HAL Id: inria-00072326
https://hal.inria.fr/inria-00072326
Submitted on 23 May 2006
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub-
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,
Modeling and Analysis of Multi-class Threshold-based Queues with Hysteresis Using Stochastic Petri Nets
Louis-Marie Le Ny, Bruno Tuffin
To cite this version:
Louis-Marie Le Ny, Bruno Tuffin. Modeling and Analysis of Multi-class Threshold-based Queues with Hysteresis Using Stochastic Petri Nets. [Research Report] RR-4261, INRIA. 2001. �inria-00072326�
ISRN INRIA/RR--4261--FR+ENG
a p p o r t
d e r e c h e r c h e
Modeling and analysis of multi-class threshold-based queues with hysteresis using
Stochastic Petri Nets
Louis-Marie Le Ny Bruno Tuffin
N˚4261
Septembre 2001
THÈME 1
/
?@BA*CEDFGIHKJLCEMN?MPO)Q:R)S3JTA*U*@WVXAYWU[Z
\^]`_baPcedgfihgjlkcnmpoBqrcbsktKkus_baPclk
vwxpyucbszgwuaPx{w
hgmp|4|*x{wus}4cwcl~]`cbw~]`c9#Bdef Kcb|4scba)4wcBd3fi|%mp.clk
;ln4. \^]4k^|%mp|*cbw^k^}4cnmp4Nsu]rao4su~bm{kk ¡o`cbo`cb4PkutBkuscbaPk¢]`cbwcgsu]4wclk]B
x{}4k£mpwc^`~bo`}4cl}PPx{w}4cbw£sxkuaPx¡x{su]Nsu]`c^¤mpwumpsux{`k£xp¥*su]4wx{o4]4|4o4sXmp`}N}4cbmlt+#t+aPxK}B
¥¦tK4su]`c #o`cbo`c*cb]%ml¤Kx{o4wn§¨gtKkuscbwclkk5k©mpkx`kcbwuscl}«ª¡kxsu]%mps£su]`c~lx{#suwx{aPcl~]%mp4kua
¬`x{sgkus~]WsxKxNa)o`~]§®g`c,aPx{su¤mpsux{=¥¯x{wo`ku4eao4su|4c~bm{kkclkxp¥£~bo`kusx{aPcbwkgk
sk~nmp|%mp4s°t±sxraPxK}4cb$]`cbscbwx{.cb`clx{o`ksuwm²e~lk³.c}`mpsmBª*¤.x{~lcNmp`}´¤¡}4clx4§µ´x{wclxn¤.cbwnª
su]4wclk]`x{}´ ¡o`cbo`clk3]%ml¤.caemp¡t´mp|4|4~nmpsux{`k´su]`c+suwmp`ku|x{wus|4wx{sxK~lx{kxp¥X~lx{aNa)o44~nm
sux{e`cbsXx{wu³Bkn§£\^]`c3mp%mptKkk£k£}4x{`co`ku4 ¡sxK~]%m{kusu~gv$cbsuwu¶gcbsk¢mp`}e·;o4}r ¡sxK~]%m{ksu~
v;cbsuwu¶3cbskn§¸\^]4kN|*xnXcbw¥¦o4|%mpwm{}Ba]`cb|`kPsx¹x{4smpºm´¤.cbwutIkaN|4c»wcb|4wclkcb#smpsux{
xp¥su]`ckutKkscbaPkgmp`}±su]`cmp%mptBkukkgsuwmp`ku|%mpwcb#so`ku4»mp´mn¤{mpmp4c+v$cbsuwu;`cbs|%m{~³{mp.c§
¶go4aPcbwx{o`k¡o4aPcbwu~nmp$o`ksuwmpsux{`kgmpwc,¤.cbWWx{w}4cbwsxN¤mp}`mpsc,su]`co`kcxp¥5su]4wclk]`x{}
¡o`cbo`clksu]=]¡tKkscbwclkukgm{k¢cb$m{ksu]`cbwgwcb|4wclkcb#smpsux{±#tW Kv£¶3kmp`}=·£ Kv£¶3kgmp`}¼|*cbw
¥¯x{wuaemp`~lclk,xp¥¢¤{mpwux{o`k,k~]`cl}Bo44Wk~]`cbaPclkmpwcN~lx{aN|%mpwcl}¹:x{w}4cbwsx»aN4aN½ncm»~lxkus
¥¦o4`~bsux{§
¾=¿.À*ÁÂà Ä; ¨tBkuscbwclkukŪK\^]4wclk]`x{}¼ #o`cbo`clknªBv;cbw¥¦x{wuaemp`~lc+mp%mptKkknª` ¡sx¡~]%m{kusu~v$cbsuwu
¶3cbsknª4·;o4}± ¡sxK~]%m{kusu~)v$cbsuwu;¶gcbskn§
ÆǬȰÉËÊnÌÈXͬÎÉËϯÐlÑ
Ò5ÓÕÔÖl×{Ø;ÙÛÚËÙÕÜËÝÅÞßàÚ
á$âãËäÅå
ÖØ;ÙÛÚËÙÕÜËÝÅÞßæÚ
Unité de recherche INRIA Rennes
"9 1;'345(*% Ë +&(7+>8 ;%(
`"*'`
/
+
cbsmpwusu~bc»suwmpsc=}4c`clke}Õmpsuscb#sc=ao4su~bm{kkclkx }4clkPkcbo4kNkx{¡s
¡suwx¡}Bo4skW}4c±aemp4_bwcImpsusjb¡o`cbw=clkr¤{mpwumpsux{`kW}4c´}4jbmp,}Õmpsuscb¡sc:cbs¼}4c¹}4jb4s¼cb
aPxK}Bmp#sc+~lx{aN|*x{wuscbaPcb#s)}4cm`c§ c+!]#tBkusjbwjlkukclkusmpo`kku;`~bo¹}4ckx{wusc ¡o`c+c
aPjl~nmp4kaPcX}4c¢~lx{#suw#"{c¢`c©~]%mp4.c¢|%m{k¬suwx{|¥wjl ¡o`cbaNaPcb#s5}Ûjbsmpsn§%$&o`kmp.c¢}4cX}B'«jbwcb#sclk
~bm{kkclkP}4c=~bcb¡skP|*cbwuaPcbse}4c¼|4wcb`}BwcWcb ~lx{aN|4scW!]`jbsjbwx{.jb`jbsj±}4clk)(`oBq+*¦}4x{4`jlclkŪ
¤.x{qIcbs+¤K}4jlx-,L§.c|4o`knªclk`clk)´kcbo4kx{#sP}4c`x{a)4wcbo`kclkemp|4|4~nmpsux{`ke}`mp`kclk
|4wx{sxK~lx{clk»}4c´suwmp`ku|x{wus»}4clkrwjlkcnmpoBqº}4c´~lx{aNa)o44~nmpsux{§/$Õmp%mptKkc}4c´~lcWs°t¡|*c´}4c
ktKkus_baPcclkus©wjnmpkjlcw10{~lc ,!o4sukmpsux{»}4clk©wjlkcnmpoBqe}4cgv$cbsuwu*kusxK~]%m{kusu ¡o`clk¢~bm{kku ¡o`clk
cbs2(`o4}4clkn§ cN|4o4kkmp#s)x{o4su¢}4cNaPxK}4jbkmpsux{:|*cbwuaPcbs}4cN}4x{4`cbw)o4`cPwcb|4wjlkcb#smpsux{
kaN|4cr}4clkkutBkus_baPclkcbscbo4wPmp%mptKkc»clkussuwmp`ku|%mpwcb¡sc»w10{~lc3=!o4sukTmpsux{ }o4 }4clk
x{~bcbkW}4c±wjlkcnmpoBq }4cv$cbsuwu,}Bk|x{44clkn§9vo`kucbo4wk¼o`ksuwmpsux{`k¼#o4aPjbwu ¡o`clk=kx{¡s
}4x{4`jlclkŪ£sjbaPx{%mp#s}4c!o4susjW}4clk`clk4±kcbo4kPml¤.cl~»]#tBkusjbwjlkukPmp`k^ ¡o`c»}4crcbo4w
wcb|4wjlkcb#smpsux{r|%mpw©}4clkX Kv£¶3k£cbs©·£ Kv£¶3kn§%56`ª#}`mp`k©c4o4s©}4c^aN4aNkcbwXo4`c^¥¯x{`~bsux{
~lx74snª%}B'*jbwcb¡sclk|*x{su #o`clkg}4ckcbwu¤¡~lckx{#s~lx{aN|%mpwjlclkn§
8 à n Á -9 ¨tBkusjbwjlkuknª`clk}Õmpsuscb¡sc:rkcbo4knªmp%mptBkcN}4clk|*cbw¥¦x{wuaemp`~lclkŪwjlkcnmpoBq
}4cv;cbsuwu$ksx¡~]%m{kusu #o`clkŪ4wjlkcnmpoBq¼}4c,v$cbsuwu$kusx¡~]%m{kusu ¡o`clk;(`o4}4clkn§
* +
g%(*+"¬
,:c~lx{`k}4cbw£Psu]4k|%mp|*cbw£su]4wclku]`x{}KË%m{kcl}e #o`cbo`clk©su]N]#tBkuscbwclkukXmp`}ao4su|4c~bm{kkclk
xp¥¢~bo`kusx{aPcbwkn§)\^]4k³K`}xp¥X ¡o`cbo`cb4=kutKkscba ]%m{kaemp¡t´mp|4|4~nmpsux{`k,su]`c}BtK%mpaN~
~lx{¡suwx{xp¥3~lx{aN|4o4scbwPkutBkuscbaPkNmp`}¸scbcl~lx{aNa)o44~nmpsux{º`cbs¢x{wu³Kkn§I·`x{w`kusmp`~lcªX~lx{B
.clksux{:~lx{#suwx{Xmp`}suwm²e~Pk]%mp|44¼k,mr4=~]%mpcb4.cN.3'¬ Kcbwu¤ª«su]`cNkcbwu¤¡~lc}B'«cbw
cb¡sumpsux{[]4~][¢}Bwu¤.cesu]`cP¥o4suo4wc-¡scbwu`cbsn§.-°`}4clcl}«ª;}B'«cbwcb#s+ #o%mps°t xp¥kcbwu¤K~lclk
*»scbwuaPkxp¥;su]4wx{o4]4|4o4snª`}4cbmlt»x{w;y!suscbw^¥¯x{wX`ksmp`~lc,^mpwcwcl #o4wcl}r¥¯x{w}B'*cbwcb¡smp|4|4
~nmpsux{`k)kuo`~] m{k¤K}4clx4ª«scbcb|4]`x{#t.ª$cbaemp˪«¥¦su|§§§®go4waPxK}4cb4¼]`cb|¹sx=mp|4|4wx.m{~]
su]`clkcP~]%mpwm{~bscbwukusu~lkŧW®¥~lx{o4wkcª$x{su]`cbwmp|4|4~nmpsux{`kxp¥a)o4su~bm{kksu]4wclk]`x{} ¡o`cbo`clk
su]su]`c+kmpaPc~lx{#suwx{|4wu`~b|4clk~nmp*c,¥¯x{o4`}«ª³.c0/Õ215]`cbwc+s3kmp|4|4cl}sxsu]`c
k%mp4ekutBkuscba `x4§43K§
5^m{k~nmpt.ª$su]`cr ¡o`cbo`clkmpwcr~lx{#suwx{cl}I#t mWkcl #o`cb`~lcxp¥¥¦x{wu^mpw} su]4wclk]`x{}4k+mp`}¸m
kcl #o`cb`~lcxp¥;%m{~³K¢mpw}=su]4wclk]`x{}4kkuo`~]Wsu]%mps]`cb¼su]`c~lx{#scb#s3xp¥;su]`c ¡o`cbo`ccLq4~lclcl}4km
¥¯x{wu¢mpw}su]4wclku]`x{}«ª{su]`cXkcbwu¤¡~lclk;xp¥`kx{aPc¢~bm{kkclk$mpwcXku|*clcl}4cl})o4|§6-)su]`cXkmpaPc©¢mnt.ª{]`cb
m)%m{~³K¢mpw}=su]4wclku]`x{}rkXwcnm{~]`cl}«ª4su]`ckcbwu¤K~lclk^mpwckuxÅXcl}¼}4xŧ&3o`cgsxsu]`ccLqKkscb`~lc
xp¥£}B'«cbwcb#s3stK|clkgxp¥£suwm²e~ª%cnm{~]´ ¡o`cbo`c,kgku|4s¡sxkcb¤.cbwmp$`}4cb|cb`}4cb¡s3 ¡o`cbo`clknªx{`c
¥¯x{w^cnm{~]»stK|cª4mp`}su]`ckcbwu¤.cbwXkmpxK~nmpscl}rsxx{`cxp¥¬su]`clkc3 ¡o`cbo`clk^m{~l~lx{w}B4Nsxm)¤.cb
|*x{~bt *¦kx{aPc|*x{~bclk¬*c}4clk~bwu*cl}¼mpscbw ,L§ Kx{aPc,}4cbmlt¼aemntr]%mp|4|*cbªB¥¯x{wcLq`mpaN|4c
]`cb[kx{aPcaemp%mp.cbaPcb#s+k`cl~lclkkmpwut´cL¥¯x{wcNaPxK}B¥tK4¼su]`c|%mpwmpaPcbscbwxp¥^su]`cN ¡o`cbo`c
kcbwu¤¡~lclkn§
µ±x{`xp~bm{kk+su]4wclku]`x{}KË%m{kcl}I ¡o`cbo`cb4¹kutBkuscbaPk)]%mn¤.crclcb¸cLqKscb`k¤.cbt kusuo`}Bcl}I
su]`cscbwmpsuo4wcªsu]`x{o4s]#tBkuscbwclkuk`wkus+7/d83Kª5Bdª51mp`}[su][]¡tKkscbwclkuk+`cLqKs/dn4ª
d9Bª«Bª«1§-°±su]`caPxksg.cb`cbwmp£kcbsusu4`ªsu]`c+ ¡o`cbo`c+kµ´mpwu³.xŤ¡mp mp`}¹mr~bxkcl}K¯¥¯x{wua
kx{o4sux{W¥¯x{wsu]`c+kuscnm{}Bt¡kusmpsc)|4wx{%mp4suclkxp¥XmP]`cbscbwx{.cb`clx{o`ka)o4sukcbwu¤.cbwsu]4wclk]`x{}
¡o`cbo`c´su] ]#tBkuscbwclkuk»k»x{4smp`cl}«§ \^]`c´Xx{wu³Bk»Xc¹mpwc´.x{4 sx¸}4clk~bwu*c±`xÅ mpwc
}4cb¤.x{scl}sx3ao4su~bm{kk© ¡o`cbo`clkn§6-:/d;21ª}B'«cbwcb#s©k~]`cl}Bo44|*x{~bclk©mps£mpz\µ kus~]
mpwc3kusuo`}Bcl}=<B|%m{~³.cbs¢xkkX|4wx{%mp4suclkgmp`}eaPcnmp»¢mpsu4NsuaPclkmpwc~lx{aN|%mpwcl}rscbwuaPk
xp¥«su]`csuwm²e~x.m{}«§>-?/d1ª.su]4wclku]`x{}e|x{~bclk©¥¦x{w¢mku4cLkcbwu¤.cbw¢ #o`cbo`cb4`cbsXx{wu³esu]
s°Xx£yx{,~bm{kkclk$mpwco`kcl},,x{w}4cbw¬sx}4cb¤Kkc£mp`}aN|4cbaPcb¡s;}B'«cbwcb#s$|x{~bclkn§;¶go4aPcbwu~nmp
wclko4sknª%x{4smp`cl}±su]Wsu]`c)|xÅXcbwkcbwuclkgmp.x{wusu]4a=ª*ku]`xÅsu]%mpssu]`c)aPx¡}4cb;kmpsuk %clksu]`c
wcl ¡o4wcbaPcb#skxp¥£]4]`cbwË|4wux{wus°t±suwm²e~]4c+x '*cbwu4¼m{~l~lcb|4smp4c|cbw¥¯x{wuaemp`~lc)¥¦x{wgsu]`c
xÅXcbwg|4wux{wust=x{`c§@-°A/Õ1ª ]`x{B(CED©mp%mptBkc)mNa)o4su~bm{kk|4wux{wust= ¡o`cbo`cb4ekutBkuscba
su]N~lx{4.clkusux{N%m{kcl}+x{su]4wclku]`x{}4kŧ 5Xm{~]P~bm{kk;k~lx{#suwx{cl}¡t+mgsuwu|4cxp¥%su]4wclku]`x{}4k
~lx{aN|*xkcl}xp¥*mpPmp%mpscbaPcb¡s©su]4wclku]`x{}«ª#mpNx{`kcbssu]4wclk]`x{}Pmp`}m3}Bk~nmpw}su]4wclk]`x{}«§65¢t
su]`cbªBm|4wux{wus°tP|x{~btNk©`~bo`}4cl}esu]`c ¡o`cbo`cex{w}4cbw¢sx,|4wxŤ¡}4c3m*cbsuscbwX ¡o%mpstPxp¥
kcbwu¤¡~lc)sxkx{aPc+~bm{kkclkŧz¹mp.x{wusu]4a sxe~lx{aN|4o4sc+|*cbw¥¦x{wuaemp`~lc+aPcnm{kuo4wclk3kg¤.cb±¥
su]`c|%m{~³.cbsmpwuwu¤{mp|4wxK~lclkk£k^m, ¡o`cbo`cLËcb4su]r}4cb|*cb`}4cb#sµmpwu³.xn¤Kmp»mpwuwu¤mp%|4wxK~lclkkn§F-°
/Õ1ª.m #o%mp¡susmpsu¤.ckusuo`}Bt)xp¥%}B'«cbwcb#sumpscl}Nkcbwu¤K~lclk$¥¦x{w$su]`cJ-°#scbwu`cbs *3'¬ Kcbwu¤ ,k;¤.cb <
su]`c,mpo4su]`x{wk~lx{aN|%mpwc,su]`cxkkmp`}¼}4cbmntr*cb]%ml¤Kx{wkwcbmpscl}¼sxs°Xxewx{o4scbwaPcl~]%mp4kuaPk
~nmpcl}su]4wclku]`x{}r}Bwx{|4|44Pmp`}e|4wux{wus°tk~]`cl}Bo44`§gk4+mprmp%mptKsu~nmp*aPcbsu]`x¡}«ªKsu]`cbt
k]`xn su]%mps¢m,k4%~nmp#s^aN|4wxn¤.cbaPcb¡ssu]4wx{o4]4|4o4s~nmpe*cgm{~]4cb¤.cl}«ª4clku|*cl~bmptN]`cb
o`k4e|4wux{wust±k~]`cl}Bo44`§3·;%mpt.ª%¢c ¡o`x{sc+mPwcl~lcb#s3Xx{wu³Wx{±a)o4su~bm{kksu]4wclk]`x{}K
%m{kcl} ¡o`cbo44NkutKkscba9su]»]#tBkuscbwclkuk5 /dd(1ª¡su]`c3#o4acbwxp¥$kcbwu¤.cbwkXk^~lx{¡suwx{cl}»#t
su]`c3su]4wclku]`x{}¼kcl #o`cb`~lclkmp`}=m)¥Ëm{kus^mp`}=m{~l~bo4wmpscscbwmpsu¤.c)kx{o4sux{r¥¦x{wcb¤mpo%mpsu4Nsu]`c
ktKkuscba |*cbw¥¯x{wuaemp`~lco4`}4cbw¤mpwut¡4Nsu]4wclku]`x{}4k3mp`}¼|%mpwmpaPcbscbwkgk¤.cb§
¡`~lc^su]`cmpxŤ.c^scbwmpsuo4wcku]`xÅk£su]%mps©mpemp%mptKsu~mp%mptKkuk£cl~lx{aPclk£ ¡o4~³Kt+suwu~³Kt.ª
mpmpscbwu%mpsu¤.c¢mnt.ªo`k4¼ ¡sxK~]%m{kusu~v;cbsuwu¶gcbsk *Ë Kv£¶3k ,Lª%kmpsuscbaN|4scl}´±su]4kg|%mp|*cbwn§
-°`}4clcl}«ª` Kv£¶3kmpwcg|4wxŤ.cb¼sx+cm|xÅXcbw¥¦o4«wcb|4wclkcb#smpsux{Wxp¥;kutKkscbaPkXsu]=kt¡`~]4wx{4
kTmpsux{x{w£~lx{`~bo4wuwcb`~btPmp`}¢cku]`xn su]%mps5su]`c^wcb|4wclkcb¡smpsux{xp¥su]4wclk]`x{}KË%m{kcl}P ¡o`cbo`clk
k¤.cbwut=kuaN|4cmp`}´~lx{#¤.cb4cb¡sn§ , ]`cbWsu]`cN Kv£¶ kµmpwu³.xn¤Kmpª*kxp¥¦s¢mpwc|%m{~³mp.clk3~nmp
|4wxŤ¡}4cmpo4sx{aempscl}P.cb`cbwmpsux{mp`}Nkx{o4sux{exp¥*~lx{#su#o`x{o`kuËsuaPcµmpwu³.xn¤~]%mp`knª¡x{su]`cbw
kcs^~nmp»cgkua)o4mpscl}«§£\^]`c3.cb`cbwmp«~bm{kk^xp¥5 Kv£¶1Xc3o`kckm{~bsuo%mpt» ¡sxK~]%m{ksu~
hgcb¢mpw}=¶3cbsk*Ë Khg¶gk , /%ª`1]`cbwccnm{~]Wksmpsc,~nmp¼c,m{kkx¡~bmpscl}=sxPmwcb¢mpw}¼wmpscmp`}
mpxÅ kx{aPc¥o4`~bsux{%mpsuclkkuo`~] m{k3o%mpw}´¥¦o4`~bsux{`k*sx»cb%mp4cNx{w`x{scb¤.cb#sk ,LªksmpscL
}4cb|*cb`}4cb`~lc^xp¥ `wu4suaPclkmp`}+cb¤.cb¡sk£mp`}+|4wux{wusuclkn§6,:c©`mpkxgo`kc^m.cb`cbwmp½Åmpsux{
xp¥ Kh¶3knª·;o4}[ ¡sxK~]%m{ksu~ev;cbsuwuX¶3cbsk:*¦·£ Kv£¶3k , /3Kª£dBª¬ 381X]4~] km»]#tK4wu}:cLqBscbB
kx{»xp¥£ Kv£¶3k^]`cbwc (`o4}¼~nmp¼aPxK}4cb«~lx{#su¡o`x{o`k~lx{aN|*x{`cb#skx{wmp|4|4wxnqKaempsc,}Bk~bwcbsc
ksmpsclksx|4wcb¤.cb#sgsu]`c,cLqK|4xkx{Wxp¥;su]`cksmpscLku|%m{~lc§
,:cPmpwcN.x{4=sx»aPxK}4cb©x{o4w,kutBkuscbaPk#t: Kv£¶3k)mp`}¹su]`cbw)cLqBscb`kux{`k³.cPXcN]%mn¤.c
}4x{`c su]`c´aPx{`xp~bm{kk=~nm{kc /Õ91§9\^]4k¼Xx{wu³ ~nmp&c´wcbmpscl} sx /dn21ªg]`cbwc:m
kx{aPcb]`xn kuaNmpw¼ao4su~bm{kk±mp%mptBkuk¼o`k4º Kv£¶gk=]%m{k¼clcb1}4x{`c4o4s¼smpwu.cbscl}sx
|*x{4ekutBkuscbaPkn§
\¬x:mp%mptBkc¼x{o4w Kv£¶ mp`} · Kv©¶ aPxK}4cbknª£¢cWmpwc».x{4¹sxo`kc»x{`c=xp¥3su]`c=ml¤mp
mp4ckxp¥¦s¢mpwc)|%m{~³mp.clknª« Kv£¶gv *E¥¯x{w(2 ( ( 28#, /Bª¬db1ªmNkxp¥¦s¢mpwc
}4cb¤.cbx{|4|*cl} mps3o4³.cg4¤.cbwkust.§¹\^]4k+sxKx{Xo`kclkNmp%mptKsu~LË#o4aPcbwu~¼aPcbsu]`xK}4k+sxkx{¤.c
µmpwu³.xn¤Kmp=`cbsk3mp`}¼kua)o4mpsc· Kv©¶gkmp`}=`x{Bµ´mpwu³.xŤ¡mp¹ Kv£¶gkŧ
\^]`cx{wu#mp4½Åmpsux{xp¥su]4k£|%mp|cbwk5su]`c¢¥¯x{xn4`§© Kcl~bsux{3|4wclkcb#sksu]`ckutBkuscbaPk5¢c
mpwc,.x{4PsxNaPxK}4cb$mp`}Wmp%mptBkc§X Kcl~bsux{´+k}4cb¤.x{scl}=sxem}4clk~bwu|4sux{´xp¥£ Kv©¶gk*±m
¤.cbwut.cb`cbwmp`kcbsusu4 ,5mp`}N·£ Kv£¶3k£mp`}N Kcl~bsux{e3|4wclkcb#sksu]`c^}4clk~bwu|4sux{exp¥a)o4su~bm{kk
su]4wclk]`x{}´ ¡o`cbo`clk3#t=aPcnmp`kxp¥^ Kv©¶gkmp`}´· Kv©¶gkn§¶go4aPcbwu~nmp£mp%mptKkuk3kg|4wxn¤K}4cl}
Kcl~bsux{B§5·;%mpt.ª¢c¤.ckx{aPc^~lx{`~bo`kux{`k©mp`}N}Bwcl~bsux{`k£¥¦x{w;¥¦o4suo4wc^Xx{wu³+ Kcl~bsux{
B§
»+%++
,:cg}4cnmp%]`cbwcsu]ea)o4su~bm{kkXkutBkuscbaPknª#~]»mpwcwcl ¡o4wcl}e]`cbr}4cnmp4)su]}B'«cbwcb#s
x# §H,:cr~lx{`ku}4cbwPmWkcbsxp¥ }B'«cbwcb#sN~bm{kkclkmpwuwu¤¡4sxmWx{`cLkcbwu¤.cbw ¡o`cbo`c§´\^]`c
¡o`cbo`c~nmp|%m{~bst´km{kkuo4aPcl}´sxrc`4scª«su]¹~nmp|%m{~bst;¥¦x{w~bm{kk *4o4s)me~lx{aNaPx{
~nmp|%m{~bs°t¹~nmp¹cN}4cb¤Kkcl}:m{kXcb ,L§ez kusmpscNxp¥^su]`cNkutBkuscba k¤.cb¹#tsu]`c#o4acbw
* ,*xp¥`~bm{kku 4~bo`kusx{aPcbwk¬su]`c©kutBkuscba mp`})su]`c©~bm{kk¬#o4acbw5xp¥4su]`c©~bo`kusx{aPcbw;
kcbwu¤¡~lc§F-°esu]4kXaPx¡}4cb˪Bcnm{~]»~bm{kkXk¢m{kkuo4aPcl}Psx]%ml¤.cm,kcb|%mpwmpscg4o6'«cbwn§¶gcb¤.cbwusu]`cbclkkŪ
su]`c+ ¡o`cbo`c)kg`x{s3kcb|%mpwmpsc)kcb¤.cbwmp;`}4cb|cb`}4cb¡s, #o`cbo`clk)*¦cb¤.cb´¥£s3~nmp´c,*cl~nmpo`kc
su]`c¢kcbwu¤K~lc©|*x{~bt)}4cb|*cb`}4k5x{su]`c¢x{%mp4kusmpsc¢xp¥`su]`c¢ ¡o`cbo`c§H,:cX~nmpPm'«cl~bs¬¥¯x{w$`ksmp`~lc
mksuwu~bs|4wux{wustPmps£cnm{~]e~bm{kknª4o4s£aemp¡t+x{su]`cbw£|*x{~bclk£~nmpN*c}4cb¤¡kcl}«§H,:c¢¥¯x{xn ]`cbwc
su]`c,.cb`cbwmp$|*x{~bt¼xp¥ /d;1$]`cbwc,s¢x~bm{kkclk ¡o`cbo`clkgmpwc)mp%mptBkcl}´mp`}=]`cbwcmP~bm{kk
~bo`ksx{aPcbw35*ckcbwu¤.cl}±su]|4wx{%mp4s°t g]`cb¹su]`cbwcNmpwc~bm{kkud~bo`kusx{aPcbwk
mp`}P~bm{kk°P~bo`kusx{aPcbwkn§£\^]`c|*x{~bclkgmp%mptK½ncl}¼ /d;1$mpwc
d§¨gcnm{}Wxp¥;`c|4wux{wus°t *¦¨® $, "!#$ "&%'¥&()4§
B§ 5^cbwu`x{o4$k~]`cbaPc* 5 ,*
!
"+%-,´mp`}./ "%0213, *¥ ()-,L§
B§
o`cbo`c $¬cb4su]\^]4wclk]`x{}±k~]`cl}Bo44.*
$¡\ ,*~bm{kkd~bo`kusx{aPcbwk3]%ml¤.ckusuwu~bsg|4wu
x{wust *4"!5 %6,¢¥789ª`˧Ûc§ª`¥5su]`c,#o4acbw3xp¥£~bm{kk°N~bo`kusx{aPcbwkgko4`}4cbwm
su]4wclku]`x{}«§£zgxŤ.csu]4kcb¤.cb˪~bm{kk°+]%m{kkusuwu~bs|4wux{wust.§
`§ o`cbo`c+cb4su]¹su]4wclku]`x{}x{~bm{kk°P4o6'«cbwsu] 5¢cbwu`x{o4£k~]`cl}Bo44 * 5 ,z
su]4wclku]`x{}¼¤mpo`c:91ko`kcl}r¥¯x{w^su]`c#o4acbwxp¥ ¡o`cbo`cl}¼~bm{kk°~bo`kusx{aPcbwkn§@,:co`kc
"!5 "+%0¥;<()emp`}==8>9 mp`}."!5 &%-,±¥+()Pmp`}==?>9§
B§ o`cbo`c3cb4su]rsu]4wclk]`x{}x{»~bm{kkdg4o6'*cbw¢su]:5^cbwu`x{o4*k~]`cl}Bo443* 5d,5su]`c
su]4wclku]`x{}¼¤mpo`ck^`xn o`kcl}r¥¯x{w~bm{kkd ¡o`cbo`c§>,:co`kc ! "+%-,W¥@)A8B<8B9
mp`}==()Pmp`}."!5 "+%0¥;<?>9 mp`}C()4§
zg:cLq`m{~bs)mp%mptKkuk,k}4x{`cN /d;21 *su]:s°Xx=~bm{kkclk ,g]`cb:su]`caPxK}4cb£kµ´mpwu³.xŤ¡mp§
\^]4kk¤.cbwut±.cb`cbwmpcl~nmpo`kc|*x{~bclk³.c]`cnm{}¹xp¥©`c|4wux{wus°t.ª 5^cbwu`x{o4£k~]`cl}Bo44
k~]`cbaPcex{w #o`cbo`cNcb4su][su]4wclku]`x{} ~nmp[cPwcb|4wclkcb#scl}[o`ku4¼¥¦o4`~bsux{`kD¢m{kXce
kclccbxÅ,§£\^]4kaPxK}4cb~nmpWcnm{kutrc.cb`cbwmp½ncl}WsxNaPx{wcsu]%mp=s°XxP~bm{kkclkn§
-`}4clcl}«ª#Xc~nmp}4c ``cFE01G^¥¯x{wu¢mpw}mp`}P%m{~³K¢mpw}ea)o4su}BaPcb`kux{%mp*su]4wclku]`x{}4kŪ
}4c ``cl}Wxn¤.cbw H
;!#JIJIJI5KLMONP)ABORQ
ko`~]¹su]%mps,]`cb mrsu]4wclku]`x{}:kwcnm{~]`cl}«ª¬su]`cN|4wx{%mp4st´¥¦o4`~bsux{`kD;!#JIJIJI#KLMmpwc
aPxK}B%cl}«§ ,:cW]%ml¤.cSE|4wx{%mp4st ¥¦o4`~bsux{`kr~lx{wuwclku|x{`}B4¸sx su]`c.ET10W¥¦x{wu^mpw}
su]4wclk]`x{}4k ]`cb su]`c[¥¦x{wu^mpw} su]4wclku]`x{} krwcnm{~]`cl}«ª3|4wx{%mp4stº¥¦o4`~bsux{`k=mpwc
ks~]`cl}:sxG
!
I,mp`}:]`cb:su]`c %m{~³¡^mpw} su]4wclk]`x{}¹k,wcnm{~]`cl}«ª$|4wx{%mp4s°t
¥¦o4`~bsux{`kmpwcgks~]`cl}r%m{~³sx
IL§>-sXkXsu]`cb¼m).cb`cbwmp½Åmpsux{=xp¥¬su]`c¢x{wu³P/d;21§
¨gtBkuscbwclkuk~lx{aPclk¥¦wx{asu]`c¥Ëm{~bssu]%mps¥¯x{wu¢mpw} mp`}¹%m{~³¡^mpw}:su]4wclku]`x{}4k}4x¼`x{s,]%mn¤.c
su]`c)kmpaPc,¤mpo`clkn§¢\^]`cbª`su]`c,¡o4a)*cbw3xp¥~lxkus¥¦o4$kus~]`clk* Waemp%mp.cbaPcb#sx{|cbwmpsux{`k ,
kcLqK|*cl~bscl}»sxP}4cl~bwcnm{kc§
\^]`cW^mlt ¢cW¡suwx¡}Bo`~lc´]¡tKkuscbwclkk su]`c±|x{~bclkrxp¥/d;1kesu]`cW¥¦x{xÅ4+*su]
E % ,
d§¨® $ $`~lx{wu|*x{wmpsu4:]¡tKkuscbwclkksx´¨® $&k~]`cl}Bo44¹Xx{o4}¸cnm{}Isx´cb]%mn¤.c»³.c
]`cb=`~lx{wu|*x{wmpsu4e]#tBkuscbwclkuksx 5d,x{w 5Bª`kxXc)}4x`x{s~lx{`ku}4cbws]`cbwc§
B§ 5 #su]`cgs¢xsu]4wclk]`x{}4kP! *%m{~³¡^mpw} ,¢mp`} ! *E¥¦x{wu^mpw} ,X}4cb|cb`}rx{su]`cg#o4acbw
xp¥¢~bm{kkud+~bo`ksx{aPcbwk¹su]`c #o`cbo`c§ ,:c+smp³.cC
!
!
$ " %O,!)mp`} /
!
" % , /
su]3, /( , ! kx»su]%mps,¥~bm{kkde #o`cbo`cN]%m{km»x{s)xp¥~bo`kusx{aPcbwknª$XcN`~bwcnm{kcPsu]`c
|4wx{%mp4st¼su]%mpssu]4k~bm{kkkkcbwu¤.cl}«§
B§
$¡\ $su]4wclku]`x{}4k+}4cb|cb`} ]`cbwcex{4t¹x{[~bm{kk°»4o6'«cbw~lx{#scb¡sn§¼\¢xWsu]4wclku]`x{}4k
/ *%m{~³K¢mpw} ,Pmp`} / *E¥¯x{wu¢mpw} ,mpwc»#suwxK}Bo`~lcl} kuo`~]Isu]%mpsC
!
!
C% ¼mp`}
/
!
" % )4§ -°sPaPcnmp`ksu]%mpso4¡su / kPwcnm{~]`cl} ~bm{kkud¼]%m{kksuwu~bse|4wux{wust.§
\^]`cbWkusuwu~bs~bm{kk°+|4wux{wust»ko`kcl}=o4#su / k]4sn§
`§
5 su]4wclku]`x{}4k5}4cb|*cb`})]`cbwc^x{4t,x{~bm{kk°4o6'*cbw5~lx{#scb¡sn§F,:c©o`kc
!
!
"+%
*¥M&()-,mp`}
/
!
+% , * ¥ +()-,L§6,:csu]`cbP]%mn¤.cs¢x,su]4wclku]`x{}4k©`kuscnm{}Pxp¥
x{`c /d;21¬mp`}»su]`c|4wx{%mp4str¥o4`~bsux{¼o`kcl} *]`cb¼*cbs¢clcb=su]`xkcsu]4wclku]`x{}4k ,
}4cb|cb`}4kgx{¼su]`cm{kussu]4wclku]`x{}=]4sn§
B§
5dsu]4wclku]`x{}4k5}4cb|*cb`})]`cbwc^x{4t,x{~bm{kkdX4o6'*cbw5~lx{#scb¡sn§F,:c©o`kc
!
!
"+%
,W¥; C( )emp`}.
/
!
"%0¥C()mp`}»su]`c,k~]`cbaPc,Xx{wu³Bk³.c 5B§
-¡scbw°mpwuwu¤{mpk+mp`}:kcbwu¤K~lclk%`wkus*cPm{kkuo4aPcl}¹sx»*cNcLqK|*x{`cb#sump˧5¤.cb:¥^su]4k
cLqB|*x{`cb#sumpm{kkuo4aN|4sux{Ik)¤mp}¹¥¯x{wkx{aPcmp|4|4~nmpsux{`kNkuo`~]¸m{kscbcb|4]`x{`cr`cbs¢x{wu³Kknª
aemp¡tImp|4|4~nmpsux{ mpwcnm{k+`clcl}IaPx{wcr.cb`cbwmp}Bkusuwu4o4sux{ m{kkuo4aN|4sux{`kn§ -°[su]`c»z\µ
mp`}0-°#scbwu`cbs`cbs¢x{wu³KkN¥¦x{w+`kusmp`~lcª©kcbwu¤¡~lclkku]`x{o4}I*crm{kko4aPcl}[sx±*c}4cbscbwuaNkusu~<
aPx{wclxŤ.cbwnªKmpwuwu¤mpkxp¥¦scbN|4wclkcb#s©kcb¥EkuaNmpw£x{w5]`cnmn¤¡t¡Ësmpcl}N*cb]%ml¤Kx{w *¦kclc¢¥¯x{w;`ksmp`~lc
/91,L§ ,:ckusuo`}Bt su]`clkc:`x{Bµ´mpwu³.xŤ¡mp su]4wclku]`x{}K #o`cbo`clkW&su]`c´¥¦x{xÅ4`§z3k
mp`x{su]`cbw¢.cb`cbwmp½Åmpsux{ªBsu]`cbwc3~nmpe*ckx{aPcg}4cbmltP*cbs¢clcbrsu]`csuaPcsu]%mpsXsu]`csu]4wclk]`x{}
krwcnm{~]`cl}1mp`}ºsu]`c´suaPc´su]%mps»su]`cW|%mpwmpaPcbscbwk±mpwc´~]%mp4.cl}«§ \^]4k¼~nmp ]%mp|4|cb ¥¯x{w
`ksmp`~lc]`cbsu]`c ¡o`cbo`caPx{4sx{wk,sk3~lx{¡scb#smps 4q4cl}x{wgwmp`}4x{a¡scbwu¤{mpk,xp¥XsuaPc§
\^]`clkc~nm{kclk$mpkxPc¡¤.clkusu#mpscl}=¡o4aPcbwu~nmpt.§
6g"'+` " 8:;%(* <9; 6g"*'+4 " 50º( <>;
± 63"*'` "98:;%(* =<9;
v;cbsuwu%`cbsk©k©m3¥¯x{wuaemp`wmp|4]e|%mpwusu~bo4mpwutN¢cbkuo4scl}N¥¦x{wwcb|4wclkcb¡su4su]`c;(%xnºxp¥*B¥¯x{w
aempsux{»mp`}P~lx{#suwx{ekutBkuscbaPksu]e~lx{`~bo4wuwcb`~btrmp`}PkutK`~]4wx{4½Åmpsux{»~]%mpwm{~bscbwukusu~lkn§
,:c+}4clk~bwu*c)]`cbwcNmpcLqKscb`kx{´xp¥^ Kv©¶gkmp`}¹ Kh¶3k]4~]¹Xcmp4o`k¤.cbtW~nmp5su]4k
aPxK}4cb$ Kv£¶+§),:csu]`cbW}4c ``c)· Kv©¶gkn§
\^]`c,~bm{kkxp¥kusxK~]%m{kusu~,v;cbsuwu¬¶3cbskXcmpwc,~lx{`ku}4cbwu4ek^¤.cb±#t¼m+suo4|4c
9G * PJ( F D
]`cbwc
k^su]`c,kcbsxp¥;|4m{~lclk * wcb|4wclkcb¡scl}=¡tr~bw~bclk ,L§5©m{~]=|4m{~lc,aemlt»~lx{#smp )b§
\^]`c 8 !xp¥«su]`cg Kv£¶ k©su]`cb}4c ``cl}e#tsu]`c¡o4a)*cbw¢xp¥«sx{³.cb`k£rcnm{~]|4m{~lc§
9ksu]`c,kcbsxp¥;suwmp`kusux{`k*wcb|4wclkcb#scl}W#t»%mpwk ,L§
k^su]`ckcbsxp¥;4|4o4smpw~lk*E¥¦wx{a m+|4m{~lcsxPm)suwmp`ksux{ ,mp`}¼x{o4su|4o4sgmpw~lk2*E¥¦wx{a
msuwmp`kusux{¹sx¼me|4m{~lc,L§ 5©m{~]Impw~k¤.cb¡t±sk)*aempwu³K4{}4cb|cb`}4cb¡s ,a)o4su
|4~bst.§
ksu]`c,kcbsxp¥4]44sx{w3mpw~lknªK¥¦wx{a m|4m{~lc,sxem+suwmp`kusux{ *wcb|4wclkcb#scl}±#t¼mp
mpw~scbwuaN%mpscl}=¡t»mPkuaemp~bw~bc,Lª`su]¼sk3m{kkxK~bmpsca)o4su|4~bst.§
ek^su]`c4*aempwu³K4{}4cb|cb`}4cb¡s ,^o%mpw}»¥¦o4`~bsux{»¥¦x{wcnm{~]=suwmp`kusux{§@-°s^km+.cb`cbw
mp½Åmpsux{´xp¥4]44sx{wmpw~lknª``cb¤.cbwusu]`cbclkkg¢c)kusu5mpkxe~lx{`k}4cbw4]44sx{wmpw~lk¥¯x{w
su]`cbwwmp|4]4~nmp¬o`kcL¥o4`clkkgmp`}r¥¦x{wkTmp³.cxp¥;.cb`cbwmps°t.§
ksu]`c4sumpaempwu³K4`§
(1ksu]`c,cLqB|4~bs|4wux{wust¼sxsuwmp`ksux{`kn§
}4c ``clksu]`c `wu4PsuaPc,}Bkusuwu4o4sux{´xp¥5cnm{~]=suwmp`kusux{§
[km)Xcb]#s¢¥¦o4`~bsux{»o`kcl}esx+~]`xKxkcgsu]`cgx{`cg]4~]»`wcg¥¬kcb¤.cbwmp]%mn¤.c3su]`c
kmpaPc `wu4PsuaPc§
ksu]`ckusmpsu~wclkTmpaN|44¼|x{~bt±¥¦x{wcnm{~]¹suwmp`kusux{:]`cb¹scl~lx{aPclk)cb%mp4cl}
mp#mp±m¥¦scbwcb4e}BkTmp4cl}»#t»su]`c `wu4exp¥£m~lx{`~bo4wuwcb#ssuwmp`ksux{§©\^]4wclc|*x{
~bclkgmpwc)|xkk4c©v£h - * |4wclcbaN|4su¤.cwcb|cnmpsg}4cb#su~nmp,Lªv£h *|4wclcbaN|4su¤.cwcb|*cnmps
}B'*cbwcb¡s ,mp`}=v©h3 *|4wclcbaN|4su¤.c,wclko4aPc,L§
}4c ``clk=su]`c:m'«cl~bsu4 wclkmpaN|44 |x{~btº¥¦x{w=cnm{~]1suwmp`kusux{1]`cb mp`x{su]`cbw
suwmp`kusux{ `wclk4o4s3su]`c+~lx{`ku}4cbwcl}´suwmp`kusux{±wcbaemp`kcb%mp4cl}«§v£h -Tªv£h3 Wmp`}
v£h mpwc)mpkx|xkk4c§
\^]`c3}BtK%mpaN~lkxp¥5 Kv£¶3k^k¢su]`cg¥¦x{xÅ4`§£z1suwmp`kusux{»k^kmp}rsx+c $ ¥;cnm{~]
xp¥sk4|4o4sg|4m{~lclk3~lx{#smp`km{kaemp¡t¼sx{³.cb`k3m{ksu]`c,ao4su|4~bst±xp¥su]`c~lx{wuwclku|x{`}B4
mpw~´mp`} ¥,su]`c±`cLqBses¢xI|4wx{|cbwusuclk»mpwcW¤.cbwu%cl}«§ ·;wkusesu]`c ( ( *¥mp#t ,Lª
ao`kus¤.cbwu¥¦tsu]%mpscnm{~]=4]44sx{w|4m{~lcao`kus~lx{#smpm+#o4acbwxp¥5sx{³.cb`kclkksu]%mp¼su]`c
ao4su|4~bstexp¥«su]`c~lx{wuwclk|x{`}B4mpw~§\^]`ckcl~lx{`}Pwcl ¡o4wcl}N|4wx{|*cbwustNk©su]%mps£su]`c¤mpo`c
xp¥4su]`co%mpw},¥ o4`~bsux{+xp¥4su]`c£suwmp`kusux{*¥`mp¡t ,«k©d§;zaPx{43mp¡cb%mp4cl},suwmp`ksux{`knªpsu]`c
x{`cgsu]»su]`cgkaempclkus`wu4suaPcgk^kmp}esx@ b§\^]`c `wu4suaPclkxp¥suwmp`ksux{`k¢¥¦x{xÅ
wmp`}4x{a}Bksuwu4o4sux{`k]4~] ~nmp *ce.cb`cbwmp* ˧Ûc§ª`x{sNx{4tIcLqK|*x{`cb#sump,L§ -Ë¥gkcb¤.cbwmp
suwmp`ksux{`kP]%ml¤.cWsu]`c=kmpaPc`wu4[suaPcª¢su]`c=x{`c¼]4~]ºgm{~bsuo%mpt `wc=kPkTmpaN|4cl}
su]¸m¼|4wx{%mp4s°t cl #o%mpXsx=sk)`}B¤¡}Bo%mp¢Xcb]¡s}B¤K}4cl}:¡t¹su]`cekuo4a xp¥Xcb]#skxp¥
mp^|*xkku4csuwmp`kusux{`kn§, ]`cb¸s `wclkŪ5su]`csuwmp`ksux{ wcbaPxn¤.clkemW#o4acbwPxp¥sx{³.cb`k
¥¦wx{a cnm{~]¹xp¥£sk4|4o4s3|4m{~lclkcl #o%mp$sxesu]`c)a)o4su|4~bstxp¥£su]`c+~lx{wuwclku|x{`}B4=mpw~+mp`}
s}4cb|*xkusk3¹cnm{~]:xp¥Xskx{o4su|4o4s|4m{~lcPm#o4acbw,xp¥¢sx{³.cb`kcl #o%mp5sxrsu]`c+a)o4su|4~bs°t
xp¥5su]`c~lx{wuwclku|*x{`}B4rmpw~ª4cnm{}B4esu]`cb=sxem+`cb1aempwu³K4`§
zI· Kv©¶ /3Kª©dBª$ 381¢k+mpIcLqKscb`kx{[xp¥mp¸ Kv£¶]`cbwcekx{aPce|4m{~lclk~nmpIc)(`oB
}[mp`}:]`cbwcekx{aPc (`o4} ~nmp (%xn su]4wx{o4]Isuwmp`kusux{`knª¬¥¯x{xn4´¤.cb wuo4clkn§r·;o4}
|4m{~lclkmpwcgwcb|4wclkcb#scl}r¡tPs¢x+~lx{`~lcb¡suwu~~bw~bclkmp`}4(`o4}»mpw~lk¢#tP}Bwcl~bscl}rsu]4~³»mpw~lkn§
\^]`c}Bt¡%mpaN~lkxp¥Xmp´· Kv©¶ ksu]`cb±.xn¤.cbwu`cl}¡t=}Bk~bwcbsccb¤.cb¡sk)*`wu4rxp¥£suwmp`kusux{`k
aPxK}B¥¦t¡4=su]`c}Bk~bwcbscmp`} (`o4}:aempwu³K4 ,,mp`} ~lx{¡su#o`x{o`k (%xnk (`o4} |4m{~lclk)*cL
s°Xclcb su]`clkc`wu4.kPm{k}4clk~bwu*cl} ¸su]`ce¥¦x{xÅ4`§,º]`cb¸su]`csuwmp`kusux{`kwcbmpscl}¸sx
(`o4}rmpw~lk *4|4o4s¢x{w¢x{o4su|4o4s ,©mpwc3cb%mp4cl}«ª (`o4})(%xnkmpx{4+su]`cgmpw~gsu]su]`cg~lx{`kusuwmp#s
su]%mpssu]`c (`o4}¼cb¤.cb«wcbaemp`k*cbs¢clcb´Nmp`}Wm+|4wclku|*cl~b%cl}¼*x{o4`}«§£·`x{w~lx{aN|4o4smpsux{%mp
kaN|4~bst.ªsu]`c (`o4} (%xÅwmpsc,k3mpsaPxkusg`cnmpw£¥¯x{wcnm{~] (`o4}=|4m{~lcF,$ª4su]`c (`o4}Wcb¤.cb
K^~]%mp4.clk3m{~l~lx{w}B4esxNsu]`c,cl ¡o%mpsux{ /381
%MG
G
]`cbwc ikrsu]`c´~bo4wuwcb¡s¼}Bk~bwcbsc´aempwu³¡4 mp`} mp`}Wmpwckx{aPc±¥¦o4`~bsux{`krxp¥su]`c
}Bk~bwcbsc,aempwu³K4`§µ±x{wclxŤ.cbwnª]`cbmNsuwmp`kusux{ `wclknªkx{aPc (`o4}±~nmpW*caNaPcl}Bmpscbt
|4o4s[x{wwcbaPxn¤.cl}¹¥¦wx{a (`o4}|4m{~lclkn§e\^]`cempw~lkwcbmpscl}¹sx¼su]`clkcaempwu³¡4{}4cb|*cb`}4cb#s
(`o4}[aN|4o4kclkNxp¥su]`c4|4o4sPmp`}[x{o4su|4o4sN~lx{4`cl~bsu4¹suwmp`kusux{`kPmp`} (`o4}I|4m{~lclkNmpwc
wcb|4wclkcb#scl}¸#t[su]4 }Bwcl~bscl} mpw~lk³.csu]`c¼mpw~lkN~lx{4`cl~bsu4¹suwmp`kusux{`kmp`}I}Bk~bwcbsc
|4m{~lclkŧX®¥5~lx{o4wkcª4su]`c4sumpaempwu³K4
(`o4}»|4m{~lclkŪ4`clcl}4kgmpkxsxPcku|*cl~b%cl}«§
+(*%g^ - & 68 <>& :68 <>
x{`k}4cbwmes¢x~bm{kkclkgkutBkuscba=ª]`cbwcª¥¦x{wg`kusmp`~lcª*~bm{kkd,k¥¯x{w3}4cbaemp`}B4¼kcbwu¤K~lc
*¦ko`~]+m{k¬¤¡}4clxgx{w¬wcnmpËsuaPc©suwm²e~,¬mp`}~bm{kk°¢¥¯x{w¬clkk$kusuwu4.cb#s;kcbwu¤K~lc *³.c©cLËaemp˪§§§,L§
-°s£kclcbaPk©cbsuscbwXsx¤.cgm]4]`cbw¢kcbwu¤K~lc|4wx{%mp4st *¦x{w¢mkusuwu~bs©|4wux{wus°t ,sxsu]`c~bm{kkd
~bo`ksx{aPcbwknªclku|*cl~bmptW]`cb¹su]`cbwcPmpwc+aemp#t~bm{kkdN~bo`ksx{aPcbwk¢mpsu4=¹su]`c+4o6'«cbwn§
·;o4wcId=wcb|4wclkcb¡sk»kuo`~]&m:kutBkuscba #tºm µ´mpwu³.xŤ¡mp1 Kv£¶su] wmpsc=¥¦o4`~bsux{`k»mp`}
o%mpw} ¥o4`~bsux{`k}4clk~bwucl}¸º\$mp4clkWd=mp`}ºB§ z .cb`cbwmp½Åmpsux{ sxaPx{wc=~bm{kkclkPk
ksuwmp]#s¥¯x{wu¢mpw}«§¢\^]`c#o4acbwxp¥5sx{³.cb`k|4m{~lc ¢¤.clksu]`c,~lx{¡suwx{¬¡scb.cbw »kuo`~]
su]%mps^|4wx{%mp4s°te¥¦o4`~bsux{`kF
I¢mpwc3o`kcl}«§©®¥$~lx{o4wkcª
!
;!#K /
/
;! K / @%'
%0 P ;! K / §\wmp`kusux{`kF9mp`} 9 ! " `wcx{4tr]`cb»¥¦x{wu^mpw}Wmp`}¼%m{~³K¢mpw}
su]4wclk]`x{}4kmpwc]4sn§ -°´su]4kgcLq`mpaN|4cªsu]4wclku]`x{}4k}4cb|cb`}´x{4tWx{~bm{kkd+ ¡o`cbo`c)4o4s3s
~nmpIcnm{kut:*cPaem{}4ceaPx{wce.cb`cbwmp2*#t¹aPxK}B¥¦t¡4´su]`cPo%mpw} ¥o4`~bsux{`kxp¥suwmp`kusux{`k
9 gmp`}9 ! "3r\;mp4c, ,L§ \wmp`kusux{`k 9 mp`}=9 mpwcg¥¯x{wmpwuwu¤{mpk^xp¥;~bm{kkd
Tinc Pcont Tdec
Tarr1
Tarr2 Pcl2
Pcl1 Pserv1
Pserv2 Tch2
Tch1 Tserv1
Tserv2
·;o4wcd;hcb|4wclkcb¡smpsux{Pxp¥*mgs¢x~bm{kkclk5su]4wclku]`x{}K ¡o`cbo`c^su]N]#tBkuscbwclkuk5¡t+mpe Kv£¶+§
mp`}~bm{kku°e~bo`kusx{aPcbwkwclk|cl~bsu¤.cbt *¦xp¥X~lx{o4wkc+su]`cbwwmpsclk3~nmp*c)aem{}4c}4cb|*cb`}4cb#s,xp¥
mp»cLqBscbwu%mp*ksx¡~]%m{kusu~3|4wx¡~lclkk¢³.c,®g$#® '´kx{o4w~lclk ,L§\^]`c3o%mpw}4kx{su]`clkc3suwmp`kusux{`k
mpwckuo`~]¼su]%mpssu]`cbwckmkcb|%mpwmpsc4o6'*cbw¢¥¯x{wcnm{~]=~bm{kk2*¦xp¥;wclku|cl~bsu¤.c~nmp|%m{~bs°t3Cmp`}
,L§£\^]4k~nmp¼*c,cnm{kut»~]%mp4.cl}WsxemNku]%mpwcl}=4o6'*cbw¡trkcbsusu4Psu]`co%mpw}¼¥¦o4`~bsux{Wxp¥
9 gmp`}9 )sx&% '% 8ON§5vm{~lclk ( mp`} +mpwcg¥¯x{w~bm{kkdmp`}
\wmp`ksux{ hgmpsc
9 !
9 */
9
9
\;mp4ced5wmpsc¥¦o4`~bsux{`kxp¥5su]`c Kv£¶ xp¥·$o4wced
\wmp`kusux{ o%mpw}
9 % % (
% ( +8E
9 % %
!
% +()
9 % 8OA
9 % 8O
9 % %%O)
% %%O)
9 % %%O)
% %%O)
\$mp4c+ 3o%mpw}»¥¦o4`~bsux{`kxp¥5su]`c Kv£¶ xp¥5·;o4wcPd
~bm{kk°N~bo`kusx{aPcbwk¢mpsu4esxPc,kcbwu¤.cl}«§©vm{~lclk )mp`} ¤.csu]`c~bm{kkxp¥
su]`cg~bo`kusx{aPcbw¢rkcbwu¤K~lc§£®g4tex{`csx{³.cb»~nmprc 3mp`} *¦cLq4~bo`ku¤.cbt ,Lª
su]4k*cb4±~lx{#suwx{cl}[#t¹o`k4±su]`ceo%mpw} x{ suwmp`ksux{`k9 7mp`} 9 =¤¡4±su]`c
~bm{kkgsx»*c+kcbwu¤.cl}«§, ]`cbsu]`c~bo`kusx{aPcbwkkcbwu¤.cl} *suwmp`kusux{`k 9 mp`}S9 ,Lª
su]`c,`cb~bo`kusx{aPcbw~bm{kksxc)kcbwu¤.cl}¼k~]`xkcbWo`ku4Nsu]`c,|4wx{%mp4suclk
;!#K / m{k
}4c ``cl}=W\$mp4c)B§
\wmp`kusux{ |4wx{%mp4s°t
9
! % % % % P
9
/ % % % % P
\$mp4c) ©vwx{%mp4st»¥¦o4`~bsux{`kxp¥5su]`c) Kv£¶ xp¥5·;o4wcPd
-°su]`c+`x{Bµ´mpwu³.xŤ¡mpI~nm{kcª*aempwu³¡4{}4cb|*cb`}4cb#s+cLqK|*x{`cb#sumpX}Bkusuwu4o4sux{`k,xp¥Xsuwmp`k
sux{`k&9 ªP9 BªP9 mp`}=9 ,mpwcgwcb|4m{~lcl}#tNaempwu³K4{}4cb|cb`}4cb¡s.cb`cbwmp
}Bksuwu4o4sux{`kn§ ,:c±#suwxK}Bo`~lcWs°XxI|4m{~lclk ( J P´mp`} J " : x{w}4cbwrsx
aPxK}4cb©mpwuwu¤mpk:*¯m{}BaNsuscl} x{w`x{s ,,mp`}¹sx¼*cPmp4cNsx¼~lx{aN|4o4scPxkk,|4wx{%mp4suclk**cL
~nmpo`kcXvz K\$z |4wx{|*cbwust+}4x¡clk;`x{smp|4|4t+mp¡t¡aPx{wc,L§5\^]`c¢aPx¡}4cbBk5}4clk~bwu*cl})N·;o4wcB§
, su]wclku|*cl~bssxsu]`caPxK}4cbxp¥Xsu]`c|4wcb¤Kx{o`k,kuo4`kcl~bsux{ªwmpsclk,mpwwcb|4m{~lcl}#t´.cb`cbwmp
Ô
ÝÚ¯Ú L
ÙÕÖ
ÔÖ
ã
ÚÝTÖÔ L
TÖ
ã
L
ÓTÜ¯Ü L ÓTܯÜO
2L
!ÓL
!O ÝÚ¯Ú"O
ÔÖ
ã
ÚÝTÖÔO
O !ÓEO
ܯÔ!ÚO
ܯÔ!ÚL
ܯÔ!ÚL
ܯÔ!ÚL
·;o4wc) o`cbo`csu]=.cb`cbwmp$}Bkusuwu4o4sux{`k
}Bksuwu4o4sux{`knª%mp`}»Xc¡suwx¡}Bo`~lc,o%mpw}r¥o4`~bsux{`k^¥¯x{wmpwuwu¤mpkmpssu]`c #o`cbo`c=\;mp4c`ª
aPcnmp44´su]%mps+su]`cP`cb>sx{³.cb$#p~bo`kusx{aPcbw #|%m{~³.cbsPk+m{}BaNsuscl}I¥su]`ce ¡o`cbo`cPk`x{s)¥¦o4˧
\^]`clkco%mpw}¼¥¦o4`~bsux{`k~nmp=*caPx¡}B%cl}¼±x{w}4cbwsxPmp|4|4t=m{}BaNkkux{W~lx{¡suwx{˧
\¬wmp`kusux{ o%mpw}
9 " % ( %%
9 M % ( 8
9 % ( %%
9 % ( 8
\$mp4c, © ¡o4|4|4cbaPcb¡smpwut 3o%mpw}»¥¦o4`~bsux{`kxp¥5su]`c Kv£¶ xp¥·$o4wc
"!
cbmnt~nmp)c5¡suwx¡}Bo`~lcl})]`cb,su]`c£kutBkuscba aPx{4sx{wk¬su]`cksmpsc£xp¥Ksu]`c© #o`cbo`cx{4t,mps4q4cl}
x{wgwmp`}4x{a `ksmp#sk3xp¥£suaPc§\^]#o`knªsu]`c)|*x{~bt»kaPxK}B%cl}Wx{4t¼]`cb´su]`c,aPx{4sx{wu4
ke}4x{`c§ ·;o4wcW´wcb|4wclkcb#skrkuo`~]ºm #o`cbo`c§ \^]`c=kutBkuscba cb]%mn¤.clkP³.c¼ su]`c=`x{B
TÖpÙ
ã
TÚ
Ù ÓÕÔ
LÖÙ
ã
Ú
ÓL ÙÕÖ
Ô
LÖ
ã
ÝÚ¯Ú"O
ÖpÙÕÜpÔ
ÝÚ¯Ú L
Ó$O
Ü¯Ô°Ú O
ܯÔ!ÚL L
!O
ܯÔ!ÚO
ܯÔ!ÚL
·$o4wc £z ¡o`cbo`csu]W}4cbmnt
}4cbmnt.cl}¼~nm{kc34o4skuo4|4|4cbaPcb#smpwut¼~lx{`}Bsux{`kmpwc3#suwxK}Bo`~lcl}¼x{»su]`c3o%mpw}r¥o4`~bsux{`kxp¥
suwmp`ksux{`k 9mp`} 9 ! "]4~]=wcb|4wclkcb#sgsu]`ckus~]`clk¼su]`c,kcbwu¤K~lc|x{~bt.§\^]`clkc
s°Xx+suwmp`kusux{`kmpwc3cb%mp4cl}¼x{4tP¥su]`c3aPx{4sx{wu4N]%m{k$y!o`kusXclcb»}4x{`cªB˧Ûc§ªK¥su]`cbwc3k
m+sx{³.cbW=|4m{~lc B§5\^]`cbª%aNaPcl}Bmpsc,suwmp`kusux{`kF9mp`} 9 ! "~nmp `wc* ¥
su]`c^x{su]`cbw~lx{`}Bsux{`kx{su]`c¢o%mpw})¥¦o4`~bsux{`k£mpwcX¥ o4`cl} ,L§5¶3cLqKsnªpsuwmp`kusux{ 9
`wclk)kx¼su]%mps,su]`cPktKkuscba^mpsk¥¯x{wmp`x{su]`cbw)|*cbwuxK}¹xp¥^suaPcPsx¼aPx{4sx{w,su]`cP ¡o`cbo`c§ez
]4]`cbw|4wux{wus°tWk3¤.cbsxsuwmp`ksux{`k:9mp`}G9 ! "su]wclku|cl~bs3sx=9: ¼sx
cb`ko4wc,su]%mps3su]`c)kcbwu¤K~lc,aPxK}B%~nmpsux{kgmp|4|4cl}±cL¥¯x{wc,|4m{~lc N*cl~lx{aPclkg}Bc
mp#mp§©\^]`c`cb1o%mpw}»¥¦o4`~bsux{`kgmpwc¤.cbWW\$mp4c B§¢®gsu]`cbw|%mpwmpaPcbscbwk3mpwc)}4c ``cl}
³.cP:su]`cPµmpwu³.xn¤Kmp `x{B}4cbmlt.cl}¸~nm{kcª¬4o4s,Xc~nmp[mpkx¼.cb`cbwmp½ncsu]`cP~nm{kcP]`cbwc
¡scbw°mpwuwu¤{mpkmp`}#px{wkcbwu¤K~lclk}4xN`x{s^¥¯x{xn mpWcLqK|*x{`cb#sump;}Bkusuwu4o4sux{§
,:c~lx{`ku}4cbw©]`cbwc3m (`o4}e ¡o`cbo`c}Bwu¤.cbe¡tB [kx{o4w~lclkŪ.4o4sXx{su]`cbw¢}Bwu¤¡4)|4wx¡~lclkkclk
~nmp[cPo`kcl}[m{k)Xcb˧33k~bwcbscrmpwuwu¤{mpkmp`} kcbwu¤K~lclkmpwcmpwcb#mpscl}[Im=~lx{¡su#o`x{o`k
(%xÅ,§5\^]4k5k5m.xKx¡}mp|4|4wxlqBaempsux{exp¥z\µsuwm²e~¢¥¦x{w;`kusmp`~lc§5\^]`c^· Kv©¶ aPxK}4cb4
su]4k+kutBkuscba7k}4clk~bwu*cl}[I·;o4wc±su]Io%mpw}[¥o4`~bsux{`kNmp`} (`o4} wmpsce¥o4`~bsux{`k
\¬wmp`kusux{ o%mpw}
9 % ( % (
% 8BE+vaPx{4sx{w+d
9 " % ( %
!
% ()
% %%0
9 % 8OC
9 % 8O
9 % %% )
% %% )
9 % %% )
% %% )
\$mp4c 3o%mpw}»¥¦o4`~bsux{`kxp¥5su]`c Kv£¶ xp¥5·;o4wc)
}4clk~bwucl}wclku|*cl~bsu¤.cbtPr\;mp4clk)mp`}:3K§\^]`c3mpwuwu¤mp (`o4}wmpsclkmpwcgaem{}4cg}4cb|*cb`}4cb#s
xp¥;su]`c3#o4a)*cbwxp¥ BNkx{o4w~lclk¥¦x{wcnm{~]=~bm{kkn§\^]`ckcbwu¤¡~lc (`o4}»wmpsclkmpwckuo`~]¼su]%mps^su]`c
|4wx{|*x{wusux{ ,Imp`} :1S, xp¥¢kcbwu¤.cl}¹~bm{kkudmp`}¹~bm{kk°:(`o4}¹}4cb|cb`}¹x{¹su]`c]¡tKkscbwcbsu~
~lx{¡suwx{^¤{mpwump4c³.cPIsu]`c}Bk~bwcbsc~nm{kc§W·$o4}[wmpsclkmpwcx{|4suaN½ncl}I[ko`~] m=^mlt
su]%mps¥¢su]`c4o6'«cbwkcbaN|4st±¥¦x{wm¤.cb:~bm{kknªsu]`cNx{su]`cbw~bm{kkkkcbwu¤.cl}`kuscnm{}«§ ,:c
ÔL O
TÖ!O
)O
ܦ×Ü ã O )O
LÖO
L
ÙÕÖ
Ô
LÖ
ã
ܦ×Ü ã L
ÝÚ¯Ú L
ÝÚ¯Ú"O ÔO
TÖL
!L
!L LÖL
·;o4wc \¢xe~bm{kkclk;(`o4}= #o`cbo`c
]%mn¤.cPaem{}4csu]`cPsu]4wclku]`x{}4k+}4cb|*cb`}4cb#sxp¥^su]`c~bm{kkd (`o4} cb¤.cb˪;4o4s)Xc~nmp aemp³.cs
}4cb|*cb`}4cb#s3xp¥;su]`c~bm{kk°(`o4}¼cb¤.cb¬x{wxp¥£m+`cnmpw~lx{a4%mpsux{´xp¥5x{su]´m{kXcb˧
\¬wmp`kusux{ o%mpw}
9 % (
% &8E
9 5+( 9 K, 5
9 " % :
!
% ()
9 5+8 9 ,5
\$mp4c+ 3o%mpw}»¥¦o4`~bsux{`kxp¥5su]`c Kv£¶ xp¥5·;o4wc
!#"
$&%'(*) +,).-0/21(34)5)6798:<;=:?>A@!BC798C:<;D:?>FEHGJILK*MON5PQRA+C)(-S/21(34)T R=U,V("!"H)6798C:<;=:<>A@WBC798:<;=:?>FEX,ILK
$&%'(Y +ZY'-0/21(3CY[)6798:<;=:?>A@!BC798C:<;D:?>FEHGJILK*MON5PQRA+#Y-S/21(3CYT R=U,V("!"H)6798C:<;=:<>A@WBC798:<;=:?>FEX,ILK
$&\']^C) _^`-S/2aH1(3Lb!"cde-0/gfDhfDbi)Ti-0/gfDhfDb!Ygjlk
NmPQC`+
@
-S/21(34)T!_^R`-S/2aH1(3Lb!""cde-S/gf=hfDbi)&nokpZ-S/gf=hfDb!YSjqk
_rsN5PQA+
E
-S/21(3CYT_tW)ur^?-0/2a=1(3Lb!"!"!"cde-0/gfDhfDbi)jqkpZ-0/gfDhfDb!Y2nok
NmPQC`+
@
-S/21(34)T!_rsNmPQ`+
E
-S/21(3CYT_tW)ur^`-S/2aH1(3Lb!""!""cdv-S/gfDhfDbi)T-S/gfDhfDb!Ynwk
$&\']^#Y _tW)ur^`-S/2aH1(3Lb!""xdt-S/gfDhf=b!YT-S/gfDhf=bi)yjzk
NmPQC`+ E -S/21(3CYT!_t!)ur[^R`-S/2aH1(3Lb!""!"xdt-S/gfDhfDb!Yn{kpZ-S/gfDhfDbi)yjlk
_rsN5PQA+ @ -S/21(34)T_^?-0/2a=1(3Lb!"!"cdt-S/gfDhf=b!YSjlkpZ-S/gfDhf=bi)&n{k
NmPQC`+ E -S/21(3CYT!_rsNmPQ`+ @ -S/21(34)T_^`-S/2aH1(3Lb!""!"cdt-S/gfDhfDb!YT-S/gfDhfDbi)un{k
\;mp4c 3 ·;o4}¼wmpsc¥¦o4`~bsux{`kxp¥5su]`c) Kv£¶ xp¥·$o4wc,
| }
~ &
\^]`ckx{o4sux{¼aPcbsu]`xK}4k¢c,mpwcg.x{4Nsx+o`kcmpwcsu]`xkc3aN|4cbaPcb¡scl}=W Kv£¶3v /4ª*db1ª`m
|%m{~³{mp.c)}4cb¤.cbx{|4|cl}´mps go4³.c 4¤.cbwkus°t.ªmp`}=mpwcsu]`c¥¦x{xÅ4`§
µ´mpwu³.xŤ¡mpe Kv£¶3k$xp¥`su]`cX|4wcb¤Kx{o`k;kcl~bsux{`k5mpwc¢kx{¤.cl}mp%mpt¡su~nmpt¡Ë#o4aPcbwu~nmpt.§©\^]`c
wcnm{~]%mp4st±wmp|4]Wk `wkus.cb`cbwmpscl}±¥ wx{a su]`c+ Kv£¶ mp`}±su]`cb±~lx{¡¤.cbwuscl}±sxmPµmpwu³.xn¤
~]%mp *¦x{waPx{wccLq4m{~bs°trsxPmPµ´mpwu³.xŤrwcb^mpw}=aPxK}4cb ,¢]4~]±kkx{¤.cl}¼¡o4aPcbwu~nmpt.§X·%x{w
kscnm{}Bt#kusmpsc^cb¤mpo%mpsux{ªXc¢4~]`xKxkc ¡scnm{}Bt#! ¡smpsc 4®3h *Ë ¡o`~l~lclkku¤.c®g¤.cbwuwcbmq4mpsux{
/Õ1,Lª.su]`c^¥¯m{ksclkus5aPcbsu]`x¡}«ª#4o4sX ¡scnm{}Bt#! ¡smpsc ,mpo`kk! Kcb}4cb /Õ1ª#mp`}e ¡scnm{}Bt¡! ¡smpscv;xn^
cbwaPcbsu]`xK}./Õ21mpwcgmpkx)ml¤mp4cr Kv©¶gvImp`}empwco`kcl}]`cbr 4 4®3h }4xKclk`x{s©~lx{#¤.cbwu.c§
·%x{wsuwmp`kucb¡skusmpsc¼kx{o4sux{¸xp¥su]`c \µ ª;kusmp`}`mpw}Io44¥¦x{wuaN½Åmpsux{ x{w+o44¥¦x{wuaN½Åm
sux{¹o`k4=su]`cN·`xlq mp`} t¡4¹aPcbsu]`xK}´¥¦x{w,~lx{aN|4o4su4±su]`cPv;x{kkx{:|4wx{%mp4suclk~nmp
*co`kcl}Ǥ
®g´su]`cx{su]`cbw]%mp`}«ª*`x{Bµmpwu³.xn¤KmpI Kv£¶3k,mp`}· Kv©¶gk,mpwckx{¤.cl}´#t´kua)o4mpsux{§
¡scnm{}Bt¡kusmpsckuao4mpsux{P4*c^|cbw¥¯x{wuaPcl}o`ku4,kuao4mpsux{Psu]N%mps~]`clkXx{w;wcb.cb`cbwm
su¤.c^kuao4mpsux{./;1*su]4k5m{kus5~nm{kcªx{o4w© Kv£¶ `clcl}4k5sx3*c©+su]`c^~bm{kk5xp¥µ´h3 Kv£¶3kC/Õ1,L§
\¬wmp`kucb#ska)o4mpsux{=~nmp»cg|*cbw¥¦x{wuaPcl}r#t~bwuo`}4cg`}4cb|*cb`}4cb#swcb|4~nmpsux{`kn§£¨3xnXcb¤.cbwnª