_8P( )&( )76m&=(*)dTaI?+-+-Ij8PCM$*il.)&pI?TK&=(*6)>)d4L)>6C-I:9:CX1Z6=)>,?+A@B&C-DE)E&=,/.YG:.HCX.p.13( )>9:S*+X, V +M)ES*$ 9*)76'g y| I?$u, S*$ CM4*6=I:1)<..I?6<Gº F . ¼ &F . J?Ë*[ IF . Ì Ë/Ë/¾[NOº H . ¼ &H . /Ë*[ EH . Ì (5Ë/¾[Oº N . ¼ & N . Ë*[ N . J?Ë?Ë/¾Q QJÊLÀhÇJ²<ÁÊz±Uµ J)&S .; 63.Y&b1I?DE4*S*&)f&(*)H&=I5&3,5+ S*&C-+MC->,5&C-I?$l9:S*)H&=IZ&=(*)mi?C-n?)>$k&3,?.Gk.)&> N J5Ë ?Ë Ë z » . Ë?Ë (?Ë J5 Ë/Ë . Ë *,( Ì Ì » F bIj8w13( )>13GOCM$ iHTaI?6 JCMS,5$ 9 ,ocN+X,5$L9e176CM&)>6C-I?$J N» F z» vË *'UN.CM$L1)bË *,( w Ë * [5&( )&=,/.YGE.)&UCX.F$*I?&g y|«.=13(*)>9:S +-, V +M)/Q

JJ

Version 2 CSE, IIT Kharagpur

JCMSW,5$ 9!,ocN+X,5$L9d&)<.0&'¼hq:4*6$ .Y)/Q

1 +C))5: 5 4) $ ( &!) 4%):0 > ) %;<:3$ = 6 T8&4)*) < %;<7. 1 %& > )#. > (? ,$ $ 4) 4%'3 7 +6))5:; 59+) > 9$ ( &,) 4% ),0 > ) %"< <:3E ;;),0 > >*. 14 %'&(> )#. > (?

#&PTaI/+M+-Ij8.Ta6I/D &( C-.&( ,5&)7n?)>$8P( )7$l,e&=,/.YGk.)&PT,?CM+X.JCMSl,5$L9 ,ocO+-,?$ 9 .U&=)>.Y&>[L8K)m.(*I?S*+X9$*I5&b17I?$ 17+MSL9:)H&( ,5&CA&CX.P$*I?& =. 13(*)>9*S*+-, V +-)PS*$ 9:)>6Ug _|'Q/}x)$*)>)>9e&IH&=)>.Y&FTaS*6&(*)>6F&=Ip13(*)>13GZCAT&( )P&=,/.YGe.Y)7&UC-.Ug _| .=13(*)>9*S*+-, V +-)?Q2|w&)<.0&F&=( ,j&17,5$ V )4z)76@ TaI/6DE)>9f&=Ib13(*)<13G8P(*)7&(*)>6,^&3,?.Gf.)&C-.g _|.=13(*)<9:S*+X, V +-)F8P(*)>$mCA&T,5C-+-.]&(*) ]C-Sp,5$ 9 ,ocO+-,?$ 9&)>.Y&JCX.]&=(*) J)7(*I:1>GOc .\&=)>.Y& Q J)7(*I:1>GOcE&)>.Y&( ,/. V )>)7$W)q:4*6=)>.=.Y)<9,/.P^(*)7I/6)>D J:Q *Q R:¸z?7'j¸@Tdj# 5V*o ¸O jZV p%o#jGFE37 ¬ R´OÊ Æj´ B GB 7 " <j¹e35 %hZ FdZj #omX + 7Q¹ V*3 R:M -2 V*7m 3¹Bj% HU3 ?3/O ¸z R:¸z/ <7 5V*j3¸O 2

T1

T2 10

T1 30

T2 40

T1 60

T2 70

90

time in msec

(a) T1 is in phase with T2

T2

T1 20

T2 30

T1 50

T2 60

80

time in msec

(b) T1 has a 20 msec phase with respect to T2

rCMi/S*6=) Ì J:2}xI?63.0& ,?.)mgP)>.4zI?$ .)m^CMDE)HTaI?6,E,?.GRf1717S*63.K}~( )7$W#&C-.CM$F( ,/.Y)H8PCM&(W#&=.b¶C-i?(*)>6 F6=CMI/6CM&0cd,/.YG:. | TaI/6Dd,5+4 6IOI5TI5T&(*CX.p^(*)>I?6=)7D CX. V )7c?I/$ 9{&(*).=1I/4L)EI?TK&=(*C-. V IOI?GQ¶bIj8K)>n?)76<[\8)d4*6IjnOCX9:)d,5$xCM$N&=S*CA&=CMn/)d6)<,?.I?$*C-$*i ,/.&=I8P(Ocl^(*)7I/6)>D J:Q D'SL.0& V )Z&6=S*)/QHr I?6H,dTaI/6Dd,5+4*6=IOI5TFI5TU&(*) ])>(*I:17GOc' z6)<.YS*+M&=.b&( )Z6=)>,/9:)76fC-.6=)Ta)76=6=)>9W&=I Qf#%$*@ &=S*CA&=CMn/)7+-c?[j8)K1>,5$pS*$L9:)763.0&3,5$ 9m&(*CX.J6=)>.S*+M&JTa6=I?D &( )UTaI/+M+-Ij8PCM$ i6)<,?.I?$*C-$*iN.7Q]rC-6=.Y&+-)&2S .J&6=c&=IbS*$L9:)763.0&3,5$ 9m&(*)KTaI?+-+MIj8PC-$*iPT,/1 &
- . 1 )0! !+ O)=)5:211&(-; 0 9 # " ) 2-# $ , < 8 0 ): ?

If.)7)8P(Ocm&( C-..Y&=,5&)7DE)>$/&2D'SL.0& V )K&=6S )?[?17I?$ .C-9*)76&(*)TaI/+M+-Ij8PCM$ i.Y&=,j&=)7DE)7$N&n?)>62,(*C-i?(*)>624*6C-I?6=CM&0c &3,?.GdC-.^6=)>,/9:c?[O&=(*)H+MIj8)764*6=CMI/6CM&0cE&=,/.YG:.^17,?$$*I?&P)q:)>17S:&)m,5$L9k( ,on/)b&=IE8,?CA&.&=( ,j&<[ ,Z+MIj8)76^4*6=CMI/6CM&0ce&=,/.YG8PC-+-+ ( ,on/)f&Id8^,5CM&PTaI?6^&( )p)7$N&C-6=)p9:S*63,j&C-I?$I5T2)q:)<1S:&=CMI/$I?T)<,?13((*C-i?(*)>64*6=CMI/6CM&0cd&=,/.YG&( ,5&,56=C-.)>.P9*S*6C-$*ie&( )p)q:)>17S:&C-I?$WI?T&=(*) +-Ij8K)>6b4*6=C-I?6=CA&0c&=,/.YGQ _I?6=)p$OS*D V )76fI5TUC-$ .Y&=,?$ 1)<.I5T,d(*C-i?(*)>64*6=C-I?6=CA&0c&=,/.YGW8PC-+M+I:171S 6>[z8P(*)7$x,d&3,?.GCX.fCM$_4 ( ,?.)'8PCM&({CA&<[

J2

Version 2 CSE, IIT Kharagpur

P8 (*)>$uCA&'CX.mC-$u4*( ,?.)E8PCA&=(sCA&Z6=,5&(*)>6H&( ,?$xI/S:&pI5T^4*( ,/.Y)E8PCM&(sCM&>Q^(*C-.p( ,?. V )7)>$sCM+-+MSL.0&=6=,5&)>9y&( 6I/S*i?(s,W.YC-DE4*+-))q*,5DE4*+-) C-$trCMiLQ Ì J:Q#%$trCMiLQ Ì J*¼h,/¾ [2,l(*C-i?( )76p4*6=C-I?6=CA&0cl&3,?.Gx Ì . ¼ Ì Ë*[ ?Ë/¾CX.pC-$s4*( ,/.Y)d8PCM&(,W+-Ij8)76p4*6=C-I?6=CA&0cl&3,?.GxJ . ¼ /Ë*[ Ì J5ËN¾ [ &=(*)d6)<.Y4zI?$L.Y)e&C-DE)dI5T^JC-. ËDd.)>1?Q¶Ij8)7n?)>6>[\C-$srCMiLQ Ì J*¼ V ¾ [J8P(*)7$s Ì ( ,?.m, J?ËkDd.)>1E4*(L,?.)?[\&=(*)d6)<.Y4zI?$L.Y)e&C-DE)dI5T J V )<1I/De)<. *?Ë*Q^(*)76=)TaI/6)/[jCAT,&3,?.GmDE)7)&3.2CA&3.; 63.0&9:)>,/9:+-CM$*)^S*$L9:)7627)>6If4*( ,/.YC-$*iL[o&(*)>$'&=(*)7cpCM&8PCM+-+ODE)7)&F,?+M+:CM&=.29:)<,?9:+-CM$ )>.>Q

deadline for T1 T1 20

100 (a) T1 meets its first deadline

deadline for T2 T1

T2 20

50

150 (b) T2 meets its first deadline

deadline for T3

T1

T3

T2 20

50

T1 100

T2 120

T3 150

190

(c) T3 meets its first deadline

r C-i?S*6=) Ì K( )>13GOCM$ i J)7(*I:177GOc' . K6=CA&=)76=CMI/$kTaI/6,/.YG:.^I5T2q*,5DE4*+-)J:Q ] 2À´1 B Jµ K(*)<13G8P(*)7&(*)>6^&(*)H&3,?.Gk.Y)7&I5T2q*,5DE4*+-)J:Q *ZCX.P,?1&S ,?+M+-ck.=13(*)>9*S*+-, V +-)fS $ 9:)76g _|pQ QJÊLÀhÇJ²<ÁÊz±Uµ ^(*I/S*i?(x&=(*)d6)<.YS +A&3.mI5T ]C-Ss,5$ 9 ,ocN+X,5$L9 .f&=)>.Y&'8)76=)d$*)7iN,j&C-n?)/[J,?.p4L)>6m&(*)k6)<.YS*+M&=.pI5TPq*,5DE4*+-) J:Q *8K)1>,5$ ,?4*4*+-cd&(*) J)7(*I:177GOcd&)<.0&b,?$ 9I V .)76=n?)&(*)HTaI/+M+-Ij8PC-$*i r I?6K&(*)&=,/.YGeºGFo+ &F OF^(*I/+-9*..CM$ 17=) J?2Ë 1 &65 Ì Ë?2Ë 1 &65jQ^( )76=)TaI?6=)?[/CA&^8I?S*+X9dDE)7)7&CM&=.U; 63.0&^9:)>,/9:+MC-$*)E¼aCM&^9*IN)<.U$ I5&K(L,on?) ,?$Nc&=,?.G:.&( ,5&P( ,on?)H(*C-i?(*)>6P4*6=CMI/6CM&0c*¾ Q r I?6P&=(*)m&=,/.YGº H Uº F CX.PCM&=.( CMi/(*)764 6C-I?6=CA&0c&=,?.G,?$ 9l1I/$ .C-9:)>6C-$*idËE4*( ,/.YC-$*iL[*CA&8KI/S*+-9I:1717S*6I/$ 1) V )TaI/6)m&=(*)'9:)<,?9:+-C-$*)mI5T º H QF^( )76=)TaI?6=)?[\¼ & F & H ¾ H (*I/+-9 ..YC-$ 170) J?Ë /Ë . (59Ë 1 &65 Ì (?2Ë 1 & 55Q^(*)>6)7TaI?6=)?[:º H DE)7)&3.PCM&=.^; 63.Y&P9*)>,?9*+MC-$*)?Q r I?6F&=(*)&3,?.GZOº N?^3¼ J2& F J2& H &N7¾ ENb(*I?+X9*.>[N.CM$L1=) J!6J?Ë J!/Ë Ë . Ì 2Ë 1 &65 J5Ë?9Ë 1 &65jQ}{)( ,on?)b17I?$ .CX9:)76=)>9 J%! &F2,5$ " 9 J ! &HF.CM$L1)FGº F2,?$ 9mOº HI:1717S*6]&08PCX1)F8PCM&( CM$'&(*)U; 6=.Y&9:)<,?9:+-C-$*)FI5T*º N Q2^(*)>6)7TaI?6=)?[<º N De)>)&3.JCM&=.]; 6=.Y&9*)>,?9*+MC-$*)?Q2OI [<&=(*) i/CMn/)7$d&3,?.GE.)&^CX..=13(*)<9:S*+X, V +-)bS*$L9:)76Pg _|'Q*^(*)H.13(*)<9:S*+X, V C-+-CA&0ce&)<.0&TaI?6^º N (L,?.4*CX1 &I/6CX,5+-+-c V )7)>$.(*Ij8P$C-$rC-i Q Ì Q:CM$ 17) ,?+M+O&=(*)&=,?.G:.De)>)&&=(*)7C-62; 63.0&F9:)<,?9:+-CM$ )>.S*$ 9:)>67)>6If4*( ,/.YC-$*i [5&(*)>c',56=)g _|~.13( )>9:S*+X, V +M)^,?1>1I?639:C-$*i&I ])7( IO177GO'c .26=)>.S*+M&=.>Q

J)&US .K$*Ij8v&6=ce&I'9*)76=CMn/)b,mTaI/6Dd,5+L)q:4*6=)>.=.YC-I?$eTaI/6F&( C-.KCMDE4zI?6&=,?$/&6)<.YS +A&UI?T ])>(*I:17GOc/Q'J)& <º F 7Yº H 7 7Yº » V )b&(*)f.Y)7& I?T&3,?.G:.^&I V )'.=13(*)>9:S +M)<9\Q*])&SL.b,5+X.I,?.=.YS*DE)H&=( ,j&&=(*)m&3,?.GO.( ,on?) V )7)>$lI?639:)76=)>9CM$_9*)>.=1)7$L9:CM$ idI?639:)76I?T2&(*)>CM64 6C-I?6=CA&0c/Q ^( ,5&fCX.>[&=,?.Gl4*6=CMI/6CM&C-)>.f,56=)'6=)7+X,j&=)>9{,?.> ¼aºGF¾ 3¼ºOH>¾ ¼aº\»B¾ []8P(*)>6)e4*6=CB¼º\»h¾9:)7$*I?&)<.b&=(*)E4*6=CMI/6CM&0cWI5TF&=(*)

J8#

Version 2 CSE, IIT Kharagpur

Ti(1)

T1(1)

T1(2)

T1(3)

r CMi/S*6) Ì # 2#%$ .Y&=,5$L1)>.^I?Tº F Rn?)>6P,E:CM$*i/+M)m#%$L.0&3,5$ 17)fI?Tº » &3,?.Gkº » QbR V .)76=n?)f&(L,j&b&=(*)m&3,?.Gkº F ( ,/.^&(*)'(*CMi/(*)>.Y&b4*6=C-I?6=CA&0c,5$ 9&=,/.YGº » ( ,/.^&(*)'+M)<,?.Y&b4*6=CMI/6CM&0c?Q^(*C-.b4*6=CMI/6CM&0ckI/6=9:)>6C-$*i 1>,5$ V )H,?.=.YS*DE)<98PCM&(*I/S:&^,?$Oce+-I/.=.KI5TJi/)7$*)>6=,?+MC->,5&C-I?$k.CM$L1)&=(*)H6)<`NS*CM6=)>94*6C-I?6=CM&0ceI/6=9*)76=CM$*iZ,5DEI?$*ie,5$,56 V CA&=6=,?6cE1I/+M+-)>1&C-I?$ I?TK&3,?.GO.H1>,5$s,5+-8,oc:. V ),/13(*C-)7n?)<9 V cy,W.CMDE4*+-)d6=)7$ ,?DeC-$*iWI5TK&(*)E&3,?.G:.7Q KI?$L.YCX9:)76H&=( ,j&m&=(*)E&=,/.YGyº»P,?66=C-n?)>.f,j&m&=(*)E&C-DE) C-$ .Y&=,5$N&mË*Q KI/$ .YCX9:)>6&=(*)e)q*,5DE4*+-)e.(*Ij8P${CM$xrC-i Q Ì # 0Q S*6=CM$*i&( )Z;L6=.Y&fC-$ .Y&=,?$ 1)eI5TF&=(*)e&=,/.YGWº\»Y[&=(*6=)7)eCM$ .Y&=,?$ 1)<.fI5TF&=(*) &3,?.GºGF(L,on?)HI:171S 66=)>9\QK,?13(&=CMDE)mGº FI:1717S*6=.>[Oº\»2( ,?.&=Id8,?CA&.CM$ 17)Hº F(L,?.^(*C-i?(*)>6P4*6=CMI/6CM&0cE&( ,?$Wº»YQ J)&bS .b$*Ij8 9:)&=)76=DECM$*)p&(*)Z)q*,?1&b$OS*D V )76I5T2&C-DE)>.P&=( ,j&fGº FfI:171S 6=.P8PCM&( CM$y,k.YC-$*i?+-)pC-$ .Y&=,5$L1)pI?T2º\»YQ^(*C-.CX.i?C-n?)>$ V c QUOC-$ 17)Gº FI .K)q:)>17S:&C-I?$k&C-De)HCX. &Fj[O&(*)>$&( )b&=I5&=,?+)q:)>17S:&C-I?$k&C-De)f6=)>`NS*C-6)<99:S*)&IZ&=,/.YGEGº F V )TaI/6)&( )f9:)<,?9:+-C-$*)I?TJº\» CX. &4FjQ^( C-.U)q:4*6=)>.=.YC-I?$d17,?$E)>,?.C-+Mc V )i?)7$ )763,5+-CM>)>9'&I'17I?$ .C-9*)76&=(*))q:)<1S:&=CMI/$E&C-De)<.U,?+M+:&3,?.G:.( ,onOCM$ im(*CMi/(*)76U4*6C-I?6=CM&0c &=( ,5$lº\»P¼aCBQ )?Qº F87YOº H27 7Yº\» OF¾Q^( )76=)TaI?6=)?[*&(*)m&=CMDE)mTaI/68P(*CX13(Wº»F8PCM+-+J( ,on/)f&I8^,5CM&b9:S*)m&=I,5+-+]CM&=.( CMi/(*)764 6C-I?6=CA&0c&=,?.G:. 1>,5$ V )m)7qO4 6)<..)>9,?.> » F » &

FqO4 6)<..CMI/$ J*Q Ì/Ì i/CMn/)>.&=(*)^&I?&=,5+*&C-De)b6)<`/S CM6=)>9'&Im)7qO)<1S:&=)Pº\7» .(*C-i?(*)>64*6=CMI/6CM&0cm&=,/.YG:.TaI/6F8P(*CX13(eº\»\8I?S +-9Z( ,on?)&=Im8,?CA&
3¼ J Ì J/¾ F

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K¼ J Ì N¾ F

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9

Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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:13(*)<9:S*+-CM$*i'I5T]6=)>,5+M@B&C-De)&=,?.G:.FI/$,pS*$*C-4*6=I:1)>.=.I?6F8^,?.F,?$k,56=)>,HI?T]CM$N&=)7$ .)6=)>.)>,56313(ECM$&(*) Ì Ë?.F,?$ 9e&( )S*$L9:)76=+McOC-$*i &(*)>I?6=cdC-.$*Ij8«8)7+-+A@%9:)>n?)7+-I?4z)>9]Q $*C-4*6=I:1)>.=.I?66=)>,5+M@B&C-De)&3,?.GZ.=13(*)>9:S +MC-$*ip,5+-i?I/6CM&( DE.U17,5$ V 6=I/,/9:+-c V )1+X,?.=.YCM; )>9eC-$N&I'17+MI:13GN@9*6C-n?)>$][j)7n/)7$N&Y@%9:6=CMn/)7$][?,?$ 9 (Oc V 6CX9,?+Mi/I?6=CA&=(*Dd.7Q #%$_1+-I:13G/@%9:6=CMn/)7$W.13( )>9:S*+-)763.>[*&( )'.13( )>9:S*+-C-$*i4zI?C-$/&3.b,?6)p9:)7; $*)<9 V c&( )'C-$/&=)76=6S 4:&=.Pi/)7$*)>6=,5&)<9 V c&(*)e.Yc:.Y&)>D 17+MI:13GQ #%DE4LI/6Y&3,5$N&1+-IO13GN@%9:6=CMn/)7$W.13(*)<9:S*+-)763.P,56=)f&=, V +M)7@ V ,/.Y)<9W,5$ 9W1c:17+MCX15Q KcO17+MCX1m.=13(*)>9:S +M)>6=.P,?6) V )7C-$*i4*6=)>9:I/DECM$ ,?$N&+-cS .)>9 CM$W.DE,?+M+J)7D V )>9 9:)>9W,54 4*+MCX17,5&C-I?$ .^9:S )H&IE&( )7C-6.YC-DE4*+MCX1CM&0c,?$ 9+MIj86S*$&=CMDE)mIjn?)>6( )>,?9]Q |DEI?$ im&(*)f+X,56=i?)$OS*D V )>6KI?T]6)<.YS*+M&=.U&(L,j&,?6),ono,?CM+X, V +M)C-$k)>n?)>$/&@9*6C-n?)>$E.=13(*)<9:S*+-CM$*iZI5T]6=)>,?+A@B&C-DE)&=,/.YG:.UI?$k,'S*$*C-4*6I?@ 1)<..I?6<[N&08KIE,5+-i?I/6CM&(*Dd.P,?6)fDEI/.Y&b.YC-i?$*CM;L1>,5$N&> fr«¼hU,?6+-CM)<.0#& )>,?9*+MC-$*)prCM63.Y&3¾ F^( C-.PCX.P,5$WI/4:&C-Dd,5+]9:cO$ ,?DeCX1f4*6=CMI/6CM&0ck.=13(*)>9:S +MC-$*id,5+-i?I/6CM&(*DWQ g _| ¼hg,j&=) lI?$ I5&I/$*CX1f|b$ ,5+-c:.YCX.3¾ ^(*CX.PC-.P,?$WI?4:&=CMDd,5+].Y&=,5&CX1H4*6=CMI/6CM&0c.13( )>9:S*+-C-$*id,5+-i?I?6=CM&(*DWQ ^(*I?S i?(W frCX.,5$WI/4:&C-Dd,5+]6=)>,?+A@B&C-DE)H&=,?.Gk.=13(*)>9*S*+MC-$*i,?+Mi/I?6=CA&=(*D I?$l,ES*$ CM4*6=I:1)<..I?6<[:CA&f.YS:)763.^Ta6=I?D ,eTa)78Ä.Y(*I/6Y&@ 1I/DeC-$*iN.7Q^#&f1>,5$*$ I5&bi/S ,563,5$N&)>)H&( ,5&b&=(*)Z176CM&CX17,?+\&=,/.YG:.DE)>)&b&=(*)7C-6f6)<.Y4z)>1&C-n?)p9:)<,?9:+-CM$ )>.S $ 9:)76&63,5$L.YC-)7$N&bIjn/)76=+MIN,?9\Q )>.C-9:)<.7[jC-DE4*+-)7DE)7$N&=,5&C-I?$eI5T 6=)>.I?S 6=17)K.( ,56=CM$ i,5DEI/$*i6=)>,?+A@B&C-DE)U&3,?.G:.CX.)qO&6=)7DE)>+Mcp9:C 1S*+M&>Q^(*)>6)7TaI?6=)?[5 r@ V ,?.)>9 ,5+-i?I/6CM&(*Dd.^,56=)f6=,?6)>+McdS .)>9C-$W4*6=,/1 &=C-17)H,?$ 9g _|P@ V ,/.Y)<9.=13(*)>9*S*+MC-$*id,5+-i?I/6CM&( DE.^(L,on?) V )<1I?DE)H4zI?4*S*+X,569d&(*)fDd,5C-$6)<.YS +A&3.K17I?$ 17)76=$*CM$ ip(*Ij8w&Ie9:)&=)76=DECM$*)&( ).=13(*)>9:S +-, V CM+-CM&0ceI?TJ,'.)&^I5T\&3,?.GO.US*$ 9:)>6P frx,?$ 9 g _|'Q }{)H,5+X.IZ9:CX.17S .=.Y)<9d(*Ij8w&IeIjn?)>6=17I?DE)b.I?DE)b4 6I V +M)>Dd.F&=( ,j&,56=CX.Y)8P( CM+-)f9*)7n?)>+MI/4*C-$*iZ,Z4*63,?1 &=C-1>,5+z6)<,5+M@h&=CMDE)f.Yc:.Y&)7DWQ2#%$ 4 ,56&CX1S +-,?6>[N8K)f9:CX.17S ..)>9k(*Ij8w&Ie( ,?$ 9:+-)f.CA&=S ,j&=CMI/$ .^.YSL13(k,?.8P(*)>$&=,/.YGE4*6=C-I?6=CA&=CM)<.K9:CM)76Ta6I/D&=,/.YGd16=CM&CX17,5+-CM&C-)>.>[O,?$ 9 ,?.=.YC-i?$ CM$*i'4*6C-I?6=CM&C-)>.K&IZ&=,/.YG:.KTaI?6Pg _| .=13(*)>9:S +MC-$*ie8P(*)7$&(*)H4*6=C-I?6=CA&0cE+-)7n?)>+-..S*4*4zI?6&)>9 V cE&(*)HI/4L)>6=,5&C-$*iZ.c:.0&=)7D CX. +M)<..&=( ,5$&( )m$NS D V )76I?TJ&=,/.YG:.&=I V )p.=13(*)>9*S*+M)<9\Q ;

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§

Version 2 CSE, IIT Kharagpur

Ì QbN&=,5&)m8P(*)7&(*)>6P&( )mTaI?+-+MIj8PC-$*id,?.=.)76&C-I?$ .^,56=) ¬ 6=S*)pI?6 >P,?+-.)?QU}{6=CA&=)mI?$*)mI/6^&08KI.)7$N&=)7$ 17)>.&IH0SL.0&=CATacWc?I/S*6P13(*I?CX1)mC-$ )>,/13(17,/.Y)/Q ¼,N¾k|bn?)763,5i/)b6=)>.4LI/$ .)b&=CMDE)HC-.^,?$C-DE4LI/6Y&3,5$N&4z)76TaI?6=Dd,5$ 17)DE)7&6=C-1bTaI?6P6=)>,?+A@B&C-DE)bI?4z)763,j&=CM$ ie.c:.0&=)7Dd.( ,5$ 9*+MC-$*iE6S $:@ $*C-$*idI?T( ,?6=96)<,5+M@h&=CMDE)f&=,/.YG:.>Q ¼ V ¾ b$*+MC-G?)H&3, V +-)@%9:6=CMn/)7$.13(*)<9:S*+-)763.7[*17c:1+-C-1H.=13(*)>9:S +M)>6=.P9:IE$*I?&6)<`NS*CM6=)&I.Y&I?6=)H,Z4 6)<1I?DE4*S*&)>9W.=13(*)>9*S*+M)/Q ¼1>¾}~(*)>$yg _| C-.bS .Y)<9TaI?6f.13(*)<9:S*+-CM$ i,.Y)7&bI5T( ,?6=96=)>,?+A@B&C-DE)p4L)>6C-I:9:CX1H&=,/.YG:.>[:&(*)ZS*4*4z)76 V I/S*$ 9WI?$_,/13(*C-)7nj, V +-) S:&=CM+-C->,j&=CMI/$WCMDE4*6=Ijn?)<.,/.&(*)m$OS*D V )>6PCM$&3,?.GO.^C-$&(*)p.c:.0&=)7D V )7C-$*i9:)>n?)>+MI/4L)<9kC-$ 16=)>,/.Y)<.7Q ¼9 ¾#T,E.Y)7&^I?T4z)76=CMI:9:CX1f6)<,5+M@h&=CMDE)f&=,/.YG:.KT,5C-+X*. ])7( IO177GO'c .&=)>.Y&>[O&=(*)7$WCM&b17,5$W.=,jTa)7+-c V )p1I?$L1+-S 9:)>9k&(L,j&P&( C-.&3,?.Gk.Y)7& 1>,5$$*I5& V )HTa)>,/.YC V +-ck.13( )>9:S*+-)>9S*$L9:)76g y|pQ ¼a)<¾| &=CMDE)@%.+MCX1)<96=I?S $ 9O@6I V CM$.13( )>9:S*+-)76PSL.Y)<.^4*6)>)7DE4:&=CMn/)H.=13(*)<9:S*+-CM$*iLQ ¼T=¾W^(*)DECM$*C-D'S D 4z)76=C-IO9eTaI/6K8P( C-13(,H&3, V +-)@%9:6=CMn/)7$.=13(*)>9*S*+M)>6U.=13(*)>9:S +MC-$*ip$4z)76=C-IO9*C-1^&3,?.G:.F$*)>)>9*.F&I'4 6)7@.Y&I/6)^&=(*) .=13(*)>9*S*+M)HCX.Pi?C-n?)>$ V cDd,5q IF 7 EH97 N[:8P(*)76=) L»2CX.^&(*)m4z)76=C-IO9I5T&( )H&=,?.Gº\»0Q ¼aiO¾kg y| C-.b,5$WI?4:&=CMDd,?+J.0&3,j&=C-1f4*6=CMI/6CM&0ck.=13(*)>9*S*+MC-$*i,?+Mi/I?6=CA&=(*D &I.=13(*)<9:S*+-)H,d.)&I?T4z)76=C-IO9*C-1H6=)>,?+A@B&C-DE)&3,?.G:.PI?$W, $*I/$:@4*6)>)7DE4:&=CMn/)fI/4L)>6=,5&C-$*iE.Yc:.Y&)7DWQ ¼a(L¾|1c:1+-CX1y.=13(*)>9:S +M)>6kCX.DEI/6)_4 6I?;L1C-)7$N&k&=( ,5$,t4*S*6=)_&3, V +-)@%9:6=CMn/)7$ .=13(*)>9*S*+M)>6kTaI/6.=13(*)>9*S*+MC-$*iv,.)&I?T'( ,?6=9 6=)>,?+A@B&C-DE)&3,?.G:.7Q ¼CX¾g y|CX.^,5$I?4:&=CMDd,5+].Y&=,5&CX1b4 6C-I?6=CA&0cd.=13(*)>9*S*+M)>6^CM$k&(*)Hi?)>$*)763,5+17,/.Y)8P(*)76=)&(*)f&=,/.YGd4z)76=C-IO9 .,?$ 9k9*)>,?9*+MC-$*)>.I?T, .)&I?T( ,?6=96)<,5+M@h&=CMDE)H4z)76=CMI:9:CX1f&=,/.YG:.Dd,ock9:CMz)>6>Q ¼ ¾WO)>+AT\.S .Y4z)7$L.YC-I?$eI5Tz&=,/.YG:.2C-De4L,?1 &3.&(*)P8I?63.Y&21>,?.)6=)>.4zI?$ .)U&=CMDE)<.I5Tz&(*)^C-$ 9:C-nOC-9:SL,5+:&3,?.GO.2DZS 13(eDeI/6)P,/9:n?)>6=.)7+-c 8P(*)>$y4*6=)7)>DE4:&C-I?$_I?TF&=,/.YG:.bC-.H.S*4*4zI?6&)>9 V cW&=(*)'I/4L)>6=,5&C-$*i.c:.0&=)7D 1I/DE4 ,56=)>9W&=I&=(*)e1>,?.)'8P(*)>$_4*6=)7)>De4*&C-I?$ CX.P$*I?&P.S*4*4zI?6&)<9\Q ¼G:¾|.YS*CM&=, V +-); i?S 6)FI?T*DE)76=CA&]&=I17I?DE4 ,56=)2&( )U4z)76TaI?6=DE,?$ 1)I?T*9:CA)76=)7$N&( ,5639H6)<,5+M@h&=CMDE)&3,?.Gf.=13(*)<9:S*+-CM$*i,?+Mi/I?6=CA&=(*Dd. 1>,5$ V )H&=(*)p,on?)>6=,?i?)&3,?.G6=)>.4LI/$ .Y)f&=CMDE)>.6)<.YS*+M&C-$*ieTa6=I?D )<,?13(W,5+-i?I?6=CM&(*DWQ ¼+X¾}~(*)>$l,e.)&PI?T4z)76=CMI:9:CX1f6)<,5+M@h&=CMDE)&=,?.G:.C-. V )7C-$*i.=13(*)>9:S +M)<9S .CM$ iEg _|p[*CM&17,?$$*I?& V )H&=(*)m17,?.)f&( ,5&,Z+-Ij8)76 4*6=C-I?6=CA&0cE&3,?.GkDE)7)7&=.^CM&=.9:)<,?9:+-C-$*)?[*8P( )76=)>,?.^.I?DE)H(*C-i?(*)>6P4*6C-I?6=CM&0cE&=,?.Gk9:IO)<.^$*I5&.Y#& )>,/9:+-CM$*)mrC-6=.Y&3¾^,?+Mi/I?6=CA&=(*D 4zI/.=.Y)<..)>.i?IOI:9k&63,5$ .CM)>$N&^Ijn/)76=+MIN,?9d(L,5$ 9:+-C-$*id17,54L, V C-+MCM&0c?Q ¼a$L¾| &=CMDE)@%.+MCX1)<96=I?S $ 9k6=I V CM$W.13( )>9:S*+-)76PCX.P,5$)q*,?De4 +M)mI?T,e$*I?$*@B4*6=)7)>DE4:&C-n?)m.=13(*)>9:S +M)>6>Q ¼aIO¾kg y| ¼g,5&) _I?$*I?&I?$ C-1d|b$ ,5+-c:.YCX.=¾fCX.p,?$xI/4:&C-Dd,5+U,?+Mi/I?6=CA&=(*D TaI/6'.=13(*)>9:S +MC-$*i_.Y&=,j&=C-1E4 6C-I?6=CA&0cy$*I?$:@4*6=)7)>De4*&C-n?) 4z)76=CMI:9:CX1H6=)>,5+M@B&C-De)&=,/.YG:.^( ,onOC-$*iE( ,56399:)>,/9:+MC-$*)<.7Q ¼a4L¾ r ,?+Mi/I?6=CA&=(*D CX.m,5$xI?4:&=CMDd,5+F,?+Mi/I?6=CA&=(*D TaI?6p.=13(*)>9*S*+MC-$*i( ,5639{6)<,5+M@h&=CMDE)Z&=,?.G:.fI?$u,kS*$ CM4*6=I:1)<..I?6H8P(*)>$y&=(*) &3,?.Gk.Y)7&C-.P,EDECMqO&S*6=)HI5T24L)>6C-I:9:C-1H,?$ 9W,54z)76=CMI:9:CX1&=,?.G:.7Q ¼h`O¾WOS 4*4LIN.Y)8K)( ,on?),Z.Y)7&UI5T]6=)>,?+A@B&C-DE)C-$ 9:)74z)7$L9:)7$N&&=,?.G:.&=I V )b6=S*$I?$,pS*$*C-4*6I:17)>.=.YI/6FS*$ 9:)>6g _|.=13(*)<9:S*+-CM$*iLQ }x)dI V .)76=n?)'&( ,5&',&=,?.GlI5T^4z)76=CMI:9 Ì ËDeC-+-+MCK:)>1e( ,?.HDE)7&pCA&3.m9:)>,/9:+MC-$*)/QEr 6I/D &( C-.HI V .Y)>6nj,5&C-I?$][\CM&p8KI/S*+X9 V ) .=,jTa)f&I17I?$ 17+MSL9:)f&( ,5&b,'&3,?.G( ,onOC-$*iE4L)>6C-I:9kI?+T (ZDECM+-+-CO)>1H8I?S +-99:);L$*CA&=)7+-ck( ,on/)DE)7&CA&3.9:)>,/9:+-CM$*)<.7[ ¼a6 ¾ Kc:1+-CX1m.13(*)<9:S*+-)763.^,56=)fDEI/6)f4*6=I5;L17CM)>$/&^&=( ,5$&=, V +-)@%9:6C-n?)>$.=13(*)<9:S*+-)763.7Q ¼h.=¾#%$,m$ I?$*4*6=)7)>DE4:&=, V +M)PI/4L)>6=,5&C-$*ip.cO.Y&)>D )>De4 +MIjcOC-$*ipg _| .=13(*)<9:S*+-CM$*i'I5T\,p.Y)7&UI5T6=)>,5+M@B&C-De)P4z)76=C-IO9*C-1^&3,?.G:.7[N.Y)>+AT .S .4L)>$ .YC-I?$lI?TF,d(*C-i?(*)>64*6=CMI/6CM&0c&3,?.Gx¼h9:S*)p&=I# ?R )&315Q ¾DE,ocC-$ 16=)>,/.Y)f&( )'6=)>.4LI/$ .Y)H&=CMDE)ZI5TF,d+-Ij8K)>6P4*6C-I?6=CM&0c &3,?.GzQ ¼&3¾^(*)m8I?63.Y&Y@%17,?.)b6=)>.4zI?$ .)f&C-De)HTaI/6,Z&=,?.GI:1717S*63.^8P(*)7$CA&CX.PI/S:&PI5T24*( ,?.)H8PCA&=(WCA&3.P(*C-i?(*)>6P4*6C-I?6=CM&0cE&=,?.G:.7Q ¼aSL¾|~.4LI/6=,/9:CX1K.)76=n?)>6SL.Y)<9'&=IH( ,5$ 9*+M)P,54z)76=C-IO9*C-1^,5$L9e.4zI?63,?9:CX1F&3,?.G:.TaI?6Fg _|~.=13(*)<9:S*+-CM$*im,/13(*CM)>n?)<.( CMi/(*)76F.=13(*)>9*S:@ +X, V +-)mS:&=CM+-CM<,j&=CMI/$17I?DE4 ,56=)>9k&Id,E9:)7Ta)76=6=, V +M)m.)76=n?)>6>Q ¼n:¾}~(*C-+-)S .CM$*im,m17cO17+MCX1^.13( )>9:S*+-)762&=Ip.13( )>9:S*+-),H.Y)7&FI5T6)<,5+M@h&=CMDE)&=,/.YG:.2I/$E,fS*$ CM4*6=I:1)<..I?6<[j8P(*)7$d,m.S*CM&=, V +M)^Ta63,5DE) .CM>)'.=,j&CX.YTacNC-$*i,?+M+J&(*)m&=(*6=)7)p6=)>`NS*C-6)<9W1I?$L.0&=6=,?CM$N&=.( ,?. V )7)>$lTaI?S $ 9\[zCA&bCX.i/S ,563,5$N&=)7)>9k&(L,j&b&=(*)m&3,?.G.)&8I?S +-9 V )HTa)>,/.YC V +-ck.13( )>9:S*+-)>9 V cd&=(*)p1c:1+-CX1f.=13(*)<9:S*+-)76

Version 2 CSE, IIT Kharagpur

¼a8b¾}~(*)>$EDeI/6)K&(L,5$EI?$*)Ta63,5DE)^.,5&CX.0Tac',?+M+O&=(*)1I/$ .Y&63,5C-$/&3.JI/$'Ta63,5DE)P.CM>)8P( CM+-)P.13(*)<9:S*+-CM$ iH,H.)&I5Tz( ,5639Z6)<,5+M@h&=CMDE) 4z)76=CMI:9:CX1f&=,/.YG:.S .CM$ i,e17c:1+-C-1H.=13(*)>9:S +M)>6>[O&=(*)m+-,?6i/)>.Y&I?T&=(*)>.)fTa6=,?DE)p.YC-7)<.P.Y(*I/S*+X9 V )p13(*I/.)7$JQ ¼aq*¾ fIOI:96)<,5+M@h&=CMDE)f&=,/.YGk.=13(*)<9:S*+-CM$*id,?+Mi/I?6=CA&=(*Dd.K)>$ .S*6)fT,?CM6=$*)>.=.K&Id6=)>,?+A@B&C-DE)&3,?.G:.K8P( CM+-)p.13( )>9:S*+-C-$*i Q J*QbN&=,5&)m8P(*)7&(*)>6P&( )mTaI?+-+MIj8PC-$*id,?.=.)76&C-I?$ .^,56=) ¬ 6=S*)pI?6 >P,?+-.)?QU}{6=CA&=)mI?$*)mI/6^&08KI.)7$N&=)7$ 17)>.&IH0SL.0&=CATacWc?I/S*6P13(*I?CX1)mC-$ )>,/13(17,/.Y)/Q ¼,N¾#%$y&=, V +M)7@9:6=C-n?)7$_.=13(*)<9:S*+-CM$*ikI5T&( 6)>)'4z)76=CMI:9:CX1m&3,?.GO.bº F [ º H [ Oº N?[L&=(*)Z.=13(*)<9:S*+-CM$*ik&=, V +M)ZD'S .Y&(L,on?)'.=13(*)>9*S*+M)<.TaI/6 ,?+M+\&3,?.G:.9*6=,o8P$S*4&Ie&( )H&C-De)mC-$N&)>6nj,5+ Ë*[ Dd,jq]¼a4 Ì [ E4 J:[ 4 /¾ B[:8P( )76=)f4 C]C-.&=(*)m4z)76=CMI:9I5T&(*)H&3,?.Gº » Q ¼ V ¾}~(*)>$~,x.)&dI?T( ,?6=96)<,5+M@h&=CMDE)4L)>6C-I:9:CX1k&3,?.G:.d,56=) V )7C-$*it.=13(*)>9:S +M)<9S .C-$*ix,u17cO17+MCX1W.13( )>9:S*+-)76<[UCMTm,x17)76&=,?CM$ Ta63,5DE).C-7)bCX.UTaI?S*$ 9d&I V )f$*I5&^.YS*CM&=, V +-)?[N&(*)>$k,5$OceTa63,5DE)b.CM>).DE,?+M+-)76U&( ,?$&=(*C-.K8I?S*+X9d$*I?&,5+X.I V )H.S*CA&3, V +-)TaI/6 .=13(*)>9*S*+MC-$*ie&( )H&=,?.G:.7Q ¼1>¾}~(*)>$x,.)&HI5TK(L,5639_6=)>,5+M@B&C-De)Z4L)>6C-I:9:CX1p&3,?.GO.H,?6) V )>CM$*il.=13(*)>9*S*+M)<9_S .C-$*i,1c:17+MCX1Z.=13(*)<9:S*+-)76<[\CATK,17,?$ 9:CX9*,j&=) Ta63,5DE)E.YC-7)Z)q*1)>)>9*.b&(*)E)7qO)<1S:&=CMI/$l&C-DE)EI5TU)>n?)76=c&=,?.Gl,5$ 9{.`NS ,?6)>+Mcl9:C-nOC-9*)>.b&(*)EDd,j0I/61c:17+M)/[&(*)>$yCM&H8I?S +-9 V )p,E.YS*CM&=, V +-)HTa6=,?De)m.CM>)f&I.=13(*)>9:S +M)f&( )mi?C-n?)7$W.)&PI5T&=,/.YG:.>Q ¼9 ¾rC-$ 9:C-$*i,5$I?4:&=CMDd,?+].13(*)<9:S*+-)fTaI?6,E.Y)7&I5TCM$ 9*)74z)7$ 9:)>$N&4L)>6C-I:9:C-1H(L,56396=)>,5+M@B&C-De)f&3,?.GO.^8PCM&( I?S:&b,?$Ncd6=)>.I?S 6=17)@ .( ,56=C-$*ie17I?$ .Y&63,5C-$N&=.^S*$L9:)76.Y&=,5&CX1H4*6C-I?6=CM&0c1I?$L9:CA&=CMI/$ .^CX.P,5$ F@17I?DE4*+-)&)H4*6=I V +M)>DQ ¼a)<¾^(*)p r,5+-i?I/6CM&(*D CX.PI/4:&C-Dd,5+\TaI/6.13(*)<9:S*+-CM$ ie6=)>,?+A@B&C-DE)f&=,?.G:.^CM$l,eS*$*C-4*6=I:1)>.=.I?6^CM$l,e$*I/$:@B4 6)>)7DE4:&C-n?)H)>$NnOCM@ 6=I?$*DE)>$/&$sg _| C-.HSL.Y)<9_&=IW.=13(*)<9:S*+-)e,W.)&mI5TU(L,5639y6=)>,?+A@B&C-DE)Z4z)76=CMI:9:CX1Z&=,/.YG:.fCM$u,S*$*C-4*6I:17)>.=.YI/6f)>$OnNC-6=I?$*DE)7$N&<[\CAT &=(*)4 6I:1)<..I?6 V )<1I?DE)<.UIjn/)76=+MIN,?9:)<9Z,?$NcZ&C-DE)f9*S*6C-$*ie.Yc:.Y&)7D)7qO)<1S:&=CMI/$9:S*)&IZIjn?)76=6=S*$ V ce&=(*)b+-Ij8K)<.0&K4*6C-I?6=CM&0c &3,?.Gz[:CM&8I?S*+X9 V )mn?)>6c9:C 17S*+A&P&=Id4*6=)>9:CX1 &P8P(*CX13(&=,?.G8I?S*+X9DeCX.=.^CA&3.9:)>,/9:+-CM$*)/Q ¼aiO¾}~(*C-+-)p.13(*)<9:S*+-CM$ ie,e.Y)7&PI5T6=)>,?+A@B&C-DE)4z)76=C-IO9*C-1b&=,/.YG:.8P(*I/.)f&=,/.YGd4z)76=CMI:9*.^,?6)f( ,56=DEI?$*CX17,?+M+-cE6)>+-,5&)<9\[O&(*)HS*4 4L)>6 V I?S*$L9I/$k&=(*)p,?13( CM)>no, V +-) ÄS:&C-+-CM<,j&C-I?$CX.^&(*)p.=,5DE)fTaI?6 V I5&=(l fr,5$L9g y| ,5+-i?I?6=CM&(*Dd. ¼a(L¾#%$s,W$*I/$:@B4 6)>)7DE4:&C-n?)E)>n?)7$N&@9:6=C-n?)7$y&=,/.YGx.13(*)<9:S*+-)76<[J.=13(*)>9:S +MC-$*i_9:)<1CX.YC-I?$ .m,?6)EDd,?9*)dI?$*+-c{,5&f&=(*)k,?66=CMnj,?+2,?$ 9 17I?DE4*+-)&C-I?$WI?TJ&=,/.YG:.>Q ¼CX¾^(*)pTaI?+-+MIj8PC-$*idCX.^&(*)Z1I?6=6=)>1 &,?663,5$*i/)7DE)7$N&PI5T2&=(*)m&( 6)>)mDE,50I?6b17+-,/..)>.^I?T6)<,5+M@h&=CMDE)m.13( )>9:S*+-C-$*ik,5+-i?I/6CM&( DE.^C-$ ,/.17)7$ 9:C-$*iEI?639:)>6I?T&=(*)7C-6P6=S*$:@B&C-De)mIjn/)76=(*)>,/9*.>Q .Y&=,5&CX1H4*6C-I?6=CM&0cd4*6)>)7DE4:&=CMn/)H.=13(*)<9:S*+-CM$*id,?+Mi/I?6=CA&=(*Dd. &3, V +-)@%9:6=CMn/)7$W,5+-i?I?6=CM&(*Dd. 9:cO$ ,?DEC-1H4*6=C-I?6=CA&0c,?+Mi/I?6=CA&=(*Dd. ¼ ¾^(*)K fr.=13(*)<9:S*+-CM$*i,?+Mi/I?6=CA&=(*D«$ )7)>9 .\&ITa6)<`/S )7$N&+-c)7q*,5DECM$ )2&(*)K6)<,?9:cf`/S )7S*)FI?TO&(*)&3,?.G:.J,j&6)>i?S*+X,56\C-$N&)76=nj,5+X. &=I9:)&=)76=DeC-$*)H8P(*CX13(&=,?.Gk.(*I?S +-9.0&3,56&P6S*$ $*CM$ id$*)qO&>Q ¼G:¾#%$g _| .13(*)<9:S*+-CM$ i [NCATJc/I?SdI V .Y)>6n/)P&( )f.)>`NS*)>$ 1)C-$k8P( C-13(k,Z.Y)7&I?T]4L)>6C-I:9:CX16=)>,5+M@B&C-De)b&=,/.YG:. <º F [Oº H [QMQ-Q^$ ,?6)d&3,5G/)7$tS*4tTaI?6')7q:)>1S*&C-I?$][2&=(*)&3,?.Gx)7q:)>1S*&C-I?$s4 ,5&Y&)>6$8KI/S*+-9t6)>4L)<,j&')>n?)76=c t;¼ F 7 H 7 7 ¾pC-$N&)76=nj,5+B[ 8P(*)>6) » C-.^&=(*)m4z)76=CMI:9I5T&(*)H&3,?.Gº » Q ¼+X¾}~(*C-+-).13(*)<9:S*+-CM$ i,W.)&mI5TCM$ 9*)74z)7$ 9:)>$N&p( ,5639y6=)>,?+A@B&C-DE)Z4z)76=C-IO9*C-1Z&=,/.YG:.fI?$u,S*$*C-4*6I:17)>.=.YI/6>[]g y| 17,5$ V ),/. 4*6=I5;z1C-)7$N&,?.P frtS $ 9:)76.I?DE)m1I/$ .Y&63,5C-$/&3.I?$&(*)H&3,?.Gk.)&>Q ¼Dd¾r I?6d.13( )>9:S*+-C-$*i{6=)>,?+A@B&C-DE)&3,?.GO.eC-$4*63,?1&CX17,?+S $*CM4 6I:1)<..I?6 V ,?.)>96)<,5+M@h&=CMDE).Yc:.Y&)7Dd.>[U.S V @I?4:&=CMDd,5+^(*)>S*6=C-.Y&CX1 .=13(*)>9*S*+MC-$*iH,5+-i?I/6CM&(*Dd.,56=)U$*I/6Dd,?+M+-cHS .Y)<9',/.JI/4:&C-Dd,5+:.13( )>9:S*+-C-$*if,?+Mi/I?6=CA&=(*Dd.,?6)1I/De4 S:&=,5&C-I?$ ,?+M+-cHCM$N&63,?1&=, V +M)/Q ¼a$L¾^(*)mg y| .=13(*)<9:S*+X, V C-+MCM&0cEI5T2,'.)&PI5TJ4z)76=C-IO9*C-16)<,5+M@h&=CMDE)&=,/.YG:.K8KI/S*+-9 V )H(*C-i?( )76^CAT&(*)>CM6^4z)76=CMI:9*.^,?6)( ,56=DEI?$*CM@ 1>,5+-+Mc6=)7+X,j&=)>91I/De4L,56=)>9k&Ie&(*)p1>,?.)H8P(*)76=)f&(*)>CM6P4z)76=CMI:9*.b,56=)$*I?&6)>+-,5&)<9\Q ¼aIO¾kg y| .(*I/S*+-9 V )f4*6=)Ta)76=6=)>9dIjn/)76F&=(*)f&C-DE)@%.Y+-C-17)>9d6=I?S $ 9O@6I V CM$,5+-i?I?6=CM&(*D TaI?6P.=13(*)>9:S +MC-$*iZ,Z.Y)7&I?T.I5T&^6)<,5+M@h&=CMDE) &3,?.GO.^I/$,eS*$ CM4*6=I:1)<..I?6nj, V +-)dS:&C-+-CM<,j&C-I?$I5T,_.)&'I?T^(L,5639u6)<,5+M@h&=CMDE)d4z)76=CMI:9:CX1E&=,/.YG:.'8KI/S*+-9s9*6I/4x8P( )7$s&3,?.G 4z)76=CMI:9*.P,?6)HDZS*+A&=CM4 +M)<.PI5T2)>,/13(kI5&=(*)7617I?DE4 ,?6)<9&=IZ&=(*)p17,/.Y)H8P(*)>$&(*)>c,56=)f$*I5&

; ; ;

2

9*

Version 2 CSE, IIT Kharagpur

¼h`O¾g y| .=13(*)<9:S*+-CM$*iI5T^,.)&HI5T6)<,5+M@h&=CMDE)Z4L)>6C-I:9:C-1Z&3,?.GO.S .CM$ ik&=(*) ]C-Sx,?$ 9 ,ocN+X,5$L9y16=CM&)76=C-I?$_DEC-i?(N&f4 6I:9:S 17) C-$:Ta)>,/.YC V +-)p.13( )>9:S*+-)>.^8P( )7$&(*)f&3,?.Gk4z)76=CMI:9*.P,?6)H9:CMz)>6)>$/&PTa6=I?D &(*)H&3,?.Gk9:)>,/9:+-CM$*)<.7Q ¼a6 ¾k|..S*DE)d&(L,j&Z,&3,?.G{.)&Z1>,5$ V ).13(*)<9:S*+-)>9uS*$L9:)76'g _|·,?$ 9x)7n?)>6cy&=,/.YG{De)>)&3.pCM&=.p17I?6=6)<.Y4zI?$ 9*CM$*il9:)<,?9:+-C-$*) 8P(*)>$k$*I'&=,/.YGE.Y)>+AT.YS .4z)7$ 9*.>Q2#%$d&( C-.^.cO.Y&)>DW[O,p&=,/.YGeDECMi/(/&^DEC-.=.KCA&3.K9:)<,?9:+-C-$*)b8P(*)>$,'(*CMi/(*)76K4*6=CMI/6CM&0c'&3,?.Gd.Y)>+AT .S .4L)>$ 9*.^TaI/6.YI/De)f; $ CA&=)p9:S*63,j&C-I?$JQ ¼h.=¾#%$l,e$*I?$ 4*6)>)7DE4:&=CMn/)H.=13(*)<9:S*+-)76<[*.13(*)<9:S*+-CM$ iE9*)>1CX.CMI/$ .P,56=)Dd,/9:)mI?$*+-ck,5&&=(*)p,56=6=CMnj,5+],?$ 91I?DE4*+-)&=CMI/$I?T&3,?.G:.7Q ¼&3¾| &=CMDE)p.+MCX1)<96=I?S $ 9k6=I V CM$W.13( )>9:S*+-)76PSL.Y)<.^4*6)>)7DE4:&=CMn/)H.=13(*)<9:S*+-CM$*iLQ ¼aSL¾#&CX.P$*I?&^4zI/.=.C V +-)f&Id( ,on/)f,d.c:.0&=)7D &=( ,j&CX.P.=,jTa)m,5$ 9W,5&&=(*)p.=,5DE)f&C-De)mCX.PS*$ 6)>+MCX, V +-)?Q ¼n:¾ U6)<1)>9*)7$ 17)I/6=9:)>6C-$*ie,5DEI?$*iE,E.Y)7&PI5TJ&3,?.G:.KCX.^)>.=.)7$N&CX,5+-+Mc9*)&)>6DEC-$*)>9 V cE&(*)p9 ,j&=,e9:)>4L)>$ 9:)7$L1c,?DEI?$*i'&(*)>DQ ¼a8b¾}~(*)>$y,k.)&I5TF4z)76=CMI:9:CX1m6=)>,5+M@B&C-De)p&=,?.G:.b,?6) V )7C-$*ik.=13(*)<9:S*+-)>9lI/$_,dS*$*C-4*6=IO17)>.=.YI/6S .CM$ ig _| .13( )>9:S*+-C-$*i [z,5+-+ &3,?.GO.^8I?S +-9.Y( Ij8.CMDEC-+-,?61I?DE4*+-)&=CMI/$k&=CMDE)^0CM&Y&=)766=.Y&=,?$ 9 V cu7Q¹ V*3 R: ¸O j¸LI5TK,&=,?.G_.=13(*)>9:S +MC-$*iW,5+-i?I?6=CM&(*

D w¶Ij8 ,56=)p&( )E.=13(*)<9:S*+-CM$*i4LI/CM$N&3. 9:)&=)76=DECM$*)<9C-${¼CX¾1+-I:13GN@9:6=C-n?)7$J[z¼CMC¾K)7n?)>$N&Y@%9:6C-n?)>$][¼aC-CMC¾K(Nc V 6=CX9.13( )>9:S*+-)763. W¶Ij8 8PC-+M+c/I?S*6^9:);L$*CA&=CMI/$I?T.=13(*)>9:S +MC-$*i 4LI/CM$N&3.bTaI/6b&=(*)e&(*6=)7)E1+X,?.=.)>.I5TK.=13(*)>9*S*+M)>6=.f13( ,?$*i?)Z8P(*)7$v¼,/¾f.)7+MT@.S .4L)>$ .CMI/$_I5TF&3,?.G:.7[],?$ 9¼ V ¾f1I?$N&=)qO&H.8PCM&=13(*C-$*i Ijn?)>6(*)<,?9*.KI5T&=,/.YG:.P,56=)f&=,?G?)7$C-$/&=Id,?1717I?S*$N&,?+A@B&C-DE)U&3,?.G:.$ )7)>9'&IH.=,j&CX.YTacHTaI?6Fg _|&=I V )P,5$'I/4:&C-Dd,5+*.=13(*)>9*S*+M)>6 TaI?6^&=(*)p.Y)7&PI5T&=,?.G:. (*QgP)>,?+A@B&C-DE)f&=,?.G:.P,56=)$ I?6=DE,?+M+-ck17+-,/..CA;L)>9CM$N&IE4z)76=CMI:9:CX15[L,54z)76=CMI:9:CX15[*,?$ 9.4zI?63,?9:CX1b6=)>,?+A@B&C-DE)f&=,?.GQ ¼,N¾}~( ,5&',56=)'&=(*) V ,/.YCX1E16=CA&=)76=C-, V ,?.)>9{I?$x8P(*CX13(x,6=)>,?+A@B&C-DE)'&3,?.Gy17,?$ V )9:)&=)76=DECM$*)<9_&=I V )>+MI/$*i&IWI?$*)EI?TK&=(*) &=(*6)>)p17,5&)7i/I?6=CM)<. ¼ V ¾#09:)>$N&CMTac.I?DE)m13( ,563,?1&)76=CX.0&=C-1>.U&=( ,j&,?6)HS*$*CX`NS*)H&IE)<,?13(I5T&(*)H&=(*6)>)m17,j&=)7i/I?6=CM)<.KI?TJ&3,?.GO.>Q ¼1>¾ fC-n?)H)q*,?De4 +M)<.^I5T&=,?.G:.^CM$W4*63,?1&CX17,?+.c:.0&=)7Dd.^8P(*CX13( V )>+MI/$*ie&IE)>,/13(I?T&=(*)H&(*6=)7)m1>,j&)>i?I/6C-)>.>Q

QP}~( ,j&U9*Ifc/I?SeS*$ 9:)>6=.Y&=,?$ 9 V c',5$EI?4*&C-DE,?+ .=13(*)>9:S +MC-$*im,5+-i?I/6CM&(* D k#0.CM&&6=S*)^&( ,5&&(*)^&=CMDE)b17I?DE4*+-)q:CM&0cpI5T\,5$eI?4:&=CMDd,?+ .13( )>9:S*+-C-$*i,?+Mi/I?6=CA&=(*D·TaI/6f.=13(*)<9:S*+-CM$*i,k.)&HI5TF6=)>,?+A@B&C-DE)p&=,/.YG:.CM$x,S*$ CM4*6=I:1)<..I?6C-.4*6=I?(*C V CM&C-n?)7+-cW)q:4z)7$ .CMn/)p&=I V ) I5T2,5$Oc4*63,?1&CX17,5+S .) _q:4*+X,5C-$c/I?S*6,?$ .Y8)76.)H0CM&Y&)>6=.Z17,?S .Y)<9 ¶bIj8 1>,5$ &(*)>c V )mIjn?)7631I/DE) * QbOS*4*4zI/.)d,l.Y)7&pI5TK&(*6=)7)d4z)76=CMI:9:CX1e&=,/.YG:.HCX.f&I V ).13( )>9:S*+-)>9xS .C-$*il,l1c:1+-C-1E.=13(*)>9*S*+M)>6mI?$s,S*$*C-4*6=IO17)>.=.YI/6>Qd|..S*DE) &( ,5&&=(*) S:&C-+-CM<,j&C-I?$x9:S*)e&I&( )'&=(*6)>)'&=(*6=)7)Z&=,?.G:.fC-.f+-)>.=.b&=( ,5$ Ì Qp|b+-.I [],/..S*DE)'&=( ,j&fTaI?6H)<,?13(_I?TU&( )'&=(*6)>) &=,/.YG:.>[&(*)_9*)>,?9*+MC-$*)>.e)<`/SL,5+X.e&(*)W6=)>.4L)<1 &C-n?)W4z)76=CMI:9*.>Q~OS*4*4zI/.)&( ,5&E8)l,56=), V +-)&=Ix; $ 9v,5$w,54*4*6=I?4 6CX,j&=)kTa63,5DE) .YC-7)W¼a8PCM&( I?S:&p( ,onOC-$*i&Il.4*+MCM&p,5$Oc_I?TU&( )E&=,?.G:.=¾&(L,j&'.=,j&CX.Y; )>.&( )E&(*6=)7)d1I/$ .Y&63,5C-$/&3.fI5TKDEC-$*C-DeC->,5&C-I?$xI5T^1I?$N&=)qO& .Y8PCM&=13( )>.>[*DECM$*C-DECM<,j&=CMI/$I?T2.=13(*)<9:S*+-)H&=, V +M)p.CM>)?[ ,?$ 9l.=,j&CX.YT,?1 &=CMI/$I?T29*)>,?9*+MC-$*)>.>Q IO)>.^&=(*CX.PCMDE4*+-c&( ,5&bCA&CX.P4zI/.=.YC V +-) &I,/..)76&^&( ,5&b8K)p1>,5$WTa)<,?.C V +-c.=13(*)<9:S*+-)H&(*)m&=(*6=)7)H&=,/.YG:.PSL.YC-$*iE&( )'1c:1+-CX1m.13(*)<9:S*+-)76 _#Tc/I?Sl,5$ .8)76, d6=Dd,j&C-n?)>+Mc/[ &(*)>$l4*6=Ijn?)mc?I/S*6b,?$ .Y8)766P$*)7iN,j&=CMn/)7+-c?[*&=(*)7${.Y(*Ij8 ,?$l)q*,5DE4*+-)pC-$Nn/I?+-nOCM$*iE&=(*6=)7)m&3,?.GO.P&( ,5&f9:CX.Y4 6Ijn/)>. &(*)p,/..)76&C-I?$JQ Q K+-,/..CMTacE&(*)m)7qOCX.Y&C-$*ie,?+Mi/I?6=CA&=(*Dd.KTaI?6.=13(*)>9:S +MC-$*ie6)<,5+M@h&=CMDE)f&=,/.YG:.CM$N&=IE,ZTa)>8 V 6=I/,/9k1+X,?.=.)>.>QFqO4 +-,?CM$&(*)HC-DE4LI/6Y&3,5$N& Ta)>,5&S*6=)>.^I?TJ&( )>.) V 6IN,?91+X,?.=.Y)<.^I5TJ&3,?.Gk.=13(*)>9:S +MC-$*id,5+-i?I/6CM&(*Dd.>Q Ì Ë*Q KI?$ .CX9:)76^,'6=)>,?+A@B&C-DE).c:.0&=)7D 8P(*CX13(17I?$ .C-.Y&=.KI5T&(*6=)7)&=,/.YG:.KGº Fo[OOº H5[*,5$L9º N [O8P(*CX13(k( ,on/) V )7)>$13( ,?6=,/1 &=)76=CM>)>9EC-$k&=(*) TaI?+-+MIj8PC-$*iZ&=, V +M)/Q

Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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Ì

Version 2 CSE, IIT Kharagpur

b)7&)>6DEC-$*)d8P(*)&=(*)76'&(*)&=,?.G{.)&pCX.p.=13(*)>9*S*+-, V +-)dI?$t,WS*$*C-4*6=I:1)>.=.I?6HS .CM$*i_ rQ2O(*Ij8,5+-+FCM$N&=)76=De)<9:CX,j&).Y&)>4 .pC-$ c?I/S*6P1I?DE4*S*&=,j&=CMI/$]Q J9*Q#b)7&)>6DEC-$*)'8P(*)7&(*)>6f&(*)ZTaI?+-+MIj8PC-$*ik.)&HI5TF4z)76=C-IO9*C-1Z6)<,5+M@h&=CMDE)m&3,?.G:.bCX..=13(*)<9:S*+X, V +-)'I/${,S $*CM4 6I:1)<..I?6bS .YC-$*ig _|pQ O(*Ij8 &(*)dC-$N&)76=DE)>9:CX,j&=)d.0&=)74 .HC-$uc?I?S 6p1I?DE4*S*&=,j&=CMI/$]QE#0.pg _|I/4:&C-Dd,5+8P(*)>$x&(*)E&3,?.Gy9:)>,/9:+-CM$*)<.p9:CMz)>6HTa6I/D &=(*) &=,/.YG4z)76=C-IO9 . ,/.YG N&3,56&Y@B&C-De)d¼Dd:)>1>¾ F6=I:1)<..CM$ i5@B&C-De)e¼aDO)<1>¾ 2)76=CMI:9y¼DO)>1<¾ )>,?9*+MC-$*)¼aDO)<1>¾ Gº F J?Ë J9( Ì (?Ë Ì Ë?Ë Oº H #NË #/Ë #/Ë Oº N /Ë ?Ë (5Ë ÌË ºP J( ?Ë J5Ë ÌË J2# Q KI?$ .Y&6=S 1&K,5$d)7q:,?DE4*+M)CM$On/I?+-nNC-$*iH&08Ip4z)76=CMI:9:CX16=)>,?+A@B&C-DE)P&=,/.YG:.2TaI/6K8P(*CX13(17,?$ V )Ta)>,/.YC V +-ce.=13(*)<9:S*+-)>9 V c V I?&(g _| ,5$ 9y frK[ V S:&H&(*)E.13( )>9:S*+-)ei?)7$ )763,j&)<9 V c_g _| 9:CMz)>6=.Ta6=I?D &(L,j&Hi?)7$ )763,j&)<9 V c_ frQ b63,o8Ä&(*)Z&08I.=13(*)>9*S*+M)<. I?$W,Z&C-De)m+-C-$*)p,5$ 9(*C-i?(*+-C-i?(N&(*Ij8 &=(*)H&08Ie.=13(*)>9*S*+M)<.P9:CMz)>6>Q KI/$ .YCX9:)>6^&(*)H&08Ie&=,?.G:.P.YSL13(k&=( ,j&PTaI/6P)>,?13(&=,/.YG ¼,N¾d&=(*)m4L)>6C-I:9C-.&=(*)p.,?DE)H,/.P9:)>,/9:+-CM$*) ¼ V ¾4z)76=CMI:9CX.P9:CA)76=)7$N&PTa6=I?D·9*)>,?9*+MC-$*) J (:Q 6C-5) L cf)q:4*+X,5C-$p8P(*C-+-)K.=13(*)>9:S +MC-$*i,.Y)7&I?T*( ,5639m6=)>,5+M@B&C-De)U4L)>6C-I:9:C-1U&=,/.YG:.>[>8P(Ocmg _|v17,?$p$*I?&,?13( CM)>n?) Ì Ë?Ë 4*6=I:1)>.=.I?6 S:&C-+-CM<,j&C-I?$8PCM&(*I/S:&DEC-.=.YC-$*ie&=,/.YG9:)>,/9:+MC-$*)<.7Q J *Q ,5$DZS*+M&C-4*6I:17)>.=.YI/6K6=)>,?+A@B&C-DE)&=,/.YG.=13(*)<9:S*+-CM$*ie,5+-i?I/6CM&(*Dd. V )fS .)>9.,5&CX.0T,/1 &I/6C-+-ceC-$9*C-.Y&6=C V S:&)<9.c:.0&=)7Dd.7QFqO4 +-,?CM$ &(*) V ,?.C-1P9:CM)76=)7$ 17) V )7&08K)>)7$e&(*)13( ,563,?1&)76=CX.0&=C-1>.I?T,H6=)>,?+A@B&C-DE)^&=,/.YG'.=13(*)<9:S*+-CM$*ip,?+Mi/I?6=CA&=(*D TaI/6FD'S*+M&C-4*6=I:1)>.=.I?63.,?$ 9 ,e6)<,5+M@h&=CMDE)f&=,/.YGk.=13(*)<9:S*+-CM$*id,?+Mi/I?6=CA&=(*DTaI?6,?4*4*+-C-1>,j&C-I?$L.^6S*$ $*CM$ ieI/$9*C-.Y&6=C V S:&)<9.c:.0&=)7Dd.>Q J Q KI?$ .Y&6=S 1&^,?$k)q*,?De4 +M)fCM$On/I?+-nNC-$*iZ&(*6=)7)H,56 V CM&63,56=cE6)<,5+M@h&=CMDE)b4z)76=C-IO9*C-1&=,/.YG:.K&I V )H.=13(*)<9:S*+-)>9I?$,eS*$ CM4*6=I:1)<..I?6<[?TaI/6 8P(*I?D &(*)H&3,?.Gk.13( )>9:S*+-)>.^8I?6=G?)<9I/S:& V ck fr,?$ 9g _|Ä8KI/S*+X9 V )p9:CMz)>6)>$/&)4L)>6C-I:9:CX1P6)<,5+M@h&=CMDE)P&3,?.G:.b¼TaI/6U)<,?13(E&=,/.YG[?&=,?.Ge4L)>6C-I:9d.Y(*I/S*+X9 V ))>`NS ,?+*&I'CA&3. 9:)>,/9:+-CM$*)o¾8P(*CX13(k8I?S +-9 V )H.13(*)<9:S*+X, V +-)bS $ 9:)76P r V S*&S*$L.13(*)<9:S*+X, V +-)bS $ 9:)76Pg y|pQ SL.0&=CATacd8P(OcEc?I/S*6K)7q*,5DE4*+-)bCX. 1I/66=)>1&>Q J Q KI?$ .Y&6=S 1&K,5$d)7q:,?DE4*+M)bCM$On?I/+MnOC-$*ip,p.)&UI?T]( ,5639E6=)>,5+M@B&C-De)P4z)76=C-IO9*C-1&=,?.G:.2&(L,j&,?6)b$*I5&K.=13(*)<9:S*+X, V +-)S*$ 9*)76Kg _| V S*& 1I/S*+-9 V )HTa)>,?.C V +Mc.13(*)<9:S*+-)>9 V c _|pQ )>6CMTackc/I?S*6P,?$ .Y8)76<[*.(*Ij8PCM$ ie,?+M+\C-$N&)76=DE)>9:CX,j&=)p.0&=)74 .>Q /Ë*QP^(*6=)7)m( ,?6=96)<,5+M@h&=CMDE)m4z)76=CMI:9:CX1H&3,?.GO.^º F . ¼ (5Ë?DO)>1?[ Ì Ë/Ë5DO)>1?[ Ì Ë/Ë5DO)>1<¾ [*º H6. ¼ Ë?DO)>1?E[ J5Ë/Ë5DO)>1?'[ J5Ë/Ë5DO)>1<¾ [ ,?$ 9 Oº N . ¼ /Ë5DO)>1?6[ #/Ë?Ë?DO)>1?[ #NË?Ë?Dd:)>1>¾],56=)&I V )^.13( )>9:S*+-)>9pI?$',PS $*CM4 6I:1)<..I?6S .CM$*ifg _|'Q ,?$m&(*)K&=,/.YGm.)& V )UTa)>,?.C V +Mc V )Z.13(*)<9:S*+-)>9 OS*4*4zI/.)Z17I?$N&)7qO&.Y8PCM&=13(lIjn/)76=(*)>,/9kI?T Ì DECM+-+-C2O)<1I/$ 9*.CX.P&=I V )p&3,5G?)>$lCM$N&=Ik,?1>1I?S $/&<[L9:)7&)>6DEC-$*)p&=(*) .13( )>9:S*+X, V CM+-CA&0c/Q Ì Q KI?$ .CX9:)76&( )HTaI?+-+MIj8PC-$*ie&(*6=)7)H6=)>,?+A@B&C-DE)f4z)76=C-IO9*C-1&=,/.YG:.>Q ,/.YG N&=,?6Y&@h&=CMDE)d¼aDO)<1>¾ F6=I:1)>.=.CM$*i?@h&=CMDE)e¼aDO)>1<¾ 2)>6C-I:9y¼Dd:)>1>¾ b)<,?9:+-C-$*)/¼Dd:)>1>¾ Gº F J5Ë J9( Ì (5Ë Ì (5Ë ºH #/Ë (5Ë (5Ë ÌË ºN ?Ë (5Ë J5Ë?Ë J?Ë?Ë ¼,N¾ K(*)<13Gu8P(*)&=(*)76'&(*)&(*6=)7)i?C-n?)>$u&=,?.G:.',?6)k.=13(*)<9:S*+X, V +-)S*$ 9*)76Eg _|pQFO( Ij8,?+M+C-$/&=)76=DE)>9:CX,j&=)k.0&=)74 .ZC-$tc?I/S*6 17I?DE4*S:&3,j&C-I?$JQ

#J

Version 2 CSE, IIT Kharagpur

¼ V ¾|..S*DECM$ iH&( ,5&U)>,/13(e17I?$N&)7qN&F.8PCA&313(ECM$ 17S*63.F,5$EIjn?)>6( )>,?9'I5T Ì DO)>1?[/9:)7&)76=DECM$ )P8P(*)&=(*)76&=(*)^&=,/.YG:.F,?6)P.=13(*)>9*S:@ +X, V +-)mS*$ 9*)76g _|'Q |+X.I [ 9:)7&)>6DEC-$*)f&(*)p,on/)763,5i?)f1I/$/&=)qO&.Y8PCM&=13( CM$*iEIjn/)76=(*)>,/94z)76PS*$*CM&I5T&=,/.YGk)q:)>17S:&C-I?$]Q ¼1>¾|..S*DE)l&(L,j&Gº Fo[^Oº H5[P,5$L9wº N .)7+MTm.YS .4z)7$ 9vTaI/6 Ì Ë?Dd:)>15#[ J5ËuDO)<15[P,5$L9 Ì (jDO)<16)<.Y4z)>1&C-n?)7+-c?Q b)7&)>6DEC-$*) 8P(*)7&(*)>6&=(*)m&=,/.YGW.)&b6=)7Dd,5C-$ ..=13(*)<9:S*+X, V +-)mS*$ 9:)>6g y|pQL^( )'1I/$/&=)qO&.8PCA&313(*C-$*idIjn?)>6(*)<,?9I5T Ì Dd.)>1m.(*I?S*+X9 V )Z17I?$ .C-9*)76=)>9CM$lc/I?S*6b6)<.YS*+M&>Q I/S_17,?$_,?.=.YS*DE)H&=( ,j&f)>,?13(&3,?.GS*$L9:)76=i?IO)>.b.Y)>+ATF.S .Y4z)7$L.YC-I?$lI/$*+McI?$L1)'9:S 6C-$*i )<,?13(I5T2CA&3.^)q:)>17S:&C-I?$]Q ¼9 ¾|..S*DECM$ ip&(L,j&Kº F ,5$ 9dº H ,56=)b,?.=.YC-i?$ )>9e&( )f.=,5DE)4*6=C-I?6=CA&0cenj,5+-S*)?[O9:)&=)76=DECM$*)&( ),?9 9:CA&=CMI/$ ,5+9:)>+-,oceCM$k6)<.Y4zI?$ .) &=CMDE)H&(L,j&º H 8KI/S*+X9kC-$ 1S 6b1I/De4L,56=)>9d&=IE&(*)p1>,?.)H8P(*)7$&( )7c,?6)H,?.=.CMi/$*)>99:CX.0&=CM$ 1&4*6=CMI/6CM&C-)>.>Q2#%i?$*I/6)f&( )p.Y)>+AT .S .4L)>$ .YC-I?$&C-DE)>.,?$ 9&(*)p17I?$N&)7qO&P.8PCM&=13(Ijn?)76=(*)<,?9dTaI/6^&(*CX.P4 ,?6Y&PI?TJ&( )p`/S )>.Y&C-I?$]Q ¼a)<¾|..S*DE)&=( ,j&º Fj[OIº H5[O,?$ 9dº N [O)>,/13(d6)<`NS*CM6=)b17)76&=,5C-$16=CM&CX17,5+z.Y)<1 &=CMI/$ 9:S*6=CM$*i'&(*)>CM6^1I/DE4*S:&=,5&C-I?$]Q}xI?S*+X9dCM& V ) 17I?6=6)<1 &F&=IZ,?.=.)76&F&( ,5&Gº F,5$ 9dº N 8KI/S*+-9E$ I5&^S*$ 9:)>6i/I',5$Oce4*6C-I?6=CM&0cZC-$On?)763.CMI/$9:S*)&=I'Oº H S .Y&CMTacdc?I/S*6U,5$L.Y8)76$ .YC-I?$&C-DE)>.,?$ 9&(*)p17I?$N&)7qO&P.8PCM&=13(Ijn?)76=(*)<,?9*.UTaI?6P&=(*CX.^4 ,56&I5T&(*)p`NS*)<.0&=CMI/$]Q ¼T=¾W|..S*DE)p&=( ,j&bOº NmCX.GO$*Ij8P$W&=I V )p&( )'DEI/.Y&16=CM&CX17,5+JI5T&( )m&(*6=)7)p&=,?.G:.7QFq:4*+-,?CM$l,.S*CM&=, V +M)Z.13(*)>DE) V c8P(*CX13( CM&PDE,oc V )4zI/.=.C V +-)&I')>$ .S*6)&(L,j&^Iº N9:IO)>.$*I?&DECX..CM&=.^9:)>,/9:+-CM$*)<.US $ 9:)76&=6=,?$ .YC-)7$N&Ijn?)76=+-I/,?9E17I?$ 9:CM&C-I?$L.K8P( )7$ &=(*)H&=,/.YGk.)&CX.P.=13(*)>9:S +M)<9SL.YC-$*idg _|'Q ¼aiO¾k|..S*DE)P&(L,j&Kc/I?SE( ,on/) V )>)7$,?.G?)<9Z&IpC-DE4*+M)>DE)7$N&,?$E ry&=,/.YGE.=13(*)>9:S +M)>6TaI?6,5$d,54*4 +MCX17,5&C-I?$d8P(*)>6)P) d17CM)>$ 1c I?T&=(*)p.13( )>9:S*+-C-$*id,5+-i?I?6=CM&(*D CX.,en?)>6cdC-DE4LI/6Y&3,5$N&b1I/$ 1)>6$]- ChQPFqO4 +-,?CM$&(*)p9 ,j&=,E.Y&6=S 1 &=S*6=)fc/I?S8KI/S*+X9kS .)f&IdDd,5C-$N&=,?CM$&(*)m6=)>,/9:cd+-C-.Y&>Q}~( ,5&8KI/S*+X9 V )H&(*)p17I?DE4*+-)q:CM&0c I?TC-$ .)76&C-$*id,5$ 96)>DEIjnNC-$*iZ&=,/.YG:.Ta6=I?D &=(*)m6)<,?9:ck+MCX.0&$N&CMTac&( )m)7n?)>$N&=.^8P(*CX13(W8KI/S*+-9k&6=C-i?i?)>6^c?I?S 6^.=13(*)<9:S*+-)76,/9:+MC-$*)rC-63.0& ¾m.13( )>9:S*+-)76'TaI?6e.13(*)<9:S*+-CM$ i_,_.Y)7&'I5T6=)>,?+A@B&C-DE)E&=,/.YG:.'1>,5$ V ) C-DE4*+M)>DE)7$N&)<9DEIN.0&) d17CM)>$N&+-c?Q}~( ,5&C-.&=(*)p1I/De4 +M)7qOCM&0cI?T( ,?$ 9:+-CM$ iE,Z&3,?.Gk,56=6C-nj,5+\C-$c/I?S*6PC-DE4*+-)7DE)7$N&=,5&C-I?$ FqO4 +-,?CM$c?I/S*6P,5$ .8K)>6>Q ¼CX¾|..S*DE)E&( ,5&pº H ,?$ 9xOº Nj[J)<,?13(x6)<`/S CM6=)d1)76&=,?CM$u16=CM&CX17,5+6=)>.I?S 6=17) g Ì 9:S 6C-$*i&(*)>CM6p17I?DE4*S:&3,j&=CMI/$]Qdº H $ )7)>9 . g Ì TaI/6 Ì ËDO)>1d,?$ 9xOº NE$*)7)<9*. g Ì TaI?6 J5ËDO)>1?Qk|+X.YIL[]&3,?.GO.Hº F ,?$ 9yº H [)<,?13(x6)<`/S CM6=)d16=CA&=C-1>,5+6=)>.I?S*631) !g Jk9:S*6=CM$ i&( )7C-6f17I?DE4*S:&3,j&C-I?$JQº F $ )7)>9 . g Ì TaI?6 Ì (Dd:)>1',?$ 9lº H $ )7)>9 . ;g JETaI?6 (dDO)<15QH|b.=.YS*DE)Z&( ,5& )<,?13(E&=,/.YGeC-$ .0&3,5$ 17)P&6=C-)>.&=I'i/)&K,?+M+LCA&3.U6=)>`NS*C-6)<9E6)<.YI/S*631)>. V )TaI/6).0&3,56&C-$*im&I'S .Y)f,5$Oc'I?T\&(*)6)<.YI/S*631)>.>Q|b+-.I [N, &3,?.GdCM$ .Y&=,?$ 1)f6=)&S 6$ .^,Z6)<.YI/S*631),/.^.YIOI?$,?.CA&17I?DE4*+-)&)<.^1I?DE4*S*&C-$*iES .YC-$*ieCA&.e$*I?&E&6=cu&Is,?1>`/S CM6=)CM&,5iN,5C-$]Qt#T ¼4*6=CMI/6CM&0cs1)7C-+-CM$*iu4*6=I5&=I:1I?+¾mCX.ES .)>9TaI?6E6=)>.I?S*631) ,?6 V CM&63,j&=CMI/$][K9*)&)>6DEC-$*)WCATf&( )W&=,?.Gt.)&CX.d.13(*)<9:S*+X, V +-)W8P(*)7$&( )_1I?$N&=)qO&.Y8PCM&=13(*C-$*iuIjn?)>6( )>,?9tI5T Ì DO)>1CX. 17I?$ .C-9*)76=)>9x¼,?.=.S*DE)f$ IE.)7+MT.YS .4z)7$ .CMI/$I?T&3,?.G:.=¾Q ¼ ¾KcO4*C-1>,5+-+Mc8P( ,j&C-.&(*)p$OS*D V )>6bI?T24 6C-I?6=CA&0c+M)>n?)>+-..S*4*4zI?6&)<9 V c,5$OcW1I/DeDE)>6=17C-,?+\6)<,5+M@h&=CMDE)mI?4z)763,j&=CM$ i.Yc:.Y&)7D &=( ,j&c/I?SW,56=)H,o8^,56=)bI?T l}~(L,j&CX.^&(*)mDEC-$*C-D'S*D $OS*D V )76PI?T4*6=C-I?6=CA&0cd+-)7n/)7+X.^6)<`/S CM6=)>9 V ckg20@ ^RHO# p}~(Nc9:I I/4L)>6=,5&C-$*id.Yc:.Y&)7Dd.^6=)>.Y&6=C-1&^&(*)m$OS*D V )>6PI5T24*6C-I?6=CM&0cd+M)>n?)7+X.&( )7c.S*4*4zI?6&

5£¦W©Pª Ì ]C-S QU,?$ 9 J,ocO+-,?$ 9 Q } Q«:13(*)>9*S*+MC-$*is,5+-i?I/6CM&( DE.ZTaI/6dD'S*+M&C-4*6=I?i?63,5DEDEC-$*i{C-$w( ,5639t6=)>,?+A@B&C-DE)W)7$OnOCM6=I?$*DE)>$/&9:S*+-C-$*is,5+-i?I?6=CM&(*DWFq*,?1 &13( ,?6=,/1 &=)76=CM<,j&C-I?$t,?$ 9 ,on?)763,5i/)b17,/.Y) V )7( ,onOC-I?6. Ì ÌI:Ì [()>17)7D V )>6 Ì * Q # 'O( , FQ,5$ 9g,j0GOS*Dd,?6egmQ lI:9:)l13( ,5$*i/)k4*6=I5&=I:1I?+X.'TaI?6e4*6C-I?6=CM&0c/@%9:6=CMn/)7$s4*6=)7)>DE4:&C-n?)W.13( )>9:S*+-C-$*i Q =5 Z FE $@To FZ3[ I/+hQ Ì ¼ bI :Q N¾ J8# 2J (:[ b)<1)>D V )76 Ì * Q

8

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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r

Version 2 CSE, IIT Kharagpur

lock(CR) T1 needs non−preemptable resource CR being held by T5 T1 T1 undergoing unbounded priority inversion T2

T1 gets non−preemptable resource CR held by T5

T5 preempted by T4

T3 T4

unlock(CR) lock(CR)

T5 t1

t2

t3

t4

t5

time

tn

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Version 2 CSE, IIT Kharagpur

pri(Ti)=5

pri(Ti)=5

CR

CR

Ti

Ti

CR Pri(Ti)=10

Ti

Ti

pri(Ti)=5

CR

Tj

Tj Tj

pri(Tj)=10

pri(Tj)=10 pri(Tj)=10 scenario 4

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scenario 2

scenario 3

"!# $ !%& ' ( (%*)+ , - "$!%&$ , ' ( (%*)+ . , - ++ $ , ' ( (%*) $-# * /0 *' (* (% *) , (# 1 2

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Version 2 CSE, IIT Kharagpur

T1

T1

T3

T3 releases CR

T2

T3 T1 requests CR

T2 requests CR

T3 acquires CR

Task priority

T3 gets back its original priority T2

T3

T3 t1

t2

t3

time

t4

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1

Version 2 CSE, IIT Kharagpur

CR1 T2

T2

T2

CR2

CR2

CR2

Waiting for CR1

Waiting for CR2

T1

T1 CR1

T2 Executing

T1 Executing

T1 Blocked

T2 Blocked

Snapshot 1

Snapshot 2

T1 CR1 T2 Executing T1 Blocked Snapshot 3

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Version 2 CSE, IIT Kharagpur

f(){ wd_start(t1,exception−handler);

start

wd_tickle(); }

end

t1

- FLX:H4=<35JWoq93pNA`o7r[7A1= FL5T5LH9;1=C7i1<3IEdFT/]-FTXOZ Z 54Zz.0/]"FLXZ Z75B|7hDR7i1=FT1F8G>7:5 `uH4/G$17:5T5vZ6R243 0$ 1$j)=$ !+G>7A5L5 9;3>1<9q1243rD7A1~^@FT=<3zt^\&1243M9@O3GF 3IElE43I7:E45TFL/43n£1 § 1FLKM3 H4/Fb1C9<`u=13s3>gP3>/]7i`£1<3> = 1587A@O9;3E| 1<243>/s1<243qDR7i1CGC2EBNPX61FLKr3I=f3>~^@FT=<3I9I|PFL/EBF8G>7A1FL/4Xp1<27i1 1243q1<7:9VMEB3I7PEB5TFL/43F89 KrF89<9;3Es7A/Er1<243q3>~BG>3>@B13IEBH4=<3aF89 FL/4FT1F87i13EZo.0/hGI7:93q1<243J1<7P9;VsGNPKM@45T3>139RtO3>`uN:=<3q1<243DR7i1CGC2EBNPX1FLKM3>=R3~B@4FL=<3I96uFvZ 3PZ 12431<7P9;VWG>N:KM@45L31<3I9DaFb1<24FL/hFT1<9aEB37:EB5LFL/43| 1<243>/&123pD7A17A5L5vZ & no ¡ !#"k> % $&' o) (+ ,, ¡ q 3`uNP=3E4FL9N:KMKM3>=CGF87A5 =<3I7:5bSv1FLKM3pN:@k3>=C7i1FL/4XW9\B9m1<3>Ks9>|OD 3zKzH9;1G5L3I7:=5L\,H/EB3>=C9;1<7A/OE,1<243`u37i1~^@k3IG13EdN:`7&=<3I7A5TSv1FLKr3rN:@k3>=C7i1KnZsR24FL96DaFL5L57A589;N&3>/7:t45L3rHO961NeGNPKM@7A=<3z1<243r`u3I7A1H4=<3I9p9H4@4@kN:=13Et^\EBFT3>=<3>/Q1 =<3I7:5bSv1FLKM3NP@O3I=<7A1FL/4Xe9;\B9;13>Ks9`uN:=93>5L3IG1FL/4Xe7A/]7A@4@=NP@4=F87i1<3zNP@O3I=<7A1FL/4X&9\B9m1<3>K `uNP=7A/]7A@4@5TF8G>7A1FLN:/]7i1p27A/OEZrR2FL9pDN:H5LE 7:5L9NW5L31HO9qH4/OEB3>=C9m1C7A/E&1<243MEBFb3>=<3>/OG3I9qtO3>1mD 3I3>/7W1=C7:EBFT1FLN:/O7A5NP@O3I=<7A1FL/4X,9\B9m1<3>K7A/El7W=37A5TSU1FL7:5T5L\1<24NP93R127A1 7:=36/4NP=Ks7A5L5L\W7At93>/Q1aFT/&1<=<7PEBFb1Ks9IZ ? 5LN^GCV7A/E1=3I9pDaFT12c7PEB3IYQH7A13W=<3I9N:5LHB1FLN:/_7:=3sNP/43WNA`a1<243WKMNP9;1zFLKM@ONP=;1C7A/Q1 F899 eH4]S3^/9p. FT/]h=<3I 7:5b+Sv1FLceKMd[3r_\ @=1NPX:=C7AKM]KM\bFT/4i XOZ q7A=CE=37A5TSU17A1FLN:/_EB3Ig:3>5LN:@Kr3I/Q16N:`£13I/_=3YPHFT=<3I969H4@4@kN:=1NA`1FLKr3I=z93>==N:`7M`u3>D KMF8G=FL7:5 7:@4@45LFLGI7i1FLN:/O9>Zf? 5LN^GCVB9R7A/OEs1FLKM3>=C9a7A=<3J7rg^FT1<7A5@7:=;1aN:`"3>gP3>=<\M=37A5TSU1=C7i1FL/4XM9;\B9;13IK&Z /,1243pN:1243I=R27A/E |^1=C7:EBFT1FLN:/7:5 NP@O3I=<7A1FL/4Xs9;\B9;13>Ks9R/4NP=Ks7:5T5L\WEBNM/4NA1@=Nig^F8EB3q1=3I9DaFT12e9;H G>FT3I/Q15L\W24FLX:2n=39;NP5TH41FLN:/ Z 0 _ 21 +|cedP_PZ\0ct]\0c b 43_g_ e`i w =<3I7:5bSv1FLKM3sN:@k3>=C7i1KKzHO9m19H4@4@kN:=19;1<7A1F8Gs@4=gP3>589>Zlwy@4=FLN:=g:3I5 9H4@4@kN:=13E,t^\,7:/hNP@O3I=<7A1FL/4Xr9\B9m1<3>K¥FL9aGI7A5L5T3Eh9;1<7A1F8GA|BDa243I/hNP/G3J123p@4=NPX:=C7AKMKM3>=R7:9<9;FLX:/O97r@4=KEBN^3I9 /4N:1oGC2O7A/4XP3 FT1t^\zFT1<93>5T`mZ Q1C7i1gP3>589o7A=<37:5L9NpG>7A5L5L3I6E 587:9<;>=@?BA2CD7'EF5GAIHJ5GA2?LKM;N7)OP7);RQ$Z [d3EBF89=C7i1K¥E4\Q/O7AKMFLGI7A5L5T\hGC27A/4XP3I9 123p@4=FLN:=589RNA`-1<7P9;VB9`u== 7P99FTXP/43IEWg7:5TH3I9f1NrKM7A~BFTKMFL>369;\B9;13>K1<24=NPH4X:2@4HB1IZ^HOGC2,@4=7A5L5L\rt^\M1<243NP@O3I=<7A1FL/4X 9\B9m1<3>Ky7:=36N:t^g^FLN:H95T\s/NA1q9;1<7i1Z S #`,b + #`/. Z\0_1_1d b2ce]hi 4NP=q9HG>G>3I9<9m`uH45N:@k3>=C7i1FLN:/hNA`o7M=37A5TSU17A1FLN:/ |Da243>/43Ig:3I=7M24FTXP2n@4=FLN:=~B3IGH41FL/4Xd5LNiD @4=58E_123l? 1=@4=HB13FL9YQH7A/Q1~^@=3993IEs7P9?@9PQ8TEU587:7VCEF?BAIH<WX?BA2CD7ZY ? NP/P1<3>KM@kN:=C7A=<\p=37A5TSU1=C7i13>KM@B1= NA`7`u3>D KMFLG>=Np93IGNP/E49IZ qNiD 3Ig:3>=| FL/r1=C7:EBFT1FLN:/7:5^N:@k3>=C7i1FL/4Xp9\^9;13IKs9>|i1<243RD NP=<9;1G>7P9;3 1<7P9;V@=3I3>KM@B1FLN:/1FLKM3aFL9o1m\Q@FLGI7A5L5T\pN:`O1<243aN:=CEB3>= N:`k769;3GNP/EZ-[d3EBF89~Q193IG1FLN:/W1<27i1a1<24F89a9;FLX:/4F OGI7A/Q15L\s5L7:=XP3587i1<3>/G>\sFL9aGI7AH93IEht^\W7r/4N:/BS @4=<3>3IKr@41FLg:3JV:3>==C7i1K¤/43I3IE491NW27gP37s@4=<3>3IKr@41FLg:3pV:3I=/3>57:/Ee9;2N:H458En27g:361C7:9V,@4=<3>3IKM@B1FLN:/n1Z [

Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

27P9a9GC23>Ks7i13I/lEB3>@4F8G$1<3IE&FL/&-FLXZ Z 4Z System

call

check parameters OS Service (kernel mode)

Trap

Application Program (user mode) system call next statement

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Version 2 CSE, IIT Kharagpur

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Priority Level

1

Task Queues

2 3 4 5 6

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

ROM−resident operating system

TCP/IP Embedded processor

Host System

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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T1 Spin lock Critical Resource

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Version 2 CSE, IIT Kharagpur

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Real−Time Priorities 127 Dynamic Priorities 254 255

Idle

Non−Migrating Priority

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Version 2 CSE, IIT Kharagpur

DOS

Windows NT

Windows 3.1 new code

Windows 2000

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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Editor Cross− compiler . XRAY+ Libraries

Application

Host Computer TCP/IP

P N A +

PSOS+ PHILE PROBE ROM

Target Board

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

File System

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Interconnection

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Version 2 CSE, IIT Kharagpur

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5

Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

Condition enabling high priority task T 2

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T2 T1 t1

t2

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Version 2 CSE, IIT Kharagpur

t1 T3

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t2

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Acquire Semaphore

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TRIANG

Shared Memmory Analyser

System Call RT1

RT2

RTn

Output

Timer

Y

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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"

Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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CONTROLLER

ROBOT

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

A M A E A E

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Version 2 CSE, IIT Kharagpur

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n 0?>I :! V juº'6/?hu:+1VQ/'(!#1e(+I/:! ORQ/!i(57x>!=6o./:57. "%?^"4(+!=8">:57I/6 E(+Q/!i$05>?701="%$:06/? Npu_("%6S@g(+',-!95>6/$0@(Q/!i(57x>!=6qQ/5>$2EJ!=:28.C!3:+,-v((!#Eo(5g(:V"%6 8,-v(fLM:V"%,-!=8=N S06 13!5>6/$0@g576/!8H(+"4(+'576o"4("9(+',-!Q/57$0E 8R(Q/!(5>x7!36b06q"-:06/?h6/!3( 57:xyl 135>$0$'28H05>6<813"%6b6/5>(5J1313I/:=N_u6o0,-.<57:H(V"%6^(.<57'6^((+5 :+!=">$'0m3!p28(Q<"4((+Q/!./QS@J8H213">$k5>:VEJ!3:'6 T Q/21VQb(Q/!i8U(V"4(05>6<8"%:+!15>6 T 6/!=1(!=E(+5-(Q/!i13"%A $'!286/5>(',-.C5>:(+">67(#N_ORQ 0828AC!=1="%I 8! (+Q/!13"%A $'!08_06/Q/!3:+!36^(+$'@;"iA/:+57">E 13">8H(`,-!=E/'I/,blJ!#">1VQ8H(+"%(05>6;:+!=13!30Z>!#8`!=Z>!3:+@9LM:+">,-!(:V"%6<8H,-'(H(!#Ekl/EJ281="%:VEJ06/?(+Q/578!(+Q "4("%:+! 6/5>(p"7E/EJ:+!=8+8H!#Eb(5b'(=N} Q !36P"8H(+"%(05>6r.<">8+8H!#8(+Q/!9(5>x7!36|lk'(p(:V"%6 8,-v(V8"8.!36rLM:+">,-!>l|8.$'$0@q">E/E/:!#88!=Eb(+5 '(+8$05>?701="%$k6/!='?7QSA<57:'6(Q !:06/? lJ0:+:!#8H.C!=1(0Z>!p5%L T Q/!3:+!f(Q "%(8H(+"4(+'57628./QS@J801="%$0$'@;$05J13"%(!=E576g(+Q/!X13">A/$0!>N](28"%$28H5 T 5>:(Q 6/5>(06/?;(+Q "4(p,h"%6S@o8U(V"4(+'576 8576o(Q/!96/!3( T 57:x,h"[@6 5%(AC!96/5%(p'6q(Q/!9:06/?DÁaLM5>:f!>N ? Np8H(+"4(+'576 8 Î7Î l Î (h'6r(Q/!-n'?$k"%$2859. :54ZS2EJ!=8sLM5>:"7E/EJ06/?h8U(V"4(+'576 8_(5, (+Q/!$'57?>213">$C:+06/? N

Logical Ring

Node not in the ring

n0?>I/:+! $ ]¾|57?>213"%$k06/?h06o"9O5>x7!36 _I 8

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:

Version 2 CSE, IIT Kharagpur

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,

Version 2 CSE, IIT Kharagpur

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.

Version 2 CSE, IIT Kharagpur

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Transmission Interval

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msb

lsb

N1 10

0

1

0

1

0

N2 16

1

0

0

0

0

N3 20

1

0

1

0

0

Priority bits

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Î

Version 2 CSE, IIT Kharagpur

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Transmission

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N2

Propagation Time N1

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Version 2 CSE, IIT Kharagpur

Priority

Packet Payload

P Header Mode bit

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Version 2 CSE, IIT Kharagpur

F

F

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Version 2 CSE, IIT Kharagpur

low Bandwidth 802.5

GP(U) 802.4

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GP(U)

802.5

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802.5 802.4

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Version 2 CSE, IIT Kharagpur

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Host (Receiver)

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

Eligible Time computation

Active Msgs

1

D M U X

Hold Queue

2 n−1

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Departing msg

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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Version 2 CSE, IIT Kharagpur

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ª +.AC4!,#/} o#%!TFM9B!,-_46 #92Flw+5{#%!,#%B)©`2),#%A9!$+.#%:`92FG©9468C3!$!,#%46 "©9BB)$!,9B& !$92),9J689&7: u#<2&5'v)$+5-/#b;3H)D2k4B:T#<:),K4#8!$# FM9!$#])$#84;),9"kR#/;J#%:,+.A3#<;:+53'-/#8-/9B!,¤;32)$2kR:,#0:TJ:T),#%-/:%N¡ÇJ'-/#%-b9B!,¤;32)$k4:,#%:;J9"zWhz W+5),K>;J+.:,a/¡ < #%B)$+5!$#8&.cJ4;/),K4#8+.!h:,+.-b14&5+5¥4#%;";J#%:,+.Atv6 9-/14!,#<;/),9b6 9BVgB#8V),+.9R2&R;4H)$k4:,#%:Dyo-/+.3+5-/+.£8#<:-/#<:,:$2AB#E14:$:,+53ARN P +.-/+5&72!)$9>49J'¢!,#<2&5'v)$+5-/#b;J+.:,aV'kR:,#%;;32)$k4:,#%:%cj+53'-/#8-/9B!,¤;32)$2kR:,#%:13!,9Hg +7;J#/;3H)D2k4B:T#L+5V),#%A!$+()?=)$K3!$9C3ABK),K4#bCR:T#b92F 689 g#%B)$+59B42&R;J+.:,aJ:pFM9B!&.9ABA+.3A]24;/1{#8!$+.9 ;3+.66DK3#%6Da 1{9+.B)D:8Non9]-/#8# )),K3#K3+.AKIzgH2+.&72k3+.&5+5)?/;J#8-_2R;3:9F21313&.+768H)$+59B4:%cV:,9-/# +.J'¢-b#%-/9!$r;3H)D2k4B:T#<:`92s#8!E;32)$b!,#%13&.+.6%H),+.9N [#8\32-/13&.#p92F36 9B-b-/#%!$68+.&H!,#<2&5'v)$+5-/#p;3H)D2k4B:T#o+7:6 < k =?#%6 )%Ø :j# ),!$#8-/#%wxQtKV)T),1 zWWW@N -/689k =?#<6);32)$4NnhK42)+7:%c )$K3#>;4H)$k4:,#r+7:b-_2131{#%;Z;J+5!$#%6 ),&.d+5V)$9)$K3#>1313&.+.6%H)$+59BOØ :b;4;J!,#<:,:b:,1468#c#%&5+.-/+542),+.3AY# \J1R#%4:,+5gB#rk3CJs#8!/-_2R2A#%-/#8V)$:%N nhK3## ),!$#8-/#%wx¨!$C3V),+.-b#@689-/1R9B3#8V)`+.:h;J+.!,#<6)$&5_&.+54a#%;I),9L),K3#@1313&.+.6%H),+.9cB#%&5+.-/+542),+.3AL),K3#i3#%#%;_FM9B!h!,#%-b9),#13!,9J68#%;JC3!$# 6%2&.&.:FM!$9- # \J#%68CJ),+.9142),KONrn9=13!$9HgV+7;J#/1{#8!,FM9!$-/46 #_4;14!,#<;J+.6 )$k3+5&.+5)?c# E)$!,#%-b#<wxÛC4:,#%:i+5)$:@9HW-/#8-/9B!,-_42AB#8! FM9B!b&5&.9J68H)$+59B4:b24;^;3#%2&.&.9 6%H)$+59B4:0-_B;J#rk ),K4#>;32)$k4:,#r!$C3V),+.-/#Nd§E9)b!$#8&. +53AX9Q),K3#>91{#8!DH)$+53AY:TJ:T),#%->Ø :L-b#%-/9!$ -_2R2A#%-/#8V)]2&7:T9=#8R2k3&.#%:i# E),!$#8-/#<wxm),9¤!$#8-/9Hg#L),K3#_k{92),),&.#83#<6Da9F14A+.3A¤;3H)D"+.^2R;9BCJ)0;JC3!$+54A>¡ < 9B1R#%!$2),+.94:%N ª49!i:TC3141R9B!T)$+53Ar),!D24:$6 ),+.9;J#<;J&.+.3#L-_42AB#8-/#8V)%c{# ),!$#8-/#%wx :,C3131{9!,)$:¥4g#b13!$+59B!,+5)?"&.#8gB#8&7:E)$K4H)@68k{#bB:,:,+5AB3#%;>)$9 )$!$4:,B6)$+59B4:8N µ×À [),!D2R:,B6),+.9i+7:C43+()92FJ# \J#%68CJ),+.9@+.0;32)$k4:,#21314&5+7682),+.9Ocz24;i+7:6 9R6 #813):T+.-/+5&72!O),9h)D:,a+.]39BJ'Ç;3H)D2k4B:T# 21314&5+7682),+.9ON =?9B!G;J+5{#%!,#%46 #<:Gk{# )?W`#8#%r@)D:,ab4;I]),!D24:$6 ),+.9_+.46 &.C4;J#K3+5ABKr;32)$]CR:,A#Ek b),!D24:$6 ),+.94:%Nª4C3!,),K3#%!%c +5)+7:GgB#8!$ ;J+5_68C3&5)L)$913!$#%;J+76)L),!D24:$6 ),+.9d!$#%:,1R9B4:,#_),+.-/#%:b;JC3#"),9+7:$:TC3#<:0:,C46DKQB:0¡ < :$6DK3#<;JC3&.+53ASt;J+7:,aB6868#%:$:$y clk4CJ{#%!,+.3ARc 6 9B46 C3!$!$#8468r6 9BB)$!,9B&vc{6 9B-b-/+5)2R;=!,#<6 9Hg#%!,r13!,9),9J6 9B&.:EC4:T#<;jc4#8)$6NE[:I6 9B4:T#:?)D24;3!$;dL~ 13!$92),9J689&VWK3#8bC4:,#%;L+5b!,#<2&5'v)$+5-/#h;3H)D2k4B:T#<:!$#%:,C3&5)$:l+.L-_2 @13!$9k4&5#%-/: &.94A4;]C3413!,#<;J+76)$k3&.#h;3#8&7z :%cHC3 k{9C34;3#%; 13!$+59B!,+5)?_+5 gB#8!D:T+.94:%cJ24;>;J#<;J&.9J6Da :%N ª39B!"!$#%&('),+.-/#X21413&5+7682),+.94:%c®+5-/13!$9Hg#%-/#8V)"9Fb8~ #m+7:>L~ j'¢1e oc`k3CJ)=+()=kR#%K4zg#<:"B:rkR;J&.fWK3#8Ê C3-0k{#8!>92F ),!D24:$6 ),+.94:i4;Y!,#<:T9BC3!$68#b:,K4!,+.3A¤2!$#/&.!,AB#Nr8~ #j'Ç Ê9Hg#%!$689-/#%::T9B-/#_92F`),K3#_13!$9k4&5#%-/:]92FE8~ O'1e ocsk3C3)0-_z !,#<:TC4&()+.>Wh:T)$A#92Fl&.!,AB#-b9BC3V)$:h9Fo689-/13&.# ),#<;rW`9!$asN < 1J),+.-/+.:T),+766 9R6 C3!$!,#%46 /6 9BV),!$9&t < ©©hy14!,9),9J6 9B&.:`2&.&59HW¨C34!,#<:?)$!,+76)$#%;r;4H)$0C4:$2A#kV/)$!$4:$6)$+59B4:%Nl9HW#%g#8!6 9B-/-b+5)T)$+54A=),!D24:$6 ),+.9¤)$9=>gH2&.+7;3H)$+59B)$#%:T)@2)i),K3#b),+.-/#_92Fh6 9-/-/+5),-/#8V)%N_nhK3#<:T#b13!$92)$9 689&7:W9B!,a=)$K3# kR#<:?)EC44;J#8!&.9HWÈ!$#%:,9C4!$68#6894:T),!D2+.V)$:h24;"&.9HWÈ&.9B;>:,+()$C4H)$+59B4:8N }} 0

Contention

Version 2 CSE, IIT Kharagpur

¬ ¬ÊÀ 2 ¬ }BNPV)$2),#IWK4# ),K4#8!b9Cd6894:,+.;3#8!])$K3#_FM9B&5&.9HW+54A:?)DH)$#8-/#8V)$:]),9k{# Ù9! 0NCR:?)$+(FM9BC3!04:TW`#8!0+5^#<6DK 68B:T#BN tVyrª49!p)$#8-/1R9B!$&4;32)$C4:,#%;/+./i!$#%&('),+.-/#21313&.+768H)$+59BOcB@:,# )9Fs;4H)$)$K4H)+7:Gk4:,9&.CJ),#%&506894:,+7:?)$#8V)%cB+.:pABC42!D2V)$#8#%; )$9_kR#@!$#8&7H)$+5gB#8&.I6 9R:T+7:?)$#8V)%N tMkRy>nhK3#1R#%!TFM9B!,-_46 #9F{)$K3#L~ O'1e 13!$92)$9J6 9&4+.:GkR#8)T),#%!G)$K42I),K3#EkR:,+.6L~ =13!$92)$9J6 9&RWK3#8/)$K3#;4H)$06 9V)$#8V),+.9 -b9B3AI)$!$4:$6)$+59B4:E+7:&59HW@csk3C3))$K3#L1{#8!,FM9!$-_2468#0k{#%689-/#%:W`9!D:T#@)$K42),K3#bk4B:T+76LL~ ^14!,9),9J6 9B&C3R;J#8!K3+.AK ;32)$/6 9BV),#8V)$+59B>-b9B3Ab),!D24:$6 ),+.94:%N t6%y=L~ j'¢1e Z13!,9),9J6 9B&jC4:,#%;"+5¤6 9B46 C4!,!$#8468I6 9BB)$!,9B&s+5=!$#%2&5'),+.-b#@;32)$k4:,#%:`+7:hFM!,#%#FM!,9B- ;J#%B;J&.9 6DaJ:%N t;4y=L~ j'Ç Q13!$92),9J689&4CR:T#<;I+."6 9B46 C4!,!$#8468_6 9V)$!,9B&4+."!$#%&('),+.-/#;32)$2kR:,#%:%c+7:GFM!$#8#FM!$9-13!$+59B!,+5)?b+5 g#%!$:,+.9I2R;I+7: &.:,9bFM!,#%#FM!$9-Ù;J#%B;J&59J6DaJ:%N tM#13K4B:T#BcJ+()E+7:ACR2!D2V),#%#%;r689-/-/+()$-/#8V)%N tF$y>¡Çri!$#%&('),+.-/#;32)$2kR:,#-/42AB#8-/#8V)G:,J:?)$#8-=cV_91J)$+5-/+7:?)$+.66 9B46 C3!$!$#846806 9BB)$!,9B&t < ©©hy13!$92),9J689&4:,K39C4&.;/k{# C4:,#%;=+5Fl),K3#06DK49+76 #@+7:k4:,#%;>13C4!,#%&5"9=1R#%!TFM9B!,-_46 #_tM1{#8!D6 #%V)$2AB#@92Fl)$B:TaJ:h-/#8#8),+.3A_),K4#8+.!;J#%B;J&.+53#<:$yh6894:,+7;J#8!,' 2),+.94:%N tMA y < ©©G'ÇxE©X13!,9),9J6 9B&!$#%UVC3+.!,#<:6 9B-b-/+5)T)$+53A),!D2R:,B6),+.9i)$96DK4#%6DaFM9!o1R9V:,:,+.k3&5#`6 9BJ¦4+76)$:W+5),KL&5!$#%B;J@6 9B-b-/+5)T)$#%; )$!$4:,B6)$+59B4:`kR#8FM9!$#+5)6%2=6 9-/-/+5)%N tMKRy>nhK3#I:,#8!$+72&.+5£<H),+.9X9!D;J#8!@C44;J#8!]=1{#%:$:,+5-/+7:?)$+.6_689468C3!,!$#8R6 6 9BV),!$9&p13!$92)$9 689&o+7:i),K3#I:$2-/#_:@),K3#I689-/-/+(),),+.3A 9B!$;J#%!h92Fl),K3#i)$!$4:,B6)$+59B4:8N t+7y>u#<2&5'v)$+5-/#];32)$k4:,#%:)? 13+7682&.&.IC4:,#iu[E¡?wÚ;3+.:,aJ:`FM9!E;32)$/:?)$9!D2AB#;JC4!,+.3A_:TJ:T),#%- 91{#8!DH)$+59BON t =,y < 1J)$+5-/+7:?)$+.6@©9R6 C3!$!,#%46 I©9V)$!,9B< < ©©hy13!$92)$9J6 9&7:CR:T#<;/FM9!6 9B46 C4!,!$#8468b689V),!$9&R+5"!,#<2&5'v)$+5-/#;3H)D2k4B:T#<:G2!$# FM!$#8#iFM!$9- ;3#%;3&59J6DaJ:8N taJy>[&5& < ©©13!,9),9J6 9B&.:l#<:,:,#8V),+72&.&.@1R#%!TFM9B!,- FM9B!,Wh2!D;@gH2&.+7;3H)$+59B4: =?C4:?)k{# FM9B!,#`)$K3#8+.!6 9B-b-/+5),-/#8V) 6CFE8P HIE=JE ¤9HWf2!$#h),#8-/1{9!D2&{;3H)D@;J+(s#8!$#8V)FM!,9B-Ú)$!$B;J+()$+59B42&R;3H)D +.g#:,9-/# # \32-/13&.#%:`9F)$#8-/1R9B!$&O;3H)D3N 3NP C3131{9B:,#co)$#8-/1{9!D2&;4H)$X2!$#r;J#%392)$#%;dC4:,+.3A¤),!$+.13&5#8)$:L92F)$K3#rFM9B!,- %gH&5C3#Bczg +vcl),+.-/#%:T)$-b1 >2R;),K42)0)$K3#";J+5s#8!,' #8V)_6 9-/1{93#%V)$:L92F)$K3#"),#8-/1{9!D2&;32)$XK4zg#r),K3#%+5!/C4:,C42&h-/#%3+.3AB:%Nd[:$:TC3-/#>),KRH)b),K3#=!$#8&7H),+.g#>6 9B4:T+7:T),#8R6 d:T#8) u %14!,#<:,:,C3!$#c ),#8-/1{#8!DH)$C3!,# i4; ~ HNhPJC3131{9B:,#]),K4#@),#%-b1{#8!DH)$C3!$#024;=14!,#<:,:,C3!$#]:,-b14&5#<:)$a#%H):,9-/# ),+.-/#G+.4:?)D2V)l!,#GA+.g#80kV H~~2 8©c H-_:T#<62c.}}z~H-_:T#<6 2R; %©c.} -_:T#<62c.}} ?B-_:T#<6 p!,#<:T1{#%6 ),+.g#%&5BN[`))$K3#)$+5-/#`+5R:?)D2V) }<~ /-/:,#%6c{;3# ),#%!,-/+.3#0WK4# ),K4#8!E)$K3#])$#8-/1{#8!DH),C4!,#04;¤13!$#%:$:,C3!,#]:$2-/13&.#%:2!$#]+yE2kR:T9B&5CJ)$#8&.>6894:,+7:?)$#8V)%cR+5+y!$#8&7H)$+5gB#8&. 6 9B4:T+7:T),#8V)@7A4@B 4&687= CF6P CN6=J6 4&6P<+.b;3H)D2k4B:T# IefK @+7::,#8&.#%6 ),+.909FR2L21313!$914!,+7H)$#6 9B46 C4!,!$#8468 6 9BB)$!,9B&H13!$92),9J689&2+.-/1R9B!T)D2V)j),9E-/#%# ))$K3#p)$+5-/#8&.+.3#%:$:O!$#%UVC3+.!,#%-/#8V)$:sFM9B!j),!D2R:,B6),+.9R: rÖp\J13&72+.)$K3#G;J+5s#8!$#8V)682),#%A9!$+.#%: 92Fi6 9R6 C3!$!,#%46 d689V),!$9&h13!$92)$9 689&7:L),K42)_6%2SkR#¤CR:T#<;Q+.Z!$#%&('),+.-/#¤;3H)D2k4B:T#<:8NS[E&7:T9RcG# \J13&72+.SWK3+.6DK¨682),#%A9!$92F 13!$92),9J689&s+.:hk{#%:T):,C3+()$#%;>C34;3#8!EWK42)E6 +.!$68C3-_:?)D2468#%:%N JNefK r+7:Eb),!D;J+5),+.9R2&~b13K4B:T#@&.9J6Da +53At8~ #yk4:,#%;=689468C3!,!$#8R6 r689V),!$9&j13!$92)$9J6 9&j-_z"392)Ek{#0:,C3+()D2k3&.#iFM9!C4:T#@+. !,#<2&5'v)$+5-/#@;32)$2kR:,#%: ¤Öp\J13&72+."K49HW®),K4#@),!D;J+5),+.9R2&8~ #Y13!,9),9J6 9B&O68"k{#]# \ )$#84;J#<;"),9_-_2aB#+5):,C3+5)$2k4&5#FM9!C4:T#@+. !,#<2&5'v)$+5-/#i;3H)D2k4B:T#@1313&.+.6%H),+.9R:8N NEª39B!_!,#<2&5'v)$+5-/#=21313&.+768H)$+59B4:%cG!D23aZL~ GcGP4©©cG2R; < ©©13!,9),9J6 9B&.:b+.S),#8!$-_:/92F),K3#¤1{#8!D6 #%V)$2AB#"9F)$!$4:$6)$+59B4: -/#8# )$+54A)$K3#8+.!_;J#%B;J&5+.3#<:8NZ©9B4:T+7;J#%!L&.9HW 24;QK3+.AKZ;3#8A!$#8#<:09F6 9BJ¦4+76)D:b-/93A),!D24:$6 ),+.94:%c24;^),+.AKV)_24;Q&.2\ ),!D24:$6 ),+.9>;J#%B;J&5+.3#<:8N +.g#]bk3!$+5#8F!$#%:,94+53Abk{#8K3+.4;=9BC3!24:,W`#8!

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