• Aucun résultat trouvé

Hierarchical token based mutual exclusion algorithms

N/A
N/A
Protected

Academic year: 2023

Partager "Hierarchical token based mutual exclusion algorithms"

Copied!
24
0
0

Texte intégral

(1)

HAL Id: inria-00071411

https://hal.inria.fr/inria-00071411

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,

Hierarchical token based mutual exclusion algorithms

Marin Bertier, Luciana Arantes, Pierre Sens

To cite this version:

Marin Bertier, Luciana Arantes, Pierre Sens. Hierarchical token based mutual exclusion algorithms.

[Research Report] RR-5177, INRIA. 2004. �inria-00071411�

(2)

ISRN INRIA/RR--5177--FR+ENG

a p p o r t

d e r e c h e r c h e

THÈME 1

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Hierarchical token based mutual exclusion algorithms

Marin Bertier — Luciana Arantes, Pierre Sens

N° 5177

Avril 2004

(3)
(4)

Unité de recherche INRIA Rocquencourt

,.-0/214365879/:;1479/;<2=>@?AB91C-03D-"E/2-03F:;7HG9>@<I=8J 1479/2/K7ML793G<I=

NOQPRTSTUWVYXZK[\SK]_^a`!S&bc[\da[ebfPRTSK[

g@h\i_jeS&bcXk$lnmco

Xc]qprp0i_h\btsaS h\S2u)OrSh)u)OrSwv0x@yaU;zHz{V|m~}hf€‚~ƒ_„_„_…V|ƒ_„†p‡]qˆ_S2[

‰!Š‹KŒIŽr_Œ_ ‘ ^abf^Q]qS&`ru&’^Q[\€‚iHv“€’[†]{”Q]_[\€•uT”r‚iau)–—iq˜tsa€•[ebfh\€’”r^abfSKs[\dvQu)Orhfi_vr€’™K]qb\€’i_v—]_‚ˆHi_hf€šbfOrR›[œ



vQSiq˜b\OQS†u)OQ]_‚’SvrˆHS €‚v{OQ€‚ˆHOr‚d{sa€•[žb\hf€‚”r^rb\SKs*SKv}9€’hfi_vrRTSv9b)[Ÿ ’€‚–HSp0SSh\¡Cb\iq¡¢p0SShci_hWlWhf€•s{u&i_vr£Qˆ_^a¡

h)]Ibf€‚iHvQ[)¤€’[¥b\i†prhfiI}9€•saSt[fu]_’]_”r‚S¦[ždvQu)Orhfi_vQ€‚™2]Ib\€’i_v‡[bf]_–9€’vrˆ€’v9b\i8]_uui_^rv9b@bfOrSWOr€‚SKhf]_hfu)OQ€’uK]qavrSbe§iHh\–

bfi_p0i_’i_ˆHd_œNOr€•[tpQ]_p‡SKhcprhfi_p0iH[\SK[OQ€‚SKhf]_hfu)Or€•u]_FR¨^abf^Q]qS&`ru‚^Q[\€’i_v{]q’ˆ_iHh\€‚b\OrR›[KœNOrSK[\S¨]q’ˆ_iHh\€‚b\OQRT[

]_h\S¨S&`b\SKvQ[ž€’i_v‡[tiq˜¥b\OrS8©c]q€’RT€š¡ªNh\SKOrSC«[tb\iH–_Sv—]q’ˆ_i_hf€‚b\OrR*¬0h\S2sa^Qu&€’vrˆ›bfOrSTu&iH[žb¦i_˜@’]qb\SKvQu&d{]qv‡s*b\OrS

v^rR†”‡SKh¦i_˜@RTSK[f[\]_ˆ_SK[tS&`ru)OQ]qvQˆ_SK[c”‡Sbe§SKSv{˜­]_hcOri9[eb)[œW®¯S¨prhfi_p0iH[\S b\OQh\SKS¨R›]q€’v°S&`bfSvQ[\€‚iHvQ[†±ŸeU2¤

OQ€‚SKhf]_hfu)Or€•u]_prh\i;`ad9¡¢”Q]_[\SKs¯]qprpQh\i9]_u)O²¬¥ŸCƒ_¤ ]_ˆ_ˆHh\SKˆH]Ibf€‚iHvMi_˜$hfSK³9^rS2[eb)[¬]qvQs´Ÿ4µH¤Wbfi_–_SKv“prh\SKSRTpabf€‚iHv

”d!u‚i9[žSKhOriH[žbf[Kœ

®¯Sui_RTpQ]_h\S2sMbfOrS!p0Sh\˜ i_hfR›]qvQuS%iq˜bfOrSK[\S]_‚ˆHi_hf€šbfOrR›[ i_v]_vSR†^r•]Ib\S2s¶lWhf€’s¯bfSK[žb\”0SKsFœ¯®—S

[žb\^‡sad·b\OrS—€‚RTpQ]Hu¸bi_˜SK]Hu)O¹iq˜nb\OrS—S&`b\SKvQ[\€‚iHvQ[¬¦[žOriI§€’vrˆ“bfOQ]Ibb\OrS¯u&i_R†”r€’vQ]Ibf€‚iHv¹iq˜ b\OQSRºu]_v

ˆHh\S2]Ibf‚d›€’RTprh\iI}HS¦p0Sh\˜ i_hfR›]qvQuSK[$iq˜b\OQS i_hf€‚ˆH€‚vQ]_F]q’ˆ_i_hf€‚b\OrR*œ

»{¼9½¿¾fÀ¨Á I‹_ S`ap‡SKh\€’SRTSv9b2¬rR¨^abf^Q]qFS`ru&’^Q[ž€’i_v~¬b\i_–HSv²¬aOQ€‚SKhf]_hfu)Or€•u]_4¬ˆHh\€•s

Ã@ÄaÅ)ÆqǸÈCÅfÉ4ǸÊËÈ4Ì¥Í9ÎÏÑÐ2҂ǸȭÓtÅfÉCÊËÔÕ;Ì@Í;Ì@ÖrÅ)È4ÊË×~Ø2Ù_ÚFÛÜÝ

Þ

Ï ÛܲÏÑß

(5)

‹  o¥«S`au‚^‡[ž€’i_vR¨^abf^rS’‚SnS2[eb^rv”r‚iauWsaSn”Q]_[\SnsaS¦C«]q’ˆ_i_hf€‚b\OrRT€•³H^QSWsaSn[\d9v‡u)Orh\iHvr€•[\]qb\€’i_v

sr€’[žb\hf€‚”Q^rZ_œtv°saS2[tsaZ&£0[tsr]qv‡[‚S2[Sv}€’h\iHvrvrSRTSKvHb)[$˜ i_h\b\SKR8SKv9bcsa€’[žb\hf€’”r^rZK[¨Ÿ­u&iHRTR8S ’SpQ]_€‚h\¡I¡¢pQ]q€’h

iH^›‚S2[¥ui_va£QˆH^rh)]Ib\€’i_v‡[@saStˆHh\€’‚’S2¤DSK[žbsaSt˜ iH^rhfvr€‚h$saSK[[ždvQu)OQh\iHvr€’[f]Ibf€‚iHvQ[D[fu]q•]q”Q‚SbfSvQ]_vHb$u&i_RTpabfS¦saS

•]bfi_p0i_’i_ˆ_€’SDOr€’Zh)]qh)u)Or€•³H^QS@sa^hfZK[\SK]q^~œS@h)]qprp0i_h\b²prhfi_p0iH[\S¥saSK[]q’ˆ_iHh\€‚b\OrRTS2[²sF«S&`ru&’^Q[\€‚iHv R¨^abf^rS’‚S

OQ€‚ZKhf]_hfu)Or€•³9^rSK[KœS2[]q’ˆ_i_hf€‚b\OrRTSK[[žiHv9bsaS2[$S&`b\SKvQ[ž€’i_v‡[saSWC«]_‚ˆHi_hf€šbfOrRTScjeS&b\iHvsaS ©¦]q€’R8€‚¡ªN~hfSOrSK4¬

hfZKsr^r€’[f]qv9b ’STuiab¨srS›’]•]Ib\SKvQu&STSb¨sa^“vri_R†”rh\S›saS›RTS2[\[f]qˆHSK[WZKu)OQ]_vrˆ_Z2[WSv9b\hfST‚S2[[ž€‚b\S2[ sa€•[eb)]qv9bKœ

©ci_^Q[pQh\iHp‡i9[žiHvQ[²bfh\iH€’[S`9bfSvQ[\€’i_vQ[prhf€’vQu&€’pQ]q’SK[K±¥ŸžU2¤]qprpQh\iau)OrS$”Q]_[\ZS[\^rhDsaSK[pQh\i;`ada[Or€‚ZKhf]_hfu)OQ€’³9^rSH¬

ŸCƒ_¤C«]_ˆ_hfZˆH]qb\€’i_vsaSK[saSKR›]qvQsaS2[¬aSb¨Ÿ­µ9¤$’]8prhfZSKR8prb\€’i_vpQ]qhtsaS2[t[\€šbfSK[’iuK]q^a`Fœ

©ci_^Q[W];}_iHvQ[tu&iHRTpQ]qhfZ 4«S&`aZ2u&^abf€‚iHvMsaS†uSK[¦]q’ˆ_i_hf€‚b\OrRTSK[c[ž^rhW^rv°”‡]qvQus²«S2[\[f]q€ZR¨^Q‚Z8saS¨ˆHh\€’‚’S_œ

©ci_^Q[$Zb\^Qsa€’i_v‡[C«€‚RTpQ]Hu¸bsaS u)OQ]_u^rvrS¦srSK[$S&`b\SKvQ[\€‚iHvQ[¬RTi_v9bfhf]_vHb³9^rSn‚SK^rh$ui_R†”r€‚v‡]q€•[žiHv!]qRTZ’€’i_hfS

ui_vQ[\€•saZh)]q”r’SRTSKvHb’SK[p0Sh\˜ i_hfRT]_vQu&S2[saS 4«]q’ˆ_iHh\€‚b\OQR8SWi_hf€’ˆ_€’vQ]qCœ

Á Œ2‹ ¾  ‹ S&`ap0Zhf€‚SKRTSv9bf]qb\€’i_v²¬S&`ru‚^Q[\€’i_vR¨^abf^rS’‚SH¬IjeS&bfi_v²¬QOr€‚SKhf]_hfu)OQ€’³9^rSH¬9ˆHh\€’’‚S

(6)

% &

†~›¥&

']H[ž€•u›u&•]_[f[ž€•u]_@]q’ˆ_iHh\€‚b\OrR›[ ]_h\S%ui_RTRTi_vr’dM^Q[\SKs“”d¯sa€’[žb\hf€’”r^ab\S2s]qpQpr‚€•u]qb\€’i_vQ[Kœ(ciI§SK}_SKhK¬²§€‚b\O

bfOrSSKR8SKh\ˆHSvQuS iq˜@p0SSKhž¡Cb\i_¡Cp0SSKht]qvQs°lWhf€’sMu&i_RTpr^rb\€’vrˆQ¬Qb\OrS2[žS¨]_prpr’€’uK]Ibf€‚iHvQ[c[\prhfSK]_siI}HSht]›•]qhfˆ_SKh

v^rR†”‡SKhtiq˜DvriasaS2[œ*)r^rh\b\OQShfR8iHh\SH¬r€’v°[ž^Qu)O*SKv9}€’h\iHvrRTSv9bf[t’]qb\Sv‡u&d!ˆ9]qpQ[t”‡Sbe§SKSv*OriH[žbf[t€‚v9b\SKhfui_va¡

vQSKu¸b)[]qhfS¦}HShfd%€’R8p0i_h\bf]_v9bKœDNOrShfS&˜ iHh\SH¬asa€’[žb\hf€’”r^ab\S2s*]q’ˆ_i_hf€‚b\OrR›[[žOQi_^r•s!”0S ]_sr]_pab\S2s%bfiTbf]_–_SW€‚v9b\i

]Huui_^rv9b@bfOriH[\Scu)OQ]_hf]Hu¸b\SKh\€•[žb\€•u[Kœm6§$S’‚¡C–vriI§vTS&`r]_R8pQ‚S¦iq˜²[ž^‡u)O!]q’ˆ_iHh\€‚b\OrR›[D€•[R¨^abf^Q]q0S&`ru&’^Q[\€‚iHv

]_‚ˆHi_hf€šbfOrR*¬§Or€’u)O*SKvQ[ž^Qh\S2[S`ru&’^Q[ž€’}_S ]Huu&S2[\[bfi%]8[\OQ]_h\S2s%hfSK[\i_^rh)u&SHœ

‘ ]_vdM]q’ˆ_iHh\€‚b\OrR›[WOQ];}HS8”0SSKv“prh\iHp‡i9[žS2s{bfi*[\i_’}_S8bfOrS›prhfi_”r’SR i_˜R†^ab\^Q]_@S&`ru‚^Q[\€’i_vM€’v"sa€•[e¡

bfh\€’”r^abfSKs{[\da[ebfSR›[œNOrSKduK]qv{”Q]H[ž€•u]_‚’d!”0S¨sa€’}€’srSKs{€’v9b\i›be§$i›ˆ_hfi_^rp‡[±,+- #$. 0/12 Ÿ4o~]qR8¡

p0i_h\b43‚U5C¬HX€’uK]qh\bž¡ªmtˆHhf];§]q•]63˃25¢¬ $]qhf}I]q’Oriq¡ªXi_^‡u]q€’hfi_73µ 5¢¬ ‘ ]_S–I];§]83…95 ¤]qvQs:;<0/1 nŸ>=^r™K^r–€š¡

? ]_™K]_R8€@3Ëy25¢¬$Xc];d9RTiHvQsA3B25¢¬$©¦]q€’RT€š¡ªN~hfSOQS63z5¢¬$©cS€’’[\Sva¡ ‘ €’™^rvQiC3D 5¢¬ OQ]qvrˆ‡¬*=€’vrˆHOQ]qt]_vQs´o²€’^

3E25 ¤¸œ›NOrS8£Qh)[eb ˆHh\iH^rpMi_˜$]q’ˆ_iHh\€‚b\OQRT[n]_h\S8”Q]_[\SKsMi_v—b\OrSTprhf€’vQu&€’pr’S8i_˜$ui_vQ[\SvQ[\^Q[W”0S&be§$SSv¯Ori9[eb)[¬

€CœS_œ’¬²]!Ori9[eb ˆHS&bf[W€’v9b\i*]uh\€‚b\€•u]_[\SKu&b\€’i_v—i_vr’d°]I˜ÑbfShnOQ];}€‚vQˆ!hfSKu&SK€‚}HSKsMp‡SKh\RT€•[\[\€‚iHv{˜ hfi_R ]q’DiqbfOrSh

OQiH[žbf[KœAFªv´b\OQSM[žS2u&iHvrˆ“ˆ_hfi_^rp·iq˜]q’ˆ_iHh\€‚b\OQRT[K¬]"[žda[žb\SR8¡¢§€’srS{^rvr€•³H^QS*b\i_–HSv´€•[![\OQ]qhfSKs·]qRTi_vQˆ

OQiH[žbf[!]_vQs´bfOrSMp0iH[f[žS2[\[\€’i_v¹iq˜€‚bˆH€‚}HSK[]Ori9[eb%bfOrS¯S&`ru&’^Q[\€‚}HS°h\€’ˆ_O9b%bfi¶SKvHbfSh€‚v9bfi"b\OrS“u&hf€‚b\€•u]q

[\SKu&b\€’i_v²œngShfRT€’[f[\€‚iHva¡C”‡]_[\SKs{]q’ˆ_iHh\€‚b\OQRT[cˆ_SKvrSh)]q’‚d{[\^HG¿Sh¦˜ h\iHR ‚€’RT€šbfSKs¯[\uK]q•]q”r€’‚€‚bed_œIFªv—ui_v9b\h)]_[žbK¬

bfi_–HSva¡¢”Q]_[\SKs]q’ˆ_iHh\€‚b\OQRT[O‡];}_S ]qv{];}_SKhf]_ˆ_SW‚iI§ RTSK[f[\]_ˆ_S u&i9[ebc]_vQs^Q[ž^‡]q’‚dh\S2[ž^r‚bc€’v*‚iHˆH]qhf€‚b\OrRT€•u

RTS2[\[f]qˆHSWui_RTpr’S&`a€šbed  Ÿ ’i_ˆ‡Ÿ4©¦¤\¤¥§€‚b\O{hfSˆ9]qh)sTb\iTbfOrS v^rR¨”0Shi_˜Ori9[eb)[œ

NOrS—R›]Ijei_hf€‚bed¶iq˜  Ÿ­‚iHˆ‡Ÿ4©¦¤ž¤›b\iH–_Svr¡C”Q]H[žS2s´]q’ˆ_i_hf€‚b\OrR›[%]_h\S*bfh\SKS&¡¢”Q]_[\SKsF¬€CœS_œ’¬c]"’i_ˆ_€•u]_b\hfSS

[žb\hf^Qu&b\^rhfS{S&`aprhfSK[f[žS2[Tb\OQSMsa€JG0SKh\SKvHbb\iH–_Sv´hfSK³9^rS2[eb)[%]qvQs·bfi_–HSv¹prhfi_pQ]_ˆH]qb\€’i_v·pQ]IbfOQ[!]qb]"ˆ_€’}_SKv

bf€‚RTSHœ¶Xt];dRTi_vQsF«]q’ˆ_iHh\€‚b\OQRK3B 5i_hfˆH]_vr€’™SK[b\OrS*Ori9[eb)[8€‚v·]—[žbf]qb\€•u!’i_ˆH€’uK]qb\hfSS*[ebfh\^Qu&b\^rhfS_œNOQ€’[

bfh\SKS¦hfSR›]_€‚vQ[$^rv‡u)OQ]qvrˆHSKsF¬”r^rb$bfOrS sa€’h\S2u¸b\€’i_viq˜€šb)[S2saˆ_S2[u]qvu)OQ]qvQˆ_SnsadvQ]qRT€•u]q’’d%]_[b\OrSWbfi_–_SKv

pQh\iHpQ]qˆ9]Ib\S2[œ iHvQ[\SK³9^rSv9bf‚dH¬bfOrSsr€‚hfSKu&b\€’i_vQ[¨iq˜b\OQS!SKsrˆ_SK[8]q’§];d[p‡iH€‚v9b¨bfi°bfOrS!p0iH[f[ž€’”r’S%bfi_–_SKv

OQi_•saSh2œ—©cS€’’[\Sv¶]_vQs ‘ €’™^QvriL3D25S&`b\SKvQsaS2s“b\Or€•[8]q’ˆ_i_hf€‚b\OrR ”d¯p‡]_[f[ž€’vrˆ{bfOrS!bfi_–HSvsa€’h\S2u¸bf‚d¯b\i

bfOrS°hfSK³9^rS2[ebf€‚vrˆ"OQiH[žb!€‚v‡[ebfSK]_s´i_˜nb\Orhfi_^rˆHO´€‚v9b\SKh\RTS2sa€’]qb\S°OQiH[žbf[Kœ.©¦]q€’R8€‚¡ªN~hfSOrSK4«[%]_‚ˆHi_hf€šbfOrRM3z5

R›]_€‚v9bf]_€‚v‡[]8srd9v‡]qRT€’uW’i_ˆH€’uK]q¿b\hfSSH¬r[ž^‡u)ObfOQ]IbbfOrS hfi9i_b$i_˜bfOrSnb\hfSS €•[]q’§];d[bfOrS ’]H[ebOri9[ebbfOQ]Ib

§€’’²ˆ_Sbb\OrS bfi_–HSv*]qRTi_vrˆ8bfOrS¨u&^Qh\hfSv9bh\S2³9^rSK[žb\€’vrˆTi_vrS2[œ OQ]qvrˆN=€’vrˆHOQ]q~]_vQs*o²€’^O3E95~€‚RTprhfiI}_S2s

bfOr€•[c]q’ˆ_iHh\€‚b\OQR¬0]q€’RT€‚vrˆ%]qbchfSKsa^Qu€‚vQˆ›b\OrS¨v9^QR¨”0Shci_˜DR8S2[\[f]qˆHSK[$bfi›£QvQs*bfOrS•]_[žbchfSK³9^rSK[žb\€’vrˆ›Ori9[eb

€’vbfOrS‚iHˆ_€•u]qb\hfSSHœ ‘ ^rS’’ShP3‚U2„25t]q•[ži—prh\iHp‡i9[žS2s]qv¶S&`b\SKvQ[ž€’i_v¶b\i¯©c]q€’RT€š¡ªNh\SKOrSC«[8]q’ˆ_iHh\€‚b\OQR¬

€’v9b\hfiasa^Qu&€’vrˆ›bfOrS†ui_vQuSpab¦iq˜@prhf€‚iHh\€‚bed!€’v°€‚bKœcm b\iH–_Sv{hfSK³9^rS2[eb¦€’[¦]_[f[žiau&€•]IbfSKs*§€‚b\OM]%prh\€’i_hf€‚bed]qv‡s

bfOrS]q’ˆ_iHh\€‚b\OQR £Qhf[žbt[\]qb\€•[e£‡SK[$b\OQS h\S2³H^QSK[žbf[§€‚b\O*Or€’ˆ_OrSKhprh\€’i_hf€‚bed_œ

mcšbfOri_^rˆHO]q’Db\OQiH[\S  Ÿ ’i_ˆ‡Ÿ4©¦¤\¤Wb\iH–_Svr¡C”Q]H[žS2s—]_‚ˆHi_hf€šbfOrR›[ ]_u)Or€’S}HST”‡Sbžb\SKh¨p0Sh\˜ i_hfR›]qvQuS8§€‚b\O

hfSK[\p0SKu¸bcb\i›bfOrS†];}HSh)]qˆ_SWv^rR¨”0Sh¦iq˜DRTSK[f[\]_ˆ_S2[S&`ru)OQ]_vrˆ_S2sp0ShWu&hf€šbf€’uK]q[žS2u¸b\€’i_v*SKvHbfh\d§OrSKvMu&iHR†¡

p‡]qhfSKs bfi iqbfOrShDR†^ab\^Q]_aS&`ru&’^Q[\€‚iHv8]_‚ˆHi_hf€šbfOrR›[¬;bfOrSd8sainvriqb@ui_vQ[\€’srShD•]Ib\SKvQu&d†sa€QG¿ShfSv‡u&SK[€’v8OriH[žbf[

€’v9b\SKhfui_vrvrS2u¸b)[œ ®¯STprh\iHp‡i9[žS8sa€•[ebfh\€’”r^abfSKsMb\i_–HSva¡¢”Q]H[žS2s*R¨^abf^Q]qDS`au‚^‡[ž€’i_v¯]q’ˆ_i_hf€‚b\OrR›[K¬‡”Q]H[žS2s°iHv

©¦]q€’RT€š¡ªN~hfSOQSC«[]_‚ˆHi_hf€šbfOrR*¬r§Or€•u)Ob)]q–HSK[€’vHbfi%]_uKu&i_^QvHbtvQS&be§$i_hf–Tb\i_p0i_’i_ˆHd_¬Q[\p0SKu&€•]q’’d%b\OQS ’]qb\Sv‡u&d

ˆ9]qp*”0S&be§$SSv{’iau]_~]qvQs*hfSRTi_b\Su&’^Q[žb\SKhf[i_˜DRT]Hu)Or€’vrSK[Kœ  ^Qhc]q’ˆ_iHh\€‚b\OrR›[hfSKsr^Qu&SnbfOrS¨v^rR†”‡SKhf[i_˜

€’v9b\SKhž¡ªu&’^Q[žb\ShRTSK[f[f]qˆ_S2[]qvQs†ˆ_€’}_S]WOr€‚ˆHOrShDpQh\€’i_hf€šbednbfin‚iau]_aR¨^abf^Q]qQS&`ru&’^Q[\€‚iHv¨hfSK³9^rSK[žbf[Kœ~®¯SOQ];}HS

u)OQiH[\Sv8b\i¨]Hsr]qprb¥©c]q€’RT€š¡ªNh\SKOrSC«[]q’ˆ_iHh\€‚b\OrR ”‡S2u]q^‡[žSt€‚b¥^Q[\SK[]u)OQ]_vrˆ_S2]q”r’S‚iHˆ_€•u]qrb\hfSSc[žb\hf^Qu¸bf^rhfS

bfi u&i_v9bfh\iHHR†^ab\^Q]_aS&`ru&’^Q[\€‚iHv¨hfSK³9^rS2[eb)[œNOr€’[Dsrd9v‡]qRT€’u$prhfi_p0Sh\bedniq˜‡b\OrS$b\hfSS€•[D[ebfh\iHvrˆ_’dnS&`apr’i_€‚b\S2s

€’v*i_^rh[\i_’^ab\€’i_v€’viHhfsrSh$b\iTbfi_’Sh)]Ib\SWOr€’ˆ_OrSKh’]qb\SKvQu&€’SK[Kœ

(7)

F¢bT€’[†§$i_h\b\O"hfSRT€‚v‡sa€‚vQˆ°b\O‡]Ib›[žiHR8S]q^abfOri_h)[N3’U_U 563’U2ƒ5OQ];}HS%prhfi_p0iH[\SKs“R¨^rb\^Q]_S`au‚^‡[ž€’i_v¶]_š¡

ˆHi_hf€šbfOrR›[W§OrShfS†vQisrSK[ ]qhfS_¬¿˜ iHh[žiHRTS†hfSK]H[žiHv²¬FˆH]qb\OrSKh\S2s°€’vHbfi*ˆ_hfi_^rpQ[Kœ¨NOrSKd°”Q]H[ž€•u]_‚’d{prhfi_p0iH[\S

Od”rhf€’s{]_prprhfiH]Hu)OrSK[§OrSKh\Sb\OrS8]q’ˆ_i_hf€‚b\OrR ˜ i_hc€’v9b\h)]I¡¢ˆ_hfi_^rp*hfSK³9^rS2[eb)[€’[Wsa€JG0SKh\SKv9bt˜ h\iHR b\OrS†€‚v9b\SKhž¡

ˆHh\iH^rpi_vrSHœ,(tiI§$S}_SKhK¬bfOrSdsaiTvriqbcui_vQ[\€•saShtsa€JG¿ShfSvQuS €‚v*vrSbe§iHh\–%•]IbfSvQud!”0S&be§$SSKvOQiH[žbf[]_[]

˜­]Hu¸bfi_h˜ i_hDˆHh\iH^rpr€’vrˆnOriH[žbf[Kœ FªvP3’UKµ 5C¬_b\OrSt]_^ab\OriHhf[pQh\iHp‡i9[žS$b\i]Hsr]qprbbfOrStR†^ab\^Q]_rS&`ru‚^Q[\€’i_v8R8S2u)OQ]I¡

vQ€’[\Rwiq˜¿] @= ‘ [žda[žb\SR bficbfOrS’]qb\SKvQu&d Or€’Sh)]qh)u)Od¦i_˜‡]qv†€‚v9bfSh)u&i_vQvrSKu&b\€’i_vi_˜0u&’^Q[žb\SKhf[KœiHvHbfhf]_h\d¦b\i

iH^rh@prhfi_p0iH[f]qC¬;b\OQS€’h[\i_’^ab\€’i_vT€•[@”Q]H[žS2s†iHv›] u&Sv9bfhf]_‚€’™S2s¨bfi_–HSva¡¢”Q]_[\SKs†R¨^rb\^Q]_rS&`ru&’^Q[\€‚iHvTprh\i_b\iau&iH4œ

Fªv8b\OQSh\S2[eb@i_˜Qb\OQStpQ]qp0Sh2¬q§$Su&i_v‡[ž€•saSh@]WˆHSvrSKhf]_aR8iasaSKa§OrShfSSK]Hu)O†OQiH[žbO‡]_[D]n’iuK]qaRTSRTiHh\d

]_vQsuK]qv¨[\SvQs¨RTSK[f[\]_ˆ_SK[²b\iW]qvdniqb\OQSh2œi_RTR†^rvr€•u]Ibf€‚iHv ”‡Sbe§SKSv†OriH[žbf[€’[]_[f[\^rRTSKsnbfi¦”0Sp0Sh\˜ SKu&bKœ

(ciH[žbf[]_h\S sa€’}€’saS2s!€’v9b\i%u‚^Q[žb\SKhf[Kœ

®¯S sa€’[žb\€’vrˆH^r€’[\O%’iau]q¿Ori9[eb)[¥”0S’i_vQˆ_€’vrˆbfi¨bfOrSW[f]qRTSWu&’^Q[ebfSh$˜ hfi_R h\SKRTiqb\SWOri9[eb)[¥”0S’i_vrˆH€‚vQˆb\i

hfSRTi_b\S u&’^Q[žb\Sh)[Kœ )Q^rh\b\OrSKh\RTi_hfS_¬9bfOrS §iHhfsQ[OQiH[žbf[]qv‡svQisrSK[]qhfSn€‚v9bfSh)u)OQ]qvrˆHSK]_”r‚SHœ

=S2u¸bf€‚iHv“ƒsaSK[fu&hf€’”‡S2[¦©¦]q€’R8€‚¡ªN~hfSOrSK4«[n]q’ˆ_iHh\€‚b\OrR*œ6Fªv¯[žS2u¸b\€’i_v¯µr¬F§$S†pQh\S2[žSKvHbni_^Qh¦Or€’Sh)]qh)u)Or€•u]_

}HSh)[ž€’i_v‡[¥i_˜©c]_€‚RT€‚¡¢NhfSOrSK4«[]q’ˆ_i_hf€‚b\OrR*¬§Or€•u)O’€‚RT€‚bb\OrSnprhfi_p‡]qˆH]qb\€’i_v%i_˜hfSK³9^rS2[eb)[”0S&be§$SSKvu‚^‡[e¡

bfSh)[œNOrSb\OrhfSSS`b\Sv‡[ž€’i_vQ[tb\i!©¦]q€’RT€š¡ªN~hfSOQSC«[t]_‚ˆHi_hf€šbfOrR bfOQ]IbW§S¨prh\iHp‡i9[žSH¬rp0Sh¦u‚^‡[ebfShcpQh\i;`ad_¬

]_ˆ_ˆHh\SKˆH]Ibf€‚iHv¯]_vQs"bfi_–HSvprhfSSKRTpab\€’i_v²¬]qhfS]q•[\iMsaSK[fu&hf€’”‡S2s€’vb\OQ€’[T[\SKu¸bf€‚iHv²œ =SKu&b\€’i_v …MprhfSK[\Sv9bf[

ui_RTpQ]_hf]qb\€’}_S›p0Sh\˜ i_hfRT]_vQu&S!S}I]q’^Q]Ibf€‚iHviq˜cb\OrS2[žS]q’ˆ_i_hf€‚b\OrR›[K¬§OQ€‚’S!bfOrS!•]_[žb›[žS2u¸b\€’i_v u&i_v‡u&’^QsaSK[

iH^rh§$i_hf–0œ

¨+¯ž &()

©¦]q€’RT€š¡ªN~hfSOQSC«[]q’ˆ_iHh\€‚b\OQRw€’[D]cb\iH–_Svr¡C”Q]H[žS2s¨]_‚ˆHi_hf€šbfOrR*¬I§Or€’u)O8R›]q€’v9bf]q€’vQ[]W‚iHˆ_€•u]_9sadvQ]_RT€’ub\hfSS

[žb\hf^Qu&b\^rhfSt[ž^‡u)O†bfOQ]Ib¥b\OrShfiiqb@iq˜0b\OQSb\hfSS€•[¥]_‚§];da[~bfOrSt•]_[žb@vriasaSbfOQ]Ib@§€’‚‡ˆ_SbDb\OrSbfi_–HSv›]qRTi_vQˆ

bfOrSu&^Qh\hfSv9bh\S2³H^QSK[žb\€’vrˆTvriasaSK[Kœ

k¥]Hu)O*vriasaS[žb\i_hfSK[bfOrSn˜ i_’‚iI§€’vrˆ8}I]qhf€’]_”r‚S2[±

NOrS8};]_h\€•]q”Q‚SH¬9§OQ€’u)O*hfSprhfSK[\Sv9bf[bfOrS prhfi_”Q]_”r‚SWiI§vrSKhiq˜~bfOrSnb\iH–_SKv²œ

NOrS }I]qhf€•]q”r’S_¬@§OQ€’u)O·h\SKprhfSK[\Sv9bf[¨b\OrS*vriasaSb\O‡]Ib›§€‚’hfSKu&SK€‚}HS%bfOrSb\i_–HSv §OrSv b\OrS

u&hf€šbf€’uK]q²[\SKu&b\€’i_v€’[hfS’SK]H[žS2s%”d!)œ

NOrSW”‡ii_’SK]_v"#%$&{}I]qhf€’]_”r‚SH¬H§OQiH[\Sc}I]q’^rSc€•[¥b\hf^rS¦€‚˜²bfOrScprhfiau&S2[\[¥iI§vQ[@bfOrS¦b\i_–HSv²¬9i_h¥˜­]q•[žS

iqbfOrShf§€’[\S_œ

NOrSt”0ii_’SK]qv'()*'+,-.0/¨}I]qhf€’]_”r’S_¬q§Ori9[žS}I]_‚^rSc€’[bfh\^QSt€š˜¿bfOrStprhfiau&SK[f[DhfSK³9^rS2[eb)[b\OrScb\i_–HSv²¬

i_h˜­]_’[\Sniqb\OQShf§€’[\S_œ

NOrS€’srSv9b\€‚£QSh8iq˜n€•[¨hfSpQh\S2[žSKvHbfSKs“”d—b\OrS}I]qhf€’]_”r‚S 1)¬@§OQ€‚’S324567#8 9:'8;€•saSv9bf€š£QS2[†]

^Qvr€’³9^rS vQisrS_¬r]qRTiHvrˆ›]q’FvriasaSK[K¬b\OQ]qbt€‚vQ€šbf€’]_‚’d!OriH’sQ[$b\OrSnbfi_–_SKv²œ

)€’ˆ_^rhfSTUn[\^rRTR›]qhf€‚™KSK[©¦]q€’R8€‚¡ªN~hfSOrSK4«[]q’ˆ_iHh\€‚b\OrR*œ

mcv¶S&`r]_R8pQ‚Siq˜c©c]_€‚RT€‚¡¢NhfSOrSK4«[¨]_‚ˆHi_hf€šbfOrRS`aSKu&^rb\€’i_v§€‚b\O …MvriasaS2[¨€•[†[\OriI§v"€’v£QˆH^rhfSƒaœ

=ai_’€’s¯’€‚vrS2[nh\SKprhfSK[\Sv9b’€‚vQ–[K¬~§OQ€‚’S%sr]_[\OrS2sMiHvrSK[nhfSprhfSK[\Sv9b< W‚€’vr–a[Kœ%NOrS%sr]qhf–°vriasaS

–HSSKpQ[@bfOrS¦b\i_–HSv²œ Fªvr€‚b\€•]q’’d°Ÿ­]H¤&¬am €•[b\OrS24=67#89?>@'8;n§OQ€’u)O%OQi_•sr[b\OrS¦b\iH–_Sv~œNOQSAi_˜

(8)

!"$#%

&'()+*'(,

-/.10325476

('

-

'85, 0:9

;+<

-

'&

0:=>6

'+?,@'+A"B

-

;A'

$C

;<

-

'&EDF(' 6G2 H/I"

,@;J"' -K0

,L&*'

;+<

-

'&

0:9

I"$MI

,@;J"' -K0325476

('

NI7OQP/I7M7RSUT

&'+)+*'+(, V-%.10

,L&*'

$C

;<

-

'&XWD 9 H/IY

Z%[/\

^]_`abab

\Yc

ba dee

\

1eL+f YghiajkYbae%l>mGe@n

ÝKÌeÐ;ÍpoVq

'()+*'(,arastiu É4Ç

;+<

-

'&

;+<

-

'&

0:9

v Å)Êɲ҂ǸȲÈ4ÌweÌeÊx2ÊËÐ"yÓÌe×4×¢Åy¸Ìzo${

;+J"' - u

NIY$I!MIRSUT

&'+)+*'+(,

V-%.10324!6

('

$C -

'85,|WD 9 H/IY

ÝKÌeÐ;Ípo${

;+J"' - u

ÉCÇ

-

'85,

,@;J"' -K0325476

('

-

'85, 0}9

NI7~I"IRzNI7OQP/I7M7RSUT€

s7‚7ƒ

Z

sY‚

mGb^e

\

UiajkYbaeVm$ 7„>]i`ababin

$C

;<

-

'&ED 9 H/IY

Z%[

…Um$

n

$C

&'()*%'+(, V-%.

D‡,L&*' H/IY

Z%[/\

ˆ

c

b_f‰l‹ŠQŒ5n

;+<

-

'&

0

sY‚

$C -

'85,D 9 H/IY

-

'85,

0

s%Ž

I"$MI

ÊËÈ­×4É~È4ÌeÔÕ;Ìe×4É~ÉCÇÉ_;ÌÉ4Ǒ¸ÌeÐn×CÊËÐ"weÌÉ_;Ì>’Å)×4ÉÚ²Ý_Ùn

Z Í2ÊËÈ4ÌwªÉ‰’“¦×CÌeÐ;Ícɉ2ÌÉCǑ¸ÌeÐnÉ4Ç$ɉ2ÌDÈ4ÌeÔÕ;Ìe×4É4ÊËÐ"yX”;È4Ç!weÌe×C×

n

,@;J"' -K0325476

('

ÝKÌeÐ;͕o${

;J"' - u

ÉCÇ

s7‚

I"$MI

Z

ÛǸÐY–’ÉCÌeÈ­Ð;ÊËÓtŒÐ;ÇÍ;̸Ù;҂ǒ’ËǗ~ÊËÐ"yÉ_;ÌDÈ­Ìe×CÔÕ;Ìe×4É n

ÝKÌeÐ;ÍpoVq

'+)*%'+(,ar‰sY‚7u ÉCÇ

;<

-

'&

;+<

-

'&

0

s7‚

NI7~I"IRz˜#™5IY

Z

ܲÌweÌeÊx&ÌDɉ2Ì@É4Ǒ¸ÌeÐW҂È4ǸӶÐ;ÇÍ;Ì>‘ n

,@;J"' -š0

,L&*'

)€‚ˆH^rh\STUH±©¦]q€’RT€š¡ªN~hfSOQSC«[]_‚ˆHi_hf€šbfOrR

(9)

]_‚¿vriasaS2[p‡iH€‚v9b)[¥bfiœ Fªv¯Ÿ­”‡¤¸¬ ]H[ž–a[¥˜ i_h$b\OQS¦bfi_–HSv²¬r[\SvQsr€‚vrˆT]†h\S2³H^QSK[žbbfi8€‚bf[ Ÿ¦¤&¬Q]qv‡s

”0SKui_RTSK[tb\OrS†vrS§whfiiqb†Ÿ5 H¤¸œcNOQSv²¬ ^Qp0sr]qb\S2[c€‚bf[ ,t]qvQs Tb\i%p0i_€’v9bcb\i%œ

Fªv Ÿ­uK¤&¬ ]_[\–a[ ˜ i_hcb\OrS†b\iH–_Sv~¬‡bfOrSvMb\OrS†h\S2³9^rSK[žb¦€•[t˜ iHh\§]qh)saS2sb\i §Or€•u)O°^rp¿sr]IbfSK[¦€šb)[A,

bfi8œI'i_b\O ]qvQs ^rp¿sr]IbfSbfOrS€’hA ,%b\i8¬F[\€‚vQuSbfOrS†•]Ib\b\SKhc€•[tbfOrS¨•]_[žb¦hfSK³9^rS2[ebfShci_˜Db\OrS

bfi_–HSv"Ÿ ”0SKu&iHRTSK[bfOrShfi9i_btiq˜b\OrSb\hfSS2¤&œ®¹OQSvw§€’‚h\SK‚S2]_[\SWb\OrS¨uh\€‚b\€•u]_~[\SKu¸bf€‚iHv²¬rbfOrS bfi_–_SKv

§€’’²”‡S[\Sv9bb\i Ÿ=,ž¤¸œ

C A

B

D

(c) C A

B

D

(a)

C A

B

D

(b)

)€’ˆ_^rhfSƒa±,=a]qRTpr’S S&`aS2u&^abf€‚iHvi_˜©c]_€‚RT€‚¡¢NhfSOrSK4«[]q’ˆ_iHh\€‚b\OrR

&()+

=a€‚vQuS €‚v9bfSh\¡¢u‚^Q[žb\SKh’]qb\Sv‡u&€’SK[]qhfSnOr€’ˆ_OrSKhb\OQ]_v€’v9b\h)]I¡ªu&’^Q[ebfShi_vQSK[K¬ab\OrSnbfOrhfSSnS&`b\SKvQ[\€‚iHvQ[§Snprhfiq¡

p0iH[\SKs b\i¦©¦]q€’RT€9Nh\SKOrSC«[]_‚ˆHi_hf€šbfOrR €•[”Q]_[\SKs iHv b\OQS€•saSK]ciq˜r’€‚RT€‚b\€’vrˆ¦b\OrS$prhfi_pQ]_ˆH]Ibf€‚iHvniq˜rhfSK³9^rSK[žbf[

”0S&be§$SSKv*vriasaSK[i_˜sa€JG¿ShfSv9bcu&’^Q[žb\Sh)[Kœ@N~i8b\OQ€’[SKvQsF¬‡§S ]qpQpr‚d%b\OrS ˜ iH‚’iI§€’vrˆ¨bfOrhfSS S&`bfSvQ[\€‚iHvQ[$b\i

©¦]q€’RT€š¡ªN~hfSOQSC«[]q’ˆ_iHh\€‚b\OQR±

)€‚h)[eb2¬²§$S†€’v9b\hfisr^Qu&S8i_v¯SK]Hu)O—u&’^Q[žb\SKhK¬FS`auSpabf€‚vQˆ!bfOrSTi_vrS8b\O‡]Ibn€‚vr€‚b\€•]q’’d°Ori_•sr[¦b\OQSTb\i_–HSv²¬

]"saSKsr€’uK]Ib\S2s¶pQh\iau&S2[\[K¬uK]q’‚S2s·prh\i;`adH¬@§Or€•u)O·€•[›€’v¹u)OQ]qhfˆ_Siq˜n[ebfi_hf€‚vrˆ¯bfOrS{’]H[eb›hfSK³9^rS2[ebTb\i

h\SKRTiqb\S*u&’^Q[žb\SKhf[KœL'$S&˜ iHh\S*]_[\–€‚vrˆM˜ i_h›]Mb\i_–HSv §Or€’u)O €šb›”0S’€‚SK}_S2[†”0S’i_vQˆMbfi¯]—vriasaS*iq˜¦]

h\SKRTiqb\S›u‚^Q[žb\SKhK¬]*vriasaSt£Qh)[žb [\Sv‡sr[]h\S2³9^rSK[žbnb\i{€‚bf[ui_hfh\S2[žp0i_vQsr€‚vrˆprhfi;`ad_œ F¢˜]_vriqbfOrSh

vriasaS%iq˜b\OrS¨[f]qRTS u&’^Q[žb\SKhtOQ]_[th\S2u&Sv9bf‚d!]H[ž–HSKs!˜ i_hbfOrS bfi_–_SKv]_vQsb\OrS¨prh\i;`ad%€•[t];§]qhfS¦i_˜

€šb2¬b\OrS¦prhfi;`d8hfSKsa€’h\S2u¸b)[@bfOrSchfSK³9^rS2[ebb\iT];}Hi_€•sa€’vrˆnb\h)]qvQ[\RT€’[f[\€‚iHvTb\i†b\OrS¦h\SKR8i_b\SWu&’^Q[ebfSh2œ Fªv

˜­]_u&bK¬FbfOrS†pQh\i;`ad*i_p0Sh)]IbfSK[¦‚€’–_S8]uK]_u)OrS†iq˜¥hfSRTiqbfS†hfSK³9^rS2[eb)[œ NOr€•[WOr€’Sh)]qh)u)Or€’uK]q]q’ˆ_i_hf€‚b\OrR

€’[tprh\S2[žSKv9b\SKs€’v*[\SKu&b\€’i_v*µrœ’U_œ

NOrS[\SKui_vQs¯S`9bfSvQ[\€’i_v]q€’R›[¨]qb¨h\S2sa^Qu€‚vrˆ*bfOrS!v^rR†”‡SKh¨i_˜€’v9b\SKhž¡ªu&’^Q[žb\Sh¨R8S2[\[f]qˆHSK[n”d“]qˆq¡

ˆ_hfSˆ9]Ib\€’vrˆ8h\SKRTiqb\SnhfSK³9^rS2[eb)[œD®¹OrSKv{]Th\S2³H^QSK[žbO‡]_[$b\i›”0S hfSKsa€’h\S2u¸bfSKs!b\i%]8prhfi_”Q]_”r‚SniI§vrSKhK¬

”‡SK‚iHvrˆ_€’vrˆ¯b\i]¯hfSRTiqbfS{u&’^Q[ebfSh2¬¥bfOrS{hfSK³9^rSK[žb›€’[TvQiqb![\Sv9bTb\i"€‚b%”r^ab![žb\i_hfSKs €’v´]“³9^rSK^rS_œ

NOr€•[t³9^rS^rS]Huu^rR¨^r•]IbfSK[$bfOrShfS&˜ iHh\SnhfSK³9^rSK[žbf[˜ iHhth\SKRTiqb\S u‚^Q[žb\SKhf[Kœ F¢bt€•[t[ebfi_hfSKs€‚vbfOrS ’]H[eb

vriasaS8§Or€’u)O—§€‚’Sv9b\SKhWb\OrSTu&hf€šbf€’uK]q[žS2u¸bf€‚iHvM§€‚b\Or€’v°bfOrS›u&’^Q[ebfSh2œn®—STvQ]_R8S¨b\Or€•[nvriasaS†b\OrS

J9$ Cœc®¯S¨R¨^‡[ebchfSRT€’vQs*bfOQ]Ibn³H^QS^r€’vrˆ%i_˜@h\S2³H^QSK[žbf[OQ]H[t”0SSKv°^Q[\SKs{”diqb\OQSh¦©¦]q€’RT€š¡

N~hfSOQSC«[ž¡C”‡]_[\SKs8]q’ˆ_i_hf€‚b\OrR›[]_[D€’v 3‚U2„25¢œ (ciI§SK}_SKhK¬;€’v›i_^rh@uK]_[\S_¬q€‚b¥€•[@]qprpQ‚€’SKs8i_vQ‚d ˜ iHh@hfSRTiqbfS

u&’^Q[žb\ShhfSK³9^rS2[eb)[œ

)€‚vQ]_‚’d_¬H§Sp0Sh\˜ i_hfR ]n’iuK]qaprhfSSKRTpab\€’i_v8iq˜0b\OrSbfi_–HSv8ˆ_€’}9€’vrˆ ]WOr€’ˆ_OrSKhDprh\€’i_hf€‚bednb\i hfSK³9^rSK[žbf[

i_hf€‚ˆH€‚v‡]Ib\€’vrˆ“˜ hfi_R b\OrS—‚iauK]qcu‚^Q[žb\SKh!€’v6i_h)saSKh›b\iS`apr‚iH€šbu&’^Q[ebfSh‚iau]_‚€‚bed_œ ®¯S—saS£QvrSM]

(10)

b\OrhfSK[\OriH’s!b\OQ]qbcsaS&£‡vrSK[$bfOrSsaSˆHh\SKS¦i_˜’iau]_‚€‚bed%]qvQs];}_iH€’sQ[$[žbf]_h\}I]qb\€’i_v²œ®¹OrSKv!bfOrS v^rR¨”0Sh

iq˜t’iau]q$hfSK³9^rSK[žb¨€•[¨”0S’iI§ b\Or€•[†b\OrhfSK[\OriH’sF¬bfOrS!hfSK³9^rS2[ebf€‚vrˆMpQ]IbfO€’[†RTiasa€š£‡SKs"€’v¶iHhfsaSKh b\i

[žSKh\}HSn‚iau]_Fh\S2³9^rSK[žbf[£Qh)[eb2œ@NOrSK[\Sn’]H[ebbe§$iTS&`b\SKvQ[ž€’i_v‡[]qhfS¦prhfSK[\Sv9bfSKs€‚v{[\SKu¸bf€‚iHvµQœƒrœ

"! #$

®¯S RTiasa€š˜ d©c]_€‚RT€‚¡¢Nh\SKOrSC«[$]_‚ˆHi_hf€šbfOrR prhfSK[\Sv9bfSKs€‚v*[žS2u¸bf€‚iHv{ƒ8]H[$˜ i_’‚iI§t[K±

NOrS&%;9(' *) t}I]qhf€’]_”r’S_¬F]_srsrSKs°iHvMS2]_u)O°vriasaS)¬¿€’srSv9b\€‚£QSK[WbfOrSTu&’^Q[ebfShWb\i§Or€•u)OMvriasaS

”0S’i_vQˆH[Kœ



v·SK]Hu)O·u‚^Q[žb\SKh Af¬$S&`ruSpabf€‚vrˆ¯bfOrS*i_vrSb\O‡]Ib%OQ]H[¨bfOrS@2456 #89:'8;9¬]—vQisrS€•[TS’SKu&b\S2s

]_RTi_vrˆA)«[vQisrSK[$b\iTOQ];}HS ]8[\p0SKu&€‚£‡un€’vr€‚b\€•]q’€‚™2]Ib\€’i_vhfi_’S_œDNOr€•[vriasaS €’[uK]q’‚S2s%bfOrS,+' -/.fœ

Fªvr€‚b\€•]q’’d_¬Hb\OrS , }I]_h\€•]q”r’Siq˜0+' -/.p0i_€’vHb)[Dbfi b\OrS 24=67#89:>@'8 W]_[D§$S’‡]H[b\OrSA

}I]_h\€•]q”r’Sci_˜Fb\OrSnvriasaS2[@bfOQ]Ib”0S’i_vrˆ†b\i 24=67#89:'8 9«[$u&’^Q[žb\SKhKœ  v%bfOrSWiqb\OQSh$OQ]qvQs²¬HbfOrS<

}I]_h\€•]q”r’SWiq˜b\OrS i_b\OrSKhvriasaSK[p0i_€’v9bf[$b\iTbfOrS,+' -/.@iq˜b\OrSK€‚hhfSK[\p‡S2u¸bf€‚}HSnu‚^‡[ebfSh2œ

)€’ˆ_^rhfS µ8[\^rRTR›]qhf€‚™KSK[iH^rhOr€’Sh)]qh)u)Or€’uK]q0prhfi;`d9¡¢”Q]_[\SKs%}_Sh)[\€‚iHv!iq˜D©c]_€‚RT€‚¡¢NhfSOrSK4«[]q’ˆ_i_hf€‚b\OrR*œ

)€’ˆ_^rhfS…‡Ÿ4]H¤prhfSK[\Sv9bf[D]_v8S`r]qRTpr’S$i_˜¿]_vT€‚vr€‚b\€•]q‡u&i_vr£Qˆ_^rh)]Ibf€‚iHv¨§€‚b\O8be§$inu‚^‡[ebfSh)[¬ 21W]_vQs43_¬

§OQShfSWvQisrSK[ ¨¬%¬‡]qvQs ”‡SK‚iHvrˆ8b\i%u‚^Q[žb\SKh21r¬‡]qvQsvriasaS2[65{¬ 2 ]qv‡s7+83 ”0S’i_vQˆ†bfi 43_œ+83

€•[Wb\OQS9+:-Mi_˜ 43_œ Fªvr€‚b\€•]q’’d_¬ O‡]_[W”‡SKSv“S’SKu&b\S2sMbfi*OQ];}_S†b\OrSTbfi_–HSv Ÿ b\OrS!24=67#8 9?>@'8 I¤¸œ

®¯Su&iHvQ[\€’saSKh$b\OQ]qb €’[€’vb\OrSuh\€‚b\€•u]_²[žS2u¸b\€’i_v“Ÿ<;¥¤¸œ

Fªv{…0Ÿ ”‡¤&¬ ]_[\–a[ ˜ i_htb\OrS bfi_–HSv²œ ]qvQs ”0S’i_vrˆTbfi›b\OrS[f]qRTSu‚^Q[žb\SKhKœ =€’vQu&S w€•[€’v*b\OrS

<;¬ w[žSbf[”0iqbfO€‚bf[? ,T]qv‡s3¥}I]qhf€’]_”r’S¦bfi%œ

Fªv—…‡Ÿ­u2¤¸¬=5{¬¿§Or€•u)OMsaiSK[¦vriqbW”‡SK‚iHvrˆ%bfi%bfOrS†[f]qRTS¨u‚^Q[žb\SKh¦i_˜Db\OrS†b\iH–_SKv{Ori_•saSh2¬¿]_[\–[t˜ i_h¦b\OrS

bfi_–HSv²œF¢b[\SvQsQ[cbfOrSv“]h\S2³H^QSK[žb¦bfi€‚bf[nprhfi;`ad>+83_¬F§Or€•u)OMhfSKsa€’hfSKu¸b)[tbfOrSTh\S2³9^rSK[žb¦bfi¨œ?+83T[žSbf[

€‚bf[ bfi45°œ®¹OQSv*]qhfh\€’}€‚vrˆ†]Ib ¨¬b\OrSWhfSK³9^rSK[žb€•[˜ i_hf§$]_hfsrSKs8b\i†b\OQS¦hfiiqbWŸ†¤§Or€•u)O[\€‚RTpr’d

^Qp0sr]qb\S2[D€šb)[ ]qvQsW}I]qhf€’]_”r‚S2[b\i<5{œ 2 ]_[\–a[b\OrSKv†˜ iHhDb\OQSb\i_–HSv²œNOrSprhfi;`ad,+83‚iauK]q’‚d

hfSKsr€‚hfSKu&bf[Wb\OQS›h\S2³H^QSK[žbWbfi@5 §Or€’u)O“^rp¿sr]qb\SK[€šb)[< n]qvQs };]_h\€•]q”Q‚S2[cbfi@2›œ!m$b bfOrS%Sv‡s

i_˜DSK]_u)O°uh\€‚b\€•u]_[\SKu&b\€’i_v{S&`aS2u&^abf€‚iHv²¬rbfOrSbfi_–_SKv{§€‚’˜ i_’‚iI§ b\OrS†pQ]IbfO°p0i_€’vHbfSKs{”d }I]qhf€’]_”r‚S2[œ

NOQ€’[n[fu&Sv‡]qhf€‚i[žOriI§t[cb\OQST]Hsa}I]qv9bf]_ˆ_S†iq˜¥bfOrST]q’ˆ_i_hf€‚b\OrR [\€‚v‡u&S2 hfSK³9^rS2[ebW§$]H[¦vQiqbW˜ i_hf§$]_hfsaS2s*b\i

bfOrS hfSRTiqbfSnu‚^‡[ebfShBA_¬Q]H[€šbt§$i_^Q’s”‡SnbfOrSu]H[žSn€’vb\OrSni_hf€’ˆ_€’vQ]qF©c]_€‚RT€‚¡¢NhfSOrSK4«[]q’ˆ_iHh\€‚b\OrR*œ

DC EF 0G! BHIHKJ 0$LJ! HM:"! #$N

®¯SOQ];}HS$RTiasa€‚£QSKs†bfOrStprhfi;`adH¡¢”Q]H[žS2s]q’ˆ_iHh\€‚b\OrR iq˜0b\OrSprhfS}€’i_^Q[D[\SKu&b\€’i_v›µrœ’U$b\i hfSKsa^‡u&SS}HSvTRTi_hfS

bfOrSv^rR¨”0ShDi_˜Q€‚v9bfSh\¡¢u‚^Q[žb\SKhR8S2[\[f]qˆHSK[Kœ~NOr€•[€‚RTprhfiI}_SKRTSv9b€•[”Q]_[\SKs†i_v8]qˆHˆ_hfSˆH]qb\€’i_v i_˜‡RTSK[f[\]_ˆ_S2[

]_vQsprh\SKSRTpabf€‚iHvi_˜bfOrSnb\iH–_Sv”d%’iuK]qFvriasaS2[œ



v*SK]Hu)O!vriasaS<)¬a§$S]_srsrSKs!b\OrSn˜ iH‚’iI§€‚vQˆ†}I]qhf€•]q”r’SK[K±

NOrSPO RQS)7T)7}I]qhf€•]q”r’S_¬§Or€•u)O*€’[]›³9^rSK^rSniq˜h\S2³H^QSK[žbf[$€’[f[\^rSKs!˜ h\iHR hfSRTiqbfS u&’^Q[ebfSh)[œ

NOrSO + # + };]_h\€•]q”Q‚SH¬@§Or€•u)O hfSprhfSK[\Sv9b)[¨bfOrS*v^rR¨”0Sh›i_˜¦’iuK]qhfSK³9^rSK[žbf[†bfOQ]Ib›OQ];}HS

prhfSSRTpabfSKshfSK³9^rSK[žbf[€•[f[ž^rS2s%˜ hfi_R h\SKR8i_b\S u&’^Q[žb\SKhf[Kœ

)€’ˆ_^rhfSK[ty8]qv‡sPBTsaS2[\uh\€’”0S¦bfOrS]q’ˆ_iHh\€‚b\OQRœ

(11)

E]i

&;+8t

$ "$#%

;<

-

'&

0:=>6

'+?,@'+A"B

-

;A'

$ "$#%

&'()*%'+(,

V-%.>0}25476

('

-

'85, 0:9

C

=>6

'+?,@'+A"B

-

;A' h;?

4!66

*%(,@'&

H/I"

;<

-

'&

03=>6

'+?,@'+A"B

-

;A'

C

;+<

-

'&D (' 6G2 H/IY

,@;J"' -š0

,L&*'

;+<

-

'&

0:9

IYGMI

,@;J"' -š0325476

('

IYGMI

;<

-

'&

0

&;8t

,@;+J"' -K0325476

('

NI7OQP/I7M7RSzT

Z

`

\Yc

7„aXn

NIY$I!MIRSzT

Z

`

\Yc

7„aXn

NI7~IY$IRzNI7OQP/I7M7RSzT€

sY‚!ƒ

Z

`

\Yc

7„aXn

NI7~IY$IRz˜#™5I"

Z

`

\Yc

7„aXn

)€’ˆ_^rhfS µr±g@hfi;`d9¡¢”Q]_[\SKs]q’ˆ_iHh\€‚b\OrR

(12)

C0

B

C1

(c)D and E ask for CS C0

C

B

(a) Initial configuration A holds the Token C1

A P1 E

D

C0 C1

(b) B asks for CS

A E

B D

C P1

C A P1 E

D

)€‚ˆH^rh\Sn…‡± (c€‚SKhf]_hfu)OQ€’uK]q¿prhfi;`d9¡¢”Q]_[\SKs!]q’ˆ_i_hf€‚b\OrR S`S2u&^abf€‚iHv{[\uSvQ]_h\€’iH[

(13)

+>]i

&;+8t

$G$ "$#%

;+<

-

'&

0:=>6

'?,@'A"B

-

;A'

+X !^

$G$ "$#%

&')+*'(,

-/.10325476

('

-

'85, 039

q B

*'*' 0:9

$C =>6

'?,@'A"B

-

;A' ;?

4766

*/(,@'&

H/IY

;+<

-

'&

0:=>6

'?,@'+A"B

-

;+A!'

$C

;+<

-

'&^D (' 62

H/IY

,@;JY' - 0

,L&+*%'

;+<

-

'&

0:9

IYGMI

,@;JY' - 03254!6

('

IYGMI

;+<

-

'&

0

&;+8t

,@;J"' -š03254!6

('

NIYO/P/IYM7RSzT

&')+*'(, -/.10

,L&*'

$C

;+<

-

'&WD 9 H/I"

Z%[/\

^]i`‰bab

\Yc

ba dee

\

ˆeL+f Ygh_‰jk"bae%l>m$e@n

ÝKÌeÐ;Í oLq

'+)+*'(,arstiu É4Ç

;+<

-

'&

;+<

-

'&

0:9

q B

*'*' 039

v Å)ÊɲҒǸȲȭÌweÌeÊxKÊËÐ"yÓÌe×C×¢Åy¸ÌˆoG{

;J"' - u

NI"I7MIRSzT

&')+*'(,

-/.10325476

('

$C -

'85, WD 9 H/I"

$C

-

'85, ;?

4766

*/(,@'&

H/IY

Z%[/\

UeL+f m

†$†

1b 5eeV

c

i…zeLn

-

B&'+'5, 0

C q B

*'*'ˆWD

9

H/I"

;+<

-

'&

0

*'*' q B

*'*'

IYGMI

;+<

-

'&

0:-

'85,

ÝKÌeÐ;Í oG{

;J"' - rq B

*'*'!r -

B5&'+'5,iu É4Ç -

'85,

,@;J"' -š03254!6

('

-

'85, 0:9

)€’ˆ_^rhfSya±DmtˆHˆ_hfSˆ9]Ib\€’i_v]qvQsprhfSSKR8prb\€’i_v*]q’ˆ_i_hf€‚b\OrR*±h\S2³9^rSK[žbt]qvQsh\SK‚S2]_[\SWuh\€‚b\€•u]_²[žS2u¸bf€‚iHv

(14)

E

NXI7~I"I%RUNXI7OQP/I7MYRzSzT€

s7‚Yƒ

Z

sY‚

mGbe

\

1iajkYbaeVm$ 7„1]i`‰bab_n

$C

;<

-

'&D 9 H/IY

Z%[

…ˆmG c†

n

$C

&'()+*'(, -/.

D ,L&*' H/I"

Z%[Q\

U

c

b_f‰ElXŠQŒ5n

$C

-

'85,D

9

H/IY

-

'85,

0

sY‚

$C

sY‚ ;?

4766

*/(,@'&

H/IY

;+<

-

'&

0

sY‚

I"$MI

$C

sY‚ ;?

4766

*/(,@'&

-

B5&''5, {

&'(

; 6A H/IY

-

B5&''5, 0 -

B5&'',

Z

ÄÇ!w\Œ/”;È4ÌeÌeӔ2É4ÊËǸÐnÇ)ÒaÉ_;ÌDÉCǑ¸ÌeÐnƓtɉ;ÌD×4ÌeÐ;Í;ÌeÈn

q B

*'*' 0 -

'85, q B

*'*%'

-

'85,

0

sY‚

;+<

-

'&

0

sY‚

ÝKÌeÐ;Ípo

*'*'!r q B

*'*'r -

B5&'+'5,iu

É4ÇǗ~Ð;ÌeÈ

q B

*'*' 0:9

I"$MI

Z

ß²Í;ͦÉ_;Ì@×CÌeÐ;Í;ÌeȲÉCÇɉ;ÌDÌeÐ;ÍWÇ)ÒQÜ

B Õ;ÌeÕ;Ìn

q B

*'*' 0 q B

*'*' s7‚

;+<

-

'&

0

sY‚

I"$MI

Z ÊËÈ4×­É~È4ÌeÔÕ;Ìe×4É~ÉCÇ$É_;ÌDÉ4Ǒ¸ÌžÐW×CÊËÐ"weÌÉ_;ÌE’Å)×4ÉÚ²Ý_Ù

n

,@;J"' -š03254!6

('

Z

Í2ÊËÈ4ÌwªÉ‰’“W×CÌeÐ;Ícɉ;ÌÉ4Ǒ¸ÌeÐWÉ4Ç$ɉ2̥ȭÌeÔKÕ2̞׭ÉCÊËÐYy”;È4Ç!weÌe×C×n

ÝKÌeÐ;͕o${

;J"' - r q B

*'*'!r -

B&'+'5,iu ÉCÇ

sY‚

I"$MI Z ÛǸÐY–•É4ÌeÈ4Ð2ÊËÓtŒ9Ð;ÇÍ;̸ÙIҒǒ’ËǗ~ÊËÐ"y¥É_;Ì@ȭ̞×4ÔKÕ2̞׭É

n

ÝKÌeÐ;ÍpoVq

')+*'(,arasY‚!u ÉCÇ

;+<

-

'&

$C

sY‚ ;?

4766

*%(,@'&

H/IY

;+<

-

'&

0

sY‚

NXI7~I"I%RU˜#%™5IY€

q R

*'*'"r - R

5&''5,7ƒ

Z Ü~ÌweÌeÊx&ÌDɉ;ÌÉ4Ǒ¸ÌeÐW҂È4Ç¸Ó Ð;ÇKÍ2ÌE‘

n

,@;J"' -K0

,L&*'

q B

*'*' 0 q B

*%'*' q B

*'*%'

$C

J ;?

4766

*/(,@'&

H/I"

-

B5&'', 0 -

B5&'+'5,

$C

-

'85,D

9

H/IY

-

'85, 0

' 4 A

q B

*'*' 0 q B

*%'*'

' 4 A

I"$MI

$C -

'85, ;?

4766

*%(,@'&

H/IY

ÝKÌeÐ;͕o

*'*'!r q B

*'*'r -

B5&'+'5,iu

É4ÇǗ~Ð;ÌeÈ

q B

*'*' 0:9

NXI7~I"I%R‹P/IYP/I%€ r- ƒ

-

B5&'+'5, 03-

$C -

'85,D 9 H/IY

-

'85, 0

' 4 A

q B

*'*' 0 q B

*%'*'

' 4 A

I"$MI

$C -

'85, ;?

4766

*%(,@'&

H/IY

ÝKÌeÐ;͕o

*'*'!r q B

*'*'r -

B5&'+'5,iu

É4ÇǗ~Ð;ÌeÈ

q B

*'*' 0:9

(15)

=€’RT€‚•]qhbfi¨bfOrSni_hf€‚ˆH€‚v‡]qF©c]_€‚RT€‚¡¢Nh\SKOrSC«[]_‚ˆHi_hf€šbfOrR*¬]8hfSK³9^rS2[eb$˜ i_hSv9bfShf€‚vrˆT]8u&hf€šbf€’uK]qF[žS2u¸bf€‚iHv

Ÿ<;@¤$˜ iH‚’iI§t[$b\OrS 9«[tp‡]Ib\O*^rv9bf€‚€šbchfSK]Hu)OrSK[$€‚bf[ 4='6 4#9:''ŸÑbfOrSvriasaS i_˜bfOrS¨[f]qRTS u&’^Q[ebfSh

§OQiH[\S3°}I]qhf€•]q”r’S%€•[8[\S&b8b\i a¬@€CœS_œ’¬Db\OrS•]_[žb†vriasaSiq˜tbfOrS*u&’^Q[ebfSh†b\i¯OQ];}_Sh\S2³9^rSK[žb\S2s“b\OrS

uh\€‚b\€•u]_²[žS2u¸bf€‚iHv‡¤¸œ

®¹OrSKv°]TvriasaS hfSKu&SK€‚}HSK[]ThfSK³9^rSK[žbK¬Q€š˜€šb¦€’[vQiqbc]"4='6 49 ''vriasaS%Ÿ5 _¤&¬r€‚bt˜ i_hf§$]_hfsQ[

bfOrS$h\S2³H^QSK[žb]qv‡s^rp¿sr]IbfSK[€‚bf[ †Ÿ­i_vr’d €š˜Qb\OrS$h\S2³9^rSK[žb€•[€’[f[\^rSKsn˜ hfi_R bfOrS$‚iau]_au&’^Q[ebfSh€‚v†i_h)saSh

bfi{];}_i_€•s{hfSKsa€’hfSKu¸bf€‚iHv°bfihfSRTi_b\STu&’^Q[ebfSh)[f¤&œ$F¢˜b\OrS›hfSKuS€’}_SKh¦€•[ ]345'6 4#9 ''¦vQisrS*Ÿ5 _¤

§OQ€’u)O°§]q€‚bf[c˜ i_h¦b\OQSb\iH–_SKv¶Ÿ'()*'+,-.0/ -)0;¤&¬F§S8sa€•[ebf€‚vrˆH^r€•[žO{be§$iuK]_[\SK[K± ŸeU2¤¦NOrS†h\S2u&S€’}_S2s

hfSK³9^rS2[ebW€’[¦bfOrS¨£‡hf[žb¦iHvrS8[\€’vQu&S¨b\OrSTvriasaS†§$]_€šb)[t˜ iHh¦bfOrS†b\i_–HSv¶Ÿ­€4œS_œ< _¤&œNOrSv²¬¿bfOrS ,

€•[8[žSb¨b\iMb\OrShfSK³9^rSK[žb\SKh”0SKu]_^Q[\S]I˜ÑbfSh†b\OrSvriasaSi_”ab)]q€’vQ[¨]_vQs"hfS’SK]_[\SK[b\OrSu&hf€šbf€’uK]q[žS2u¸bf€‚iHv²¬D€šb

§€’’FOQ];}_SWb\i›[\SvQs!b\OQSnb\i_–HSvb\i8b\OQS h\S2³H^QSK[žb\Sh2œDNOrS<†€•[]q•[\i†^rp¿sr]qb\SKs 97 1b\OQS h\S2³H^QSK[žb

uK]qRTSW˜ h\iHR b\OrS ’iau]_²u&’^Q[ebfSh2œŸ4ƒ_¤$NOrS<¥€•[]q’h\S2]_sad%[\S&b2œ =€‚v‡u&SWb\OrS hfSKuS€’}_SKh€•[]4='6 4#9 ''¸¬

bfOrSrbW€‚vQS}€šb)]q”r’dp‡iH€‚v9bf[tb\i!]ThfSRTi_b\SvriasaSHœ Fªv{b\Or€•[cuK]_[\S_¬‡€š˜b\OQS¨hfSK³9^rSK[žb\SKht€•[t’iuK]qC¬‡]_vQsb\OrS

v^rR†”‡SKhtiq˜DprhfSSKRTpab\€’i_vQ[t€’[”0S’iI§ b\OrS bfOrhfSK[\Ori_•sF¬r§$Sp0Sh\˜ i_hfR ]T’iuK]q²pQh\SKSRTpab\€’i_v*i_˜bfOrS bfi_–_SKv

”d8[žSbžb\€’vrˆ< b\inbfOrSthfSK³9^rS2[ebfSh@]qv‡s†RTSKR8iHh\€’™€’vrˆWb\OQSti_•s ,€’vTb\OQS”‡SKˆ_€’vrvr€’vrˆ iq˜ 9 )*)09œ

k]_u)Ob\€’RTS¨]TvriasaS ”0SKu&iHRTSK[bfOrS vrS§45'6 4#9:'¸¬‡b\OQS 9 <)*)0n€’[¦[žSKvHbbfi›€šb2œNOrS 9 )0)*

€•[]q•[\i8€’vQu‚^QsrSKs€‚vbfOrSWb\i_–HSvRTSK[f[\]_ˆ_S_œ

)€’ˆ_^rhfSK[cz†]qv‡sD›[\OriI§ [\i_RTS [\]_RTpr‚S2[iq˜b\OrS]_‚ˆHi_hf€šbfOrR*«[$S`S2u&^abf€‚iHv²œ®—Sui_vQ[\€•saShbfOrS[\]_RTS

ui_va£‡ˆ_^rh)]Ibf€‚iHvMprhfSK[\Sv9b\S2s¯€‚v“£QˆH^rhfS8…0Ÿ ”‡¤ §OrShfS ]_[\–a[ ˜ i_h bfOrSTb\iH–_SKv²œm bfOr€’hfs“u&’^Q[žb\SKh a¬

§€‚b\O"vQisrSK[T¬ ]_vQs +"Ÿ+' ;¤ €•[€’vQu&’^QsaS2s“€‚vb\OrS›£‡ˆ_^rhfS_œ '+'4=8{i_˜prh\SKSRTpabf€‚iHv"€’[

S2³9^Q]q¿bfi›ƒrœ

Fªv´£QˆH^rhfS°zrŸ­]9¤¸¬b\OrS°vQisrS@5 ]H[ž–HSKs¶˜ i_h›bfOrS*b\iH–_SKv²œ F¢b[\SvQsQ[›]“h\S2³H^QSK[žb›b\i"€‚bf[›prhfi;`ad +83_¬

§OQ€’u)Oh\S2sa€’h\S2u¸bf[€‚bb\i ¨¬Q[žSbžbf€‚vrˆT€‚bf[iI§v ¨bfi œ  v .b\OrS hfSK³9^rS2[eb€•[prhfi_pQ]_ˆH]IbfSKsTbfiTb\OrS

45'6 4#9:''Ÿ†¤&¬H§Or€•u)O›[ž€’RTpr’d^rp¿sr]IbfSK[D€‚bf[ $Ÿ b\OrS ,Wiq˜ 6]qv‡s w]_h\Svri_b@^rp0sQ]Ib\S2sT[ž€’vQu&S

bfOrSWh\S2³H^QSK[žb\Sh€’[]¨h\SKR8i_b\S¦vriasaS2¤&œNOQSv²¬w”0S’i_vrˆH€‚vQˆb\i8u&’^Q[žb\Sh ]_[\–[ 6˜ iHh¥bfOrS¦b\i_–HSv²œDNOrS

hfSK³9^rS2[eb¦€’[c˜ i_hf§$]_hfsrSKsb\i!b\OrS 4='6 4 9:''¨Ÿ†¤&œ@=€’vQuS !«[ €•[¦]_‚hfSK]Hsad[\S&bTŸ 5!¤&¬¿b\OrS

hfSK³9^rS2[ebfSh Ÿ¤$€•[€’vQ[\Sh\b\SKs€’vbfOrS 9 )*)09œ

Fªv¶£Qˆ_^rhfSzŸ ”‡¤&¬@vriasaS32 iq˜43*]_[\–[˜ i_h¨b\OrSb\iH–_Sv~œ—NOrSprh\i;`ad +83 J !h\S2sa€‚hfSKu&bf[¨b\OrS

hfSK³9^rS2[eb¦b\i 5 Ÿ b\OrS4='6 4 '¦iq˜ ¤c§OQ€’u)O°^Qp0sr]qb\S2[¦€‚bf[A ¦]qvQs ›b\i 2›œm$b¦bfOrS›[\]_RTS

bf€‚RTSH¬ hfSKu&•]q€’R›[bfOrSb\i_–HSv²œ“NOrSh\S2³9^rSK[žb†€•[8h\S2sa€‚hfSKu&b\S2s“b\i %œL=€’vQu&S %«[ ,p0i_€’vHb)[†b\i—]

vQisrS%iq˜t]*hfSRTiqbfS!u&’^Q[žb\Sh†]qvQs¯bfOrS%v^rR¨”0Sh†iq˜’iuK]q@pQh\SKSRTpab\€’i_v"€•[”0S’iI§ b\OrS!b\OrhfSK[\Ori_•sF¬b\OrS

]_vQsnpQ]IbfOQ[¥]_h\Su)OQ]_vrˆ_S2sF±²bfOrS D]qv‡s ,ni_˜ ]qhfS^rp0sQ]Ib\S2s8b\i¨srSK[\€‚ˆHvQ]IbfSKs†b\OrS

’iau]_~vriasaS 8œ¦NOrS8i_•s*}I]q’^rS¨i_˜ %«[ ŸD5!¤c€’[¦]_srsaS2s°]Ib¦b\OrS†”‡SKˆ_€’vrvr€’vrˆ!i_˜ 9 <)*)0!Ÿ €‚bn€’[

vQiqb¦[\OriI§v*€‚v°b\OrS £‡ˆ_^rhfS2¤&œ €•[bfOrSvrSK§ 4='6 4 9 ''¸¬¿h\S2u&SK€‚}€’vrˆTb\OrSKv*b\OrS 9 <)*)0Hœ$®¹OrSKv

hfSKuS€’}_S2[b\OrS 9 <)*)0H¬H€šb$h\SKRTiI}_SK[Db\OrS¦OrSK]HsT};]_‚^QSciq˜F€‚bnŸ 5¤@]qv‡s›[žSbf[€šb)[ bfib\OQ€’[}I]q’^rS_œ

Fªv!£Qˆ_^rhfS D‡Ÿ­]H¤&¬ hfS’SK]_[\SK[Db\OrS¦b\iH–_Sv~œF¢b[žSKvQsr[¥€šb$b\i†€šb)[ DvQisrS†Ÿ8¤¸œ h\SK‚S2]_[\SK[bfOrSv!b\OrS

<;¶]qvQs[\SvQsr[bfOrSWb\i_–HSv!b\i8œ .]_vQs [\S&bb\OQS€’h:@b\i aœ Fªv“Ÿ ”‡¤&¬ SKvQsr[$b\OQSWS`aSKu&^rb\€’i_v!i_˜

bfOrS<;]qvQs›[\SvQsQ[@bfOrStbfi_–_SKv›§€šbfO%bfOrS 9 )0,)0bfibfOrSchfSRTiqbfStvriasaS 5{œ F¢b$]q•[\i¨[žSbf[¥€šb?

bfi!Tœ8m$bnb\OrSTSv‡sMi_˜¥€šb)[ [žS2u¸bf€‚iHv²¬05 §€’’[\Sv‡s°bfOrS8b\i_–HSvMb\i2 ]Huu&iHhfsr€‚vrˆ!b\i€šb)[ ¸œ8Fªv·Ÿ­u2¤¸¬

§OQSv3.SKvQsr[$S&`aSKu^ab\€’vrˆ†b\OrS =¿¬a€‚b[\Sv‡sr[b\OrS¦b\iH–_Sv!b\i2 ]_vQs›bfOrS 9 )0)*9œ®¹OrSvh\S2u&S€’}€‚vQˆ

bfOrS RTSK[f[\]_ˆ_SH¬ 2 ^rp¿sr]qb\SK[€‚bf[tvrS&`bt}I]qhf€’]_”r’Scbfi"Tœ

(16)

D P1 E

C1

G P2 F C2

F C

B

A C0

G P2 F

C2

P1 E

D C1 A

C0

B C

(a) D then F ask for CS F

(b)E and C ask for CS

)€‚ˆH^rhfSza±Dmtˆ_ˆHh\SKˆH]qb\€’i_v!]_vQsprh\SKSRTpabf€‚iHv]_‚ˆHi_hf€šbfOrR S&`aSKu^ab\€’i_v~± FªvHbfSh\¡¢u‚^‡[ebfSh)[hfSK³9^rS2[eb)[

(17)

G P2 F C2

G P2 F C2

P1 E

D C1

C A

B C0

G P2 F C2

C A

B C0

P1 E

F A

C0

B C

D P1 E F C1

(a)A then B end CS

(b) C ends CS

(c) D and E end CS C1

D

)€‚ˆH^rh\S6DQ±mcˆ_ˆHh\SKˆH]Ibf€‚iHv!]qv‡spQh\SKSRTpab\€’i_v*]q’ˆ_iHh\€‚b\OQR S&`aSKu^ab\€’i_v²±@Ni_–HSv!b\h)]qvQ[\RT€’[f[ž€’i_v

(18)

I +¨$ ¦&n

NOQ€’[[\SKu¸bf€‚iHv!prhfSK[\Sv9b)[@bfOrSnp‡SKhž˜ iHh\R›]qv‡u&ScSK}I]q’^Q]Ibf€‚iHv%iq˜[\S}HSh)]q0S&`ap0Shf€‚RTSv9b)[§OQ€’u)Ou&i_RTpQ]_h\Scb\OrS

S%u&€’SvQud%iq˜R¨^abf^Q]qFS`ru&’^Q[ž€’i_v*]q’ˆ_iHh\€‚b\OQRT[Kœ®—Sui_RTpQ]qhfSWb\OrS[\€‚`%˜ i_’‚iI§€’vrˆT]q’ˆ_iHh\€‚b\OrR›[K±

- 4= 8—b\i_–HSva¡¢”Q]H[žS2s]q’ˆ_iHh\€‚b\OrR*œ Fªv b\OQ€’[›u’]H[\[\€’uK]q]q’ˆ_iHh\€‚b\OrR*¬¥]—^rvr€•³9^rS*OriH[žbK¬¥b\OrS

4='6 $ 9 ;/ ¬cR›]qv‡]qˆ_S2[]_‚Wbfi_–_SKv6hfSK³9^rSK[žbf[]qv‡s6ˆ_h)]qv9bf€‚vrˆ¶R8S2[\[f]qˆHSK[Kœ ®¹OrSv ]Ori9[eb

§$]_v9bf[bfi Sv9b\SKh¥€’vHbfinb\OrS<;¬_€‚b[\SvQsr[]nh\S2³9^rSK[žbDb\inbfOrS 4='6,$09! ;/ 9§OrSv›] Ori9[eb@SKvQsr[

b\OrS <; €šbnˆ_€’}_S2[c”‡]_u)–*b\OQS†bfi_–HSv{bfibfOrS4='6 $09 /&¬F§Or€’u)O—˜ i_hf§]qh)sr[t€‚bnb\ib\OrSTvrS`9b

h\S2³9^rSK[žb\€’vrˆTOriH[žbKœ

' 8;6 +,W]q’ˆ_i_hf€‚b\OrR*¬¿§Or€•u)OM€’R8pQ‚SKR8SKv9bf[¦b\OrS8p0ShfR8€•[f[ž€’i_va¡¢”Q]H[žS2s{X€’uK]qh\bž¡ªmtˆHhf];§]q•]›]q’ˆ_i_¡

h\€‚b\OQR 3ƒ25Cœ8m vQisrS†§€•[žOQ€‚vrˆb\iSv9bfShn€‚v9bfi!bfOrS <;6[\SvQsr[n]h\S2³9^rSK[žb¦bfiSK}_SKh\d*iqbfOrShnvriasaS

]qvQsT§]q€‚bf[˜ iHhDb\OQS€’h¥p0ShfR8€•[f[ž€’i_v²œ®¹OrSKv%]nvriasaSh\S2u&SK€‚}HSK[D]nhfSK³9^rSK[žbK¬H€šb$[žSKvQsr[D€‚bf[¥p‡SKh\RT€•[\[\€‚iHv

b\i›bfOrS¨hfSK³9^rS2[ebf€‚vQˆ›vriasaS¨€‚˜DS€‚b\OrSKhc€‚b¦€•[tvri_bch\S2³9^rSK[žb\€’vrˆ%€‚bf[\S‚˜b\OrS¨b\i_–HSv{iHhc]qvri_b\OrSKhtvriasaSH«[

h\S2³9^rSK[žbprh\S2u&S2saSK[€‚bf[iI§v~œ

> 3 ' 4¿]q’ˆ_iHh\€‚b\OQR¬9§Or€•u)O›€‚RTpr’SRTSKvHb)[b\OrSW©c]q€’RT€š¡ªNh\SKOrSC«[@b\iH–_Svr¡C”Q]H[žS2sT]q’ˆ_i_hf€‚b\OrR

prhfSK[\Sv9b\S2s!€’v{[žS2u¸b\€’i_v{ƒaœ

+' -*]q’ˆ_i_hf€‚b\OrR*¬§Or€•u)O€’RTpr’SRTSv9bf[b\OrS]_‚ˆHi_hf€šbfOrR prhfSK[\Sv9b\S2s!€’v{[žS2u¸b\€’i_v*µrœ’U_œ

+' /;/ ' / --]q’ˆ_iHh\€‚b\OQR¬_§Or€’u)OT€’RTpr‚SKRTSv9bf[bfOrSc]_‚ˆHi_hf€šbfOrR prhfSK[\Sv9b\S2s¨€’v›[žS2u¸bf€‚iHv

µrœËƒa¬a§Or€•u)O*prhfiI}9€•saS2[¥bfi_–HSvprh\SKSRTpabf€‚iHv]_vQs!RTS2[\[f]qˆHSW]_ˆ_ˆ_hfSˆ9]Ibf€‚iHv!]qprpQh\i9]_u)OrS2[œ

+' ¿]q’ˆ_iHh\€‚b\OrR*¬K§Or€’u)Oje^‡[ebsr€’[f]q”r’SK[0bfOrS¥]_ˆ_ˆ_hfSˆ9]Ibf€‚iHvtRTSKu)OQ]_vr€’[\R i_˜ +' ?/ / ',/;--

]q’ˆ_iHh\€‚b\OrR*œ

NiSKR¨^r•]IbfS†]*lWh\€•s°SKv}9€’hfi_vrRTSv9bW§€šbfOMR¨^Qšbf€‚’S}HSvrS&be§$i_hf–’]qb\Sv‡u&€’SK[K¬F§S†OQ];}_S†^Q[žS2sM][žp0S&¡

u€š£0u$sr€’[žb\hf€‚”Q^ab\S2sbfSK[žb@pr’]qbž˜ iHh\R*¬;b\O‡]Ib¥]q’’iI§t[~€’vIjeSKu&b\€’i_vTiq˜0vrS&be§$i_hf– saS•];da[œ®—SS2[eb)]q”r’€’[\OT]¦}€’hžbf^Q]q

hfi_^rb\Shn”dM^‡[ž€’vrˆ ‘°‘ ©tk¥N 3’U… 5$]qvQs Fªg¥©cmDNnœ®—S›^‡[žS Fªg¥©¦mDNn¬~]qvOFªg R›]_[f³9^rShf€‚vQˆ]_prpr’€š¡

uK]Ibf€‚iHv²¬rbfi!sa€’}9€•saSiH^rhcvQS&be§$i_hf–!€’vHbfi%}€‚h\b\^‡]q~omc©c[Kœ ‘°‘ ©tk¥N €’[W]QS&`a€’”r’Sb\iiH~i_hf€’ˆ_€’vQ]q’‚d

srSK[\€‚ˆHvrSKs°˜ i_hWb\S2[ebf€‚vrˆ*vrSbe§iHh\–*prhfiqbfiau&i_•[KœF¢b[ž€’R¨^r•]IbfSK[W”Q]_vQsa§€•sb\O¯‚€’RT€šb)]Ibf€‚iHvQ[¬saS•];da[¬FpQ]Hu)–_Sb

’iH[f[\SK[KœPFªv"pQhf]Hu¸b\€•u&SH¬€‚b†€’v9b\SKhfuSpab)[pQ]Hu)–_S&b)[¬[\S’SKu¸bfSKs“”d“]_srsahfSK[f[]_vQs“p‡iHhžb†iq˜tsaSK[žb\€’vQ]qb\€’i_v]qv‡s

[\i_^QhfuS_¬q]qv‡s¨pQ]H[\[\SK[bfOrSRwbfOrhfi_^rˆHO†iHvrSiHhDRTi_hfSiH”ajeSKu&bf[u]_‚’SKs8³9^rS^rS2[D]qvQs†pr€’p‡S2[§Or€•u)O8[\€‚R†^r•]Ib\S

bfOrSvrS&be§$i_hf–nSG¿SKu&bf[Kœ Fªv8i_^QhS`ap‡SKh\€’RTSv9bK¬qS2]_u)O†R8S2[\[f]qˆHS¥S`au)O‡]qvrˆHSKs”0S&be§$SSKv¨be§$insa€QG¿ShfSv9b@o~m¦©c[

p‡]_[f[žS2[¥bfOrhfi_^rˆHO!bfOr€’[c[žp0SKu€š£‡uWOri9[eb2œ

6G! BHI J<0:$ HB!=H 6 ! H

NOQS S&`ap‡SKh\€’RTSv9bcsaS2[\uh\€’”‡S2s€‚v*bfOr€’[¦[žS2u¸bf€‚iHv§]_[p0Sh\˜ i_hfRTSKsi_v{]TvriHv{saSKsa€•u]qb\S2su‚^‡[ebfShti_˜vQ€‚vrS

g $[œ@®¯S¨ui_vQ[\€’srSht]8OrS&bfShfi_ˆHSvrSKi_^Q[$vrSbe§iHh\–!ui_RTp0iH[\SKsiq˜be§iTgSv9b\€’^rR F1FF*BH„_„ ‘ (t™]_vQs*[ž€‚`

gSKvHbf€‚^QR F! ƒ†l@(c™W’€’vr–_S2s%”d!]UK„_„ ‘ ”r€‚bf[#"I[$kDbfOrShfvrS&b2œ@NOrS ]q’ˆ_iHh\€‚b\OrR›[§SKh\SW€’R8pQ‚SKR8SKv9b\SKs€’v

$9];}I]Ÿ>=^rv²«[%$ ? U_œ…9¤i_vbfi_piq˜D]8o~€‚v^a`*ƒaœ…8–HShfvrSCœ

(19)

g$[8]qhfS![\prhfSK]_s¯€’v°u‚^Q[žb\SKhf[¨iq˜{Ori9[eb)[œ°NOQS%b\iHp‡iH‚iHˆ_d—€’[¨prh\SK‚€’RT€‚v‡]qhfdM–vriI§v"”d—SK}_SKh\d

[\da[ebfSR RTSKR¨”0Sht]_[§$S’~]H[$b\OrS €’vr€‚b\€•]qFiI§vrSKhiq˜~bfOrSnb\iH–_SKv²œ

)Qi_hbfOrSK[\S S&`ap0Shf€‚RTSv9b)[¬r§$S €’vHbfh\iasa^‡u&S]›saSK’];diq˜/1/1 +n˜ iHht€’vHbfSh\¡¢u‚^‡[ebfShtu&iHRTR¨^rvr€•u]qb\€’i_v²œ

k¥}_Shfd%€’v}_i_’}_S2s![\€šbfSnprh\iasa^‡u&SK[/18R¨^abf^Q]qFS`au‚^‡[ž€’i_vh\S2³9^rSK[žbf[Kœ

NOrS2[žS hfSK³9^rS2[eb)[]qhfSnu)O‡]qh)]_u¸bfShf€‚™KSKs›”d°±

€•[b\OrSnbf€‚RTSnb)]q–_SKv”d!]8vriasaSnbfiTS&`aSKu^ab\SnbfOrSu&hf€šbf€’uK]q²[\SKu&b\€’i_v²¬

[žp0SKu€š£QS2[b\OrSRTSK]_vbf€‚RTS”0S&be§$SSv†h\SK‚S2]_[\€‚vQˆtb\OQStu&hf€šbf€’uK]qa[žS2u¸bf€‚iHv†]qv‡s¨hfSK³9^rS2[ebf€‚vrˆW€‚bD]_ˆH]_€‚v²¬

€•[DbfOrStprhfSSKRTpab\€’i_v8b\OQh\S2[žOriH’s8iHvr‚d†˜ i_hB+ ]qvQs +' ?/ / ',/ --]_‚ˆHi_hf€šbfOrR›[œ

NOrS p0Sh\˜ i_hfR›]qvQuS¦RTS2]_[\^rh\S2[€‚v‡u&’^QsaST±

b\OrS MŠ ¼  Á{¼ Ž ‡¼  ¼ ‹2‹KŽ 0¼ ‹ ¬sa€’}€’srSKs¹€’v6be§$i¶u]qb\SKˆ_i_hf€’SK[{±"RTSK[f[f]qˆ_S2[›S&`¡

u)OQ]qvQˆ_SKs8”0S&be§$SSKvTbe§i Ori9[eb)[D€’vTb\OrSc[f]qRTStu‚^Q[žb\SKh¦Ÿ­‚iau]_rRTSK[f[\]_ˆ_S2[f¤]qv‡sTR8S2[\[f]qˆHSK[”0S&be§$SSKv

be§iTOri9[eb)[iq˜Dsa€JG0SKh\SKvHbtu‚^Q[žb\SKhf[ Ÿ­ˆ_’i_”Q]_FRTSK[f[\]_ˆ_SK[)¤¸œ

Á ŠŒKŽ Œ ¼M€’[b\OrSb\€’RTS%˜ i_h8]qvOQiH[žb¨”‡Sbe§SKSv"bfOrSR8iHRTSv9b¨§OrSKv€šbThfSK³9^rSK[žbf[b\OrS

u&hf€šbf€’uK]q²[\SKu&b\€’i_v*]qvQsb\OQS R8iHRTSv9b§OrSv*€‚btˆ_S&b€’v9b\i›€‚bKœ

DC F "! H H

NOQSt]q€’R i_˜‡bfOrSK[\SS&`ap0Shf€‚RTSv9b)[D€’[@b\i iH”Q[žSKh\}HSS}_iH‚^rb\€’i_v8iq˜¿b\OrSc”‡SKOQ];}€‚iHhDiq˜¿SK]_u)O›]_‚ˆHi_hf€šbfOrR §OrSKv

bfOrS8h\SK’]qb\€’i_v°”0S&be§$SSKv

]qvQs

}I]qhf€‚S2[¦]_vQs

€’vQu&hfSK]H[žS2[œI)€‚ˆH^rh\S2[ E]qvQs¶UK„[žOriI§ bfOrS8i_”ab)]q€’vr€‚vQˆ

bf€‚RTS%]H[ ]!˜ ^QvQu¸bf€‚iHv¯i_˜

¬ ]qv‡s

œN)€‚ˆH^rhfS E*ui_RTpQ]qhfSK[¦i_^Qh,+ ?/ / ,/ -. ]q’ˆ_i_hf€‚b\OrR

§€‚b\Ou’]H[\[\€•u]q@]_‚ˆHi_hf€šbfOrR›[T±> 3 ' 4ž¬ - 4=!;8{]qv‡s ' 8 6&+, ]q’ˆ_i_hf€‚b\OrR›[Kœ%®¹Or€’‚S

£‡ˆ_^rhfS{UK„{ui_RTpQ]qhfSK[WbfOrS![f]qRTS%]q’ˆ_iHh\€‚b\OQR +' /;/ ',/ --¶§€‚b\O"iH^rhiqbfOrSh8]q’ˆ_iHh\€‚b\OrR›[T±

+':-°]qvQs@+'¸œcNOrS¨£Qˆ_^rhfS%UHU¨u&iHR8p‡]qhfSK[bfOrS¨v^rR†”‡SKhci_˜@R8S2[\[f]qˆHSK[cS&`ru)OQ]qvQˆ_SKs”0S&be§$SSKv

OQiH[žbf[%sa^Qh\€’vrˆ¶]_v¹S&`ap‡SKh\€’RTSv9b%§OrSKh\S

1 1 +M]_vQs·bf]_”r’SU°[ž^QR8R›]_h\€’™S2[Tb\OrS¯[\]_RTS

S`ap‡SKh\€’RTSv9bKœ Ni¶hfSprhfSK[\Sv9b%€’v¹b\OQSM[\]_RTS{£Qˆ_^Qh\S{bfOrSMv^rR†”‡SKh!i_˜R8S2[\[f]qˆHSK[›S`ru)OQ]qvrˆHSKs·€’v¹b\OrS

”Qh\i9]_sruK]_[žbnS`ap‡SKh\€’RTSv9bK¬b\OQ€’[†v^rR¨”0Sh†iq˜RTSK[f[\]_ˆ_SK[€’[¨h\SKprh\S2[žSKv9b”9d“]°[fu]_‚ST˜ iH^rhbf€‚RTSK[†ˆ_hfSK]qb\SKh

bfOQ]qvb\OQS[\uK]q’SWi_˜bfOrS iqbfOrSht]_‚ˆHi_hf€šbfOrR›[œ

)Qi_h¥]_‚Q]_‚ˆHi_hf€šbfOrR›[§OrSvTbfOrSh)]Ib\€’i

saSKuh\S2]_[\SK[bfOrSti_”rbf]q€’vr€’vrˆWb\€’RTScsaSKuh\S2]_[\SK[bfi9i‡¬H[\€‚RTpr’d

”0SKuK]q^Q[\S%[žbf]Ibf€’[žb\€•u]_‚’dM§OQSv"]qv“Ori9[ebhfSK³9^rS2[eb)[nb\OrS%b\i_–HSv²¬~b\OrSKh\S%]_h\S›’SK[f[ hfSK³9^rS2[ebf€‚vrˆ*Ori9[eb)[]qv‡s

bfOrSd¯[eb)];d{‚S2[\[ b\€’R8S›€’v¯b\OrS <;œ%NOrST£Qh)[eb hfSR›]qhf–M]q”0i_^rbWbfOrSK[\S›S&`ap0Shf€‚RTSKvHb)[n€’[ b\OQ]qb ˜ i_h SK]Hu)O

]_‚ˆHi_hf€šbfOrR §OQ€’u)O^‡[žS2[ b\OQS!prhfSSKR8prb\€’i_v²¬b\OQS!i_”rbf]q€’vr€’vrˆ{bf€‚RTSsrSKu&hfSK]H[žS2[ §OrSKv“b\OrSprh\SKSRTpabf€‚iHv

bfOrhfSK[\Ori_•s!€’vQuh\S2]_[\SK[KœD®—S¨uK]qv*SK]H[ž€’’d%S&`apr•]q€’vb\Or€•[hfSK[\^ršbt”d!b\OrS ˜­]Hu¸bbfOQ]Ibt’iau]qu&i_RTR†^rvr€•u]Ibf€‚iHv

€•[$u)OrSK]_p‡SKh¥bfOQ]qvˆ_’i_”Q]_‡u&iHRTR¨^rvr€•u]qb\€’i_v²œmc[[\OriI§v%€’v%£QˆH^rhfS¨U_UH¬_bfOrSWv9^QR¨”0Sh$iq˜~’iau]q0RTSK[f[\]_ˆ_S2[

€’vQuh\S2]_[\SK[8§OrSv´bfOrS{v^rR¨”0Sh!iq˜nprh\SKSRTpabf€‚iHv·€’vQuh\S2]_[\SK[8§Or€’‚S*bfOrS°v^rR¨”0Sh!iq˜nˆ_’i_”Q]_$RTS2[\[f]qˆHS

srSKu&hfSK]H[žS2[œNOr€•[¥]q•[\i S&`apr•]q€’vQ[@§OdT]q’rb\OQS¦]q’ˆ_iHh\€‚b\OQRT[@prh\S2[žSKv9b\SKs8€’v›£QˆH^rh\S¨UK„ ]qhfSRTi_hfStS %u€‚SKvHb

bfOQ]qvb\OQSu&•]_[f[ž€•u]_¿]_‚ˆHi_hf€šbfOrR›[prhfSK[\Sv9b\S2s%€’v£‡ˆ_^rhfS6Erœ

NOrS +' /;/ ' / --*]_‚ˆHi_hf€šbfOrR €’[¥b\OrS¦RTiH[žbS %u€‚SKvHb]q’ˆ_iHh\€‚b\OrR prhfSK[\Sv9b\S2sTOrShfS_œDNOrS

/;/ ',/ --“R8S2u)OQ]qvQ€’[\R h\S2sa^QuSK[bfOrS8v9^QR¨”0Shniq˜@RTSK[f[f]qˆ_S2[tS`au)O‡]qvrˆHSKs*€’v°b\OQS4+'c]q’ˆ_i_¡

hf€‚b\OrR*œ8Fªv—b\OQS8+':-—]q’ˆ_iHh\€‚b\OQR¬¿bfOrS8˜­]_u&bWbfOQ]Ib €’vr€‚b\€•]qD€’vHbfSh\¡¢o]qv°hfSK³9^rS2[eb)[n]qhfS†€’v9b\Sh)u&SKpab\S2s°”d

bfOrS ’iuK]q²u‚^Q[žb\SKh‚S2]_saSKh]q’‚iI§t[$bfiTsrSKu&hfSK]H[žS¦b\OQS v9^QR¨”0Shiq˜ˆ_’i_”‡]q¿RTSK[f[\]_ˆ_SK[Kœ

(20)

3 5 7 9 11 13 15 17 19

0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3

1500 1000 500 500 500

500 500 500 1000 1500

T im e ( s )

NaimiTrehel PreemptAgg Centralized Broadcast

ε β (ms)

α (ms)

)€’ˆ_^Qh\S6Er± iHRTpQ]qhf€’[\i_v]q’ˆ_iHh\€‚b\OrR ±DiH”abf]_€‚vQ€‚vrˆ8bf€‚RTS

3 5 7 9 11 13 15 17

0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3

1500 1000 500 500 500

500 500 500 1000 1500

T im e ( s )

Proxy PreemptAgg Preempt

ε α (ms) β (ms)

)€’ˆ_^Qh\STUK„Q± i_RTpQ]qhf€•[žiHv!]q’ˆ_iHh\€‚b\OrR ±Di_”ab)]q€’vr€‚vQˆ†bf€‚RTS

(21)

500 1500 0 15,157 14,41 14,999 14,401 12,846 17,983 16,276 500 1500 0 138 464 193 420 141

1 12,059 12,577 12,316 500 1500 1 346

2 11,159 12,355 12,009 500 1500 2 380

3 10,5 12,108 11,744 500 1500 3 421

500 1000 0 10,096 10,095 9,03 9,58 8,894 14,096 11,77 500 1000 0 206 339 212 330 285

1 8,297 8,717 8,414 500 1000 1 347

2 7,675 8,475 8,103 500 1000 2 379

3 7,205 8,382 7,878 500 1000 3 409

500 500 0 7,157 5,858 6,037 5,858 5,04 10,161 8,007 500 500 0 148 393 237 299 261

1 4,704 4,897 4,597 500 500 1 359

2 4,287 4,64 4,293 500 500 2 395

3 3,992 4,54 4,116 500 500 3 441

1000 500 0 5,246 5,657 4,694 5,134 4,57 9,725 7,746 1000 500 0 216 320 205 336 351

1 4,209 4,407 4,076 1000 500 1 384

2 4,225 4,25 4,044 1000 500 2 367

3 4,097 4,105 3,903 1000 500 3 406

1500 500 0 6,648 4,528 4,34 4,174 4,142 9,226 7,266 1500 500 0 125 468 269 322 278

1 4,119 4,09 4,145 1500 500 1 266

2 4,109 4,092 4,14 1500 500 2 261

3 4,114 4,091 4,146 1500 500 3 262

5,061 1,26525

0 100 200 300 400 500 600 700 800

N b m e s s a g e s

0 1 2 3 0 1 2 3

Proxy PreemptAggregation Preempt Broadcast

Global Local

Naimi-Trehel Centralized

720 2159

ε

)€’ˆ_^Qh\S8U_UH± iHRTpQ]qhf€’[\i_v]q’ˆ_iHh\€‚b\OrR ±@©t^rR†”‡SKhiq˜R8S2[\[f]qˆHSK[$S&`ru)OQ]_vrˆ_S2s

Ndp‡S



”rbf]qvQ€‚vrˆ†b\€’RTS!Ÿ­[)¤ m}_SKhf]_ˆ_S Niqb)]q ©t”*iq˜RTSK[f[\]_ˆ_SK[

];}HSh)]qˆHS [žbf]qv‡sr]qh)s pQ]qb\O pQ]IbfO ’iuK]q ˆ_’i_”Q]_

srS}€’]qb\€’i_v ’Svrˆ_b\O ‚SKvrˆqbfO

©¦]q€’R8€‚¡ªN~hfSOrSK zœ’U2yHz U_œµHyrU ƒaœµ9z …QUE UK…<D µEHµ „rœµE

g@hfi;`ad yaœDHy9D U_œ„rUB ƒaœµHy …QUK… ƒ_µ9z ƒ9E<E „rœDq…

„ Brœ„_µ9z U_œ’U;D<B …Qœ’U… zIµQU ƒBrU U;D9y U_œËyqµ

g@hfSSKRTpabfmcˆ_ˆ U …QœzI„q… U_œzqy9z …QœËy9B D_„<B µ9y9E U…9„ ƒaœËy9B

ƒ …QœËƒ9D9z ƒaœËƒ9B<E …QœËyqµ D_„_… µ<EHy U2ƒ_„ µrœµq…

µ µrœEEHƒ ƒaœËyHzqµ …QœBD Dq…9„ µ<EHy U2ƒ_„ µrœµq…

„ yaœDHy9D „rœEE<E ƒaœzqy …<D<B …9„Hƒ U;E<B ƒaœ’U_U

g@hfSSKRTpab U …QœDE9z ƒaœ„Hy_µ ƒaœBE …zqµ …BB U2ƒq… µrœz B

ƒ …QœBq…H„ ƒaœËyaUIz ƒaœBB …zq„ …az_z UK„<E …Qœµ9z

µ …QœËyI…H„ ƒaœDD_… ƒaœBHƒ …<BHµ …DHƒ z E Brœ’U2ƒ

SKvHbfhf]_‚€’™S2s U2„rœ’U;BQU U_œEDQU UHU;E µHy_µ „rœµq…

'$hfiH]_sQu]_[žb Drœ„_„9z U_œ„rU2„ z_ƒq„ ƒaU2yE „rœµ_µ

N]_”r’S›U_±,=^rRTR›]qhfd%iq˜S&`ap0Shf€‚SKRTSv9b§€šbfO

]qvQs

SK³9^Q]_’[b\i /1/1 +

(22)



vrS“];}I]qv9bf]_ˆ_S{i_˜b\OrS +' /;/ ',/ -- ]q’ˆ_iHh\€‚b\OrR €•[!bfOQ]Ib*ˆ_’i_”‡]qchfSK³9^rS2[eb)[]_h\S—vriqb

bfhf]_vQ[\R8€‚b\S2s°bfib\OrS›Ori9[eb §Or€•u)O¯OQ]_[nhfSK³9^rS2[ebfSKs{bfOrS%u&hf€‚b\€•u]q@[\SKu&b\€’i_v²œTNOrSKh\S˜ i_hfS_¬~]H[¦’i_vQˆ*]H[Wb\OrS

bfi_–HSv¶O‡]_[Tvri_b›]_h\hf€’}_SKs¶€‚v´]“u&’^Q[žb\Sh2¬¥vQi¯OQiH[žbf[T€’v bfOrS{u&’^Q[žb\Sh›–vriI§ b\OQ]qb%]—hfSRTi_b\S*OriH[žb›OQ]_[

hfSK³9^rS2[ebfSKsMb\OrSTbfi_–HSv²œiHvQ[žS2³9^rSv9b\’d_¬²b\OrS›v^rR†”‡SKhiq˜ '-. €’[nvQiqb’€‚RT€‚b\SKs“”d

”r^ab”d

§OrSKh\S:!€•[b\OQS$v^rR†”‡SKhiq˜‡OQiH[žbf[€‚v†b\OQStu&’^Q[ebfSh2œNOrS’iau]q’€‚bed R8S2u)OQ]qvQ€’[\Rw€’[RTiHh\S$S&`apr’i_€‚b\S2s

”Q^abb\OrS]_”Q[\SvQuSWi_˜[žbf]_h\}I]Ibf€‚iHv€•[prhfSK[\Shf}_S2sFœ

&~

®¯S8OQ];}_S8prhfSK[\Sv9b\S2s{€‚v—b\OQ€’[WpQ]_p‡SKhn]vrSK§ ]qpQprh\i9]_u)O*bfiiHpab\€’RT€‚™KS8R†^ab\^‡]qS&`ru&’^Q[\€‚iHvM]q’ˆ_iHh\€‚b\OQRT[

€’v°]%lnX4F# Sv}€‚hfi_vQR8SKRTSv9bKœ$NOrSR›]q€’v{€’srSK]T€•[b\i]_sr]_pabb\OrS†]q’ˆ_i_hf€‚b\OrR ]_uui_h)sa€’vrˆ8b\i›vrSbe§iHh\–

bfi_p0i_’i_ˆHd €‚v8i_h)saShbfinui_va£‡vrSR8i9[eb@ui_RTR¨^rvQ€’uK]Ib\€’i_v‡[~bfin€‚v9b\h)]I¡ªu&’^Q[žb\SKhKœ~NOQ€’[D€’RTprhfiI}_SRTSKvHb]q’‚iI§t[

bfiTi_pabf€‚RT€’™Snb\OQS i_”ab)]q€’vr€‚vQˆ†bf€‚RTS i_˜~b\OQSnb\i_–HSv*]IbbfOrS S&`ap0SvQ[\Sniq˜˜­]q€’h\vrS2[\[Kœ

NOr€•[¦”‡SKOQ];}€‚iHhc€•[cpQ]_hžbf€’u^r•]qhfd[\OriI§v{§€šbfO°bfOrS?+'?/ / ',/ --"]q’ˆ_iHh\€‚b\OrR prhfSK[\Sv9b\S2s

€’v¶[\SKu&b\€’i_vµrœËƒaœ¯mc[†§S!OQ];}_S![\SSKv"€‚v¶b\OrSp‡SKhž˜ iHh\R›]_vQu&S%SK}I]q’^Q]Ibf€‚iHvQ[¬bfOr€’[8]q’ˆ_iHh\€‚b\OQR ]_‚’iI§t[nb\i

srSKu&hfSK]H[žS[\€’ˆ_vr€‚£‡u]_‚’db\OrS†i_”ab)]q€’vr€‚vQˆ›b\€’RTS†§€‚b\O°hfSK[\p0SKu¸b¦b\i›bfOrS8iqb\OQSh¦]_‚ˆHi_hf€šbfOrR›[prhfSK[\Sv9b\S2s*”r^ab

[\p0SKu&€•]q’’d%§€šbfO > ' 4²iHh , - 4! 8›]q’ˆ_i_hf€‚b\OrR›[Kœ

I$

3‚U5 o¥œ‡o]qRTp‡iHhžb2¬\N€‚RTS_¬‡u&’iu)–a[K¬Q]qv‡s!bfOrSiHhfsaSKh\€’vrˆ8iq˜DS}HSv9bf[€’v°]Tsa€•[ebfh\€’”r^abfSKs{[\d[žb\SKR*¬ ', # /

#4)H799-8#16"-A?' *¬‡}_iH4œrƒaUH¬avriQœ‡za¬rprp²œ0y_y9DayBq…Q¬ $_^Q‚d°UE9z9Drœ

3ƒ 5l8œFX€•u]_hžbn]qvQsMmœFmtˆHhf];§]q•]r¬\mtv—i_pabf€‚R›]q]q’ˆ_iHh\€‚b\OQR ˜ iHh¦R†^ab\^Q]_S`ru&’^Q[ž€’i_vM€‚vMui_RTpr^abfSh

vQS&be§$i_hf–[K¬ '?' S', # #4)H7 > 7 16"-?'{¬r}Hi_CœQƒI…‡¬0UEDQU_œ

3µ95  œ =Fœ,)œ $]_h\}I]_‚Ori¯]qvQs·l8œ@Xi_^‡u]q€’hfi_C¬  v¶R†^ab\^Q]_S&`ru&’^Q[\€‚iHv¶€’v·ui_RTpr^abfShTvrSbe§iHh\–a[K¬

',9#$#4)H7 > 7$#1@"-?' *¬Q}_i_CœQƒ9BQ¬avriQœQƒr¬aprp²œ²UK…<B0U…az¬0U;E<D_µrœ

3…5 ‘ œ ‘ ]_S–I];§$]Q¬\m > ]_‚ˆHi_hf€šbfOrR ˜ iHhtR¨^rb\^Q]_²S&`ru&’^Q[\€‚iHv*€‚v°saS2u&SKvHbfhf]_‚€’™S2s[\da[ebfSR›[K¬ ?'

-9-9-$9 ', # + )H: 2:#8¸¬r}Hi_CœµQ¬rvri‡œQƒa¬aprp²œ~U…9y0U;y9Er¬ ‘ ];d°UEDHyrœ

3y 5@F¸œ =^r™K^r–€~]qvQs{Nnœ0? ]_[f]qRT€4¬ žmwsa€•[žb\hf€‚”r^rb\SKs*R†^ab\^‡]q~S`ru&’^Q[ž€’i_v*]q’ˆ_iHh\€‚b\OQR¬ ?'-9-/

> 78 ',9# +=)H 2 :#$2' I¬r}_iH4œrµQ¬avriQœa…‡¬aprp²œQµ_…_…µq…Er¬0U;E<DHyaœ

3B956?Tœ‡Xt];dR8iHvQsF¬\m.b\hfSS&¡¢”Q]H[žS2s!]q’ˆ_iHh\€‚b\OQR ˜ i_hcsa€•[žb\hf€‚”r^rb\SKsR†^ab\^Q]_FS&`ru&’^Q[\€‚iHv²¬ ?' -9- /

<> 7$ ' 9# +=)H 2 :#$2' I¬r}Hi_Cœrza¬rvri‡œFU_¬aprp²œ0BrU Qz_za¬‡UEDEQœ

3Ëz25

‘

œq©c]q€’RT€4¬

‘

œqNh\SKOrSC¬q]qvQs8mœqmch\vQi_•sF¬!\m ’i_ˆTŸ­©W¤sa€•[ebfh\€’”r^abfSKs†R¨^abf^Q]qaS`au‚^‡[ž€’i_v8]q’ˆ_i_hf€‚b\OrR

”‡]_[\SKs%iHvp‡]Ib\Oh\SK}_SKhf[f]qC¬#"H )H #1%$49 ! '&. > T)H: ', # + )H>!_¬a}_i_Cœaµq…‡¬9vQiQœ¿U_¬

pQp²œ²U ¿UKµQ¬0U2„Tmtprh2œFU;E<EBrœ

3D95 ‘ œ2o¥œK©tSK€‚•[\Sv]qv‡s ‘ œ ‘ €’™^QvriQ¬žmsQ]qˆq¡¢”Q]H[žS2s¦]_‚ˆHi_hf€šbfOrR6˜ iHhsa€•[ebfh\€’”r^abfSKsnR†^ab\^Q]__S`au‚^‡[ž€’i_v²¬

€’v#$* ! #1I"-)(!( "+* 0 9 9 9G',9,1 8 ,&. > T)H:7' 9# +=)H! 2 :#$

-* '.&&' I¬r®“]_[\Or€’vrˆqbfi_v²¬ ¦¬²U;E<ErUH¬9pQp²œQµHyq…aµB_„Q¬Fªk@k¥k i_RTpr^abfSh =iau&€’S&bedHœ

(23)

3E95@F¸œ OQ]qvQˆQ¬

‘

œ=€’vrˆ_OQ]_4¬H]qvQs

‘

œ9Nnœ_o²€’^²¬ žmcvT€‚RTprhfiI}_S2s¨’i_ˆ›Ÿ­©W¤R¨^rb\^Q]_QS&`ru‚^Q[\€’i_vT]q’ˆ_i_hf€‚b\OrR

˜ iHhsa€•[žb\hf€‚”r^rb\SKs [\da[ebfSR›[K¬€‚v $ ; ! * 1 "-( * 7: > ', ,1 4 '$49 !

$ ;!q¬0mt^rˆ‡œFU;E<E_„r¬prp~œ‡ƒ9E9y µH„Hƒrœ

3’UK„95@)$œ ‘ ^rSK‚’Sh2¬ eg@hf€’i_hf€šbf€‚™KSKs·b\iH–_SKva¡C”‡]_[\SKs·R¨^abf^Q]qWS&`ru‚^Q[\€’i_v´˜ i_hsa€•[ebfh\€’”r^abfSKs6[\da[ebfSR›[¬ €’v

$ ; ! 1#(" * 7: $4 !J$ ; A # +72 )H#

! # +9 $49 !JI9

&8. $ ;!q¬ ‘ ]qh2œFU;E<EDr¬prp~œ0z EQU rz9EHyrœ

3’U_U5IF¸œ OQ]qvrˆ‡¬ ‘ œ*=€‚vQˆ_OQ]_4¬$]qvQs ‘ œ¥Nnœ¥o~€‚^~¬ žm Od”rhf€’s·]qpQprh\i9]_u)O"bfi“R¨^abf^Q]qtS`ru&’^Q[ž€’i_v¶˜ i_h

sr€’[žb\hf€‚”Q^ab\S2sM[\d[žb\SKR*¬"€‚v$* ! #18!7+(-" * 7 )79 * 0 99 9B', # + )H:

#1 9 *++ > -9',9,1 &¬U;EEH„r¬prp²œQƒDEaƒ9E_…Qœ

3’U2ƒ 5nm¨œH(ti_^‡[žvr€¿]qv‡s ‘ œN~hfSOrSK4¬ ¦€’[žb\hf€’”r^ab\S2s›R¨^rb\^Q]_‡S`au‚^‡[ž€’i_v%”dTˆ_hfi_^QpQ[D”Q]H[žS2s›i_v›bfi_–HSv%]qv‡s

p0ShfRT€’[f[\€‚iHv²¬·€‚v $ ; ! N#1$!7?' * *7: > 9S' 9,1 N F', # + )H:

2 #889 *++ > -¸¬ $_^rvQS¨ƒq„_„QU_¬9prp²œ‡ƒBrƒ9Erœ

3’UKµ95no¥œ 'iH^rˆ_S8l8œ¿mcv9b\i_vQ€‚^M]_vQs =Fœ0o]_u&iH^rh2¬ ‘

]q–€’vrˆ!]3I=

‘

u&iHvQ[ž€•[žb\Sv‡u&dprh\i_b\iau&iH~Or€’Sh)]qh)u)Od9¡

];§]qhfS_±n]qv“S›u€‚SKv9b¨[ždvQu)Orhfi_vQ€‚™2]Ib\€’i_v—[\u)OrSKRTS_¬ €’v $* ! 1 !7 17+A &8. /

> )H--9 # P ' *) :¸¬Qƒ_„_„_µQ¬prp²œ‡yrU;Bry_ƒrU_œ

3’U…5no¥œqX€’™™i‡¬¦^rRTR¨dvrSbK±]¦[\€’R8pQ‚S]qprpQh\i9]_u)O bficbfOrSS}I]q’^Q]Ibf€‚iHv¨i_˜QvrS&be§$i_hf–nprhfiqb\iaui_•[¬<?'

',9# +=)H9', # #?)H0 > 7O D¬r}_iH4œQƒ9z¬avri‡œFU_¬aprp²œ‡µrU …QUH¬‡UEE9zaœ

¨¨¨

ŒK

Á  qŒ

Á

Ž ¾  ¼ ¼ "!‚‹†Ž 0Á  ­Œ #

%$ ¼ IŽaI­_Ž Ž 0Á  ­Œ ‹ &

µQœ‚U g¥h\i;`ad9¡C”‡]_[\SKs!]_‚ˆHi_hf€šbfOrR œnœ œnœ œ œWœ œnœ œnœ œ œnœ œnœ œWœ œnœ œ œnœ œnœ œnœ œ œWœ œ z

µQœƒ mcˆ_ˆHh\SKˆH]Ibf€‚iHv!]qv‡spQh\SKSRTpab\€’i_v*]q’ˆ_iHh\€‚b\OQRT[ œ œ œnœ œnœ œWœ œnœ œ œnœ œnœ œnœ œ œWœ œ z

#(' ¼  ¢Á  ¶Ž  ¼°¼) Ž ŽaŒÁ

+*

…‡œ‚U k¥};]_‚^‡]Ib\€’i_v*S`p0Shf€’R8SKv9bui_va£‡ˆ_^rh)]Ibf€‚iHv œ œnœ œ œnœ œnœ œWœ œnœ œ œnœ œnœ œnœ œ œWœ œ U;y

…‡œƒ XtSK[\^ršb)[t]qv‡s3¦€’[fu&^‡[\[\€‚iHv6œnœ œnœ œ œWœ œnœ œnœ œ œnœ œnœ œWœ œnœ œ œnœ œnœ œnœ œ œWœ œ UB

*(, Á  ‹ Á .-

(24)

Unité de recherche INRIA Rocquencourt

Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France)

Unité de recherche INRIA Futurs : Parc Club Orsay Université - ZAC des Vignes 4, rue Jacques Monod - 91893 ORSAY Cedex (France)

Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique 615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France)

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Sophia Antipolis : 2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex (France)

Éditeur

INRIA - Domaine de Voluceau - Rocquencourt, BP 105 - 78153 Le Chesnay Cedex (France)

Références

Documents relatifs

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334