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「マルチメディア通信と分散処理ワークショップJ 平成 1 1年 1 2月 AsynchronousRecoveryPr~tocol i nDistribut~d ObJect-sased Systems KatsuyaTanaka,HiroakiHigaki,and MakotoTakizawa “ TokyoDenkiUn i v e r s i t y h i g, tak i}@t 句a k 凶 i i 日 l a b . k . d e 吋 nd討 a i . a c . j E-mail{katsu, Wed i s c u s showt ω o凶 k ec h e 町c k 卯 po i n 旬i 泊 no , 凶 b j e c t ι もb a 嗣 . s e ds y s t e m s .l fsomeo b j e c ti sf a 叫t y , n o to n l yt h eo b j e c tb u t a . l s oo t h e ro b j e c 旬 w hichh a v er e c e i v e dm e s s a g e sfromもh eo b j e c ta r e 'r e q u i r e d色ober o l l e dba . c kt o出 ec h e c k p o i n t s . b j e c t ・ Weh a v ebeeni n t r o d u c e dac o n c e p to fobjed-basedc h e c k p o i n t swhicha r es e m a n t i c a l l yc o n s i s t e n ti n出 eo ba . s edsystemw h i l ei n c o n s i s t e I 叫 w i t ht h et r a d i t i o n a lm e s s a g e b a s e dd e f i n i t i o n .l nt h i sp a p e r, wep r e s e n 七a n a s y n c h r o n o u sa . lg o r i t h mf o rt a k i n go b j e c t ・b a s e dc h e c k p o i n t s剖 nongo b j e c t s . We8 o l s oshowar e s t 配色i n gp r o も o c o l も もh ecomput8ot i o na s y n c h r o n o u s l yw i ぬo t h e ro b j e c 旬. wheree a c ho b j e c tcanr e s t a r 1 I n t r o d u c t i o n D i s t r i b u t e d8 0 p p l i c a もi o n s8 0 r ecomposedo fm u l t i p l eo b j e c t sc o o p e r a t i n g by e x c h a n g i n g mess8og~s t h r o u g h communica . t i o nn e t w o r k s . Theo b j e c tp e r f o r mmetho d sont h eb剖 i so fもheremotep r o c e d u r ec 8 o l l . On .r e q u e s tm e s s 8 0 g ew i t h8 0methodD p , o p r e c e i p to fa i sp e r f o r m e don8 0 no b j e c t0 a J l d_ 8 0r e s p ol ! s e_ m e s s a g e w i t ht h er e s u l to fopi ss e n tb8 o c k .Themethodopm 8 0 y , no t h e ro b j e c t s, . ie .i n v o c 叫i o n so f i n v o k emethodso methodsa r en e s t e d . Thec o n f t i c t i n gr e l 8 o t i o n8 o mong e m a n t i c so fもh e t h emethodsi sd e f i n e db槌 edon七hes o b j e c t0 [ 4, 1 5 ] .I fap~ir o fmethodsOPlandOP2 c o n f l i c t, 七h es t 8 0 t eo f0 o b t a i n e dbyp e r f o r m i n gOPl 叩 d OP2d ependsont h ecomput8ot i o no r d e ro fDplandOP2・ Anapproacht omakingもhesystemf a u l t t o l e r8 o n t h出 品 e a . chobject0 t80kesacheckpointwherethe 同t ei ss 8 0 v e di nもhes t a b l es t o r a g el o go fo .l f0 i s s , 0i sr o l l e db a c kt ot h ec~ec~l?oint an4出 回 出e f a u l t y computationon0 i sr e s t 8 0 r もe d . l f0 i sr o l l e db8ock, o b j e c t swhichh 8 0 v er e c e i v e dm e s s 8 0 g e ss e n tby0h8 o v . e t~ b e -r o l l e dbacks ot h 8 0 tt h e r ei snoorpk , anm essage[ 2 ], . i e .m e s s 8 0 g e ss e n tbynoo b j e c tb u tr e c e i v e dbysome o b j e c も . P a p e r s[ 1, 2, 7, 9 1 1, 1 4 )d i s c u s showm u l t i p l eo b j e c t st a k eg l o b a l l yc o n s i s t e n tc h e c k p o i n t s . Kooand 司 presentsynchronousprotocolsf o r色 胞 a k i n Toueg [ 町c k p o i n 七 旬 sandr o l l i n gbackp r o c e s s e s . Leongand c h e Agrawal[ 9 ]p r e s e n tt h ec o n c e p t .o fs i g n 棋c a n tr e q u e s t s, i .e . もhes t a t eo f8 0 no b j e c ti schangedbyp e r f o r m i n g eo b j e c t0 i sr o l r e dback, o n l y0か t h er e q u e s t .l f吐l j e c t swhichh 8 0 v er e c e i v e ds i g n i f i c a n tr e q u e s t ss e n tby o8 0 r e8 o l s or o l l e db8 o c k . Thus,叫l enumbero fo b j e c t s i nt h e t ober o l l e db 8 0 c kc 8 0 nber e d u c e d . However, ・b 剖 e ds y s t e m s, d i f f e r e n tt y p e so fmess 8 o g e s, i .e . o b j e c t r e q u e s tandr e s p o n s em e s s 8 0 g e s8 0 r ee x c h 8 0 n g e d8omong 七h eo b j e c t s . l nt h ep a p e r[ 9 ],出et r a n s m i s s i o n so f r e q u e s 七sa ndr e s p o n s e s8 0 r en o tc o n s i d e r e dandi n v o c a t i o n so fmethodsa r en o tne 叫e d .S i n c et h ec o n s i s C h e c k p o i n t s8 0 r ed e f i n e di nむermso fm e s s 8 0 g e se x t e n t旬,ぬed e f i n i t i o ni sr e f e r r e dも0 槌 changedamongo b j e c m e s s a g e b a s e d . The8 o u t h o r s[ 1 3 ]de 五n eo b j e c ιbasedconsistent(0・ c o n s i s t e n t ) c h e c k p o i n t sw hichc 8 0 nbe同 kenb a s e don もh ec o n f i i c t i n gr e l 8 o t i o namongt h emethodsi nv a r i o u sk i n d so fi n v o c 叫i o n sl i k esy~chronous 8 0 n da s y n c h r o n 9 U so n e si no b j e c t b a s e ds y s t e m sevenもhough i もmayb e 'i n c o n s i s t e n tw i t h出 e .t r a d i t i o n a lm e s s a g e b a s e dd e f i n i t i o n . H i g a k ie ta t[ 5 ] d i s c u s s8 0 na s y n c h r o n o u sc h e c k p o i n t i n gp r o もo c o l i n出 em e s s a g e -b a s e d s y 叫 em , whereo b j e c 旬a.sy n c h r o n o u s l yn o to n l yt a k e 8 or t e d . I n theωyn ・ c h e c k p o i n t s but a l s oa r er e s t c h r o n o u sc h e c k p o i n t s, t h eo b j e c t s~onoも suspend d u r i n g出 ec h e c k p o i n t s . l nt h i sp a p e r, o b j e c t s i n g同 k 旬 b e c 8 0 u s eo b j e c t s町 e a s y n c h r o n o u s l yt 8 0 k ec h e c k p o i n r e q u i r e dもomorefrequentlyt a k ec h e c k p o i n t st obe h i g h l ya v a i l a b l e .Wed i s c u s showt ot 8 0 k e0・c o n s i s t e n t c h e c k p o i n t si n8 o n .a s y n c h r o n o u smannerbye x t e n d i n g h eo b j e c t ・b a s e ds y s t e m .By t h eH i g a k i ' sa l g o r i t h mもot t h e0・c o n s i s t e n tc h e c k p o i 川 町 出en umbero fc h e c k k e nbyo b j e c 旬 c 8 0 nQer e d u c e d . p o i n t s七a wef i r 凶 p r e s e n も もh esystemmode l .I n I ns e c t i o n2, s e c t i o n3, wed i s c u s sぬei n f l u e n t i 8 0 lm e s s 8 0 g e sandd e ・ f i n et h eo b j e c t b a s e dc h e c k p o i n t .l ns e c t i o n s4 ' a n d5, weshowap r o t o c o lf o rt a k i n g0・c o n s i 凶e n tc h e c k p o i n t s 同. r t i n gt h eo b j e c 回. andr e s 2 SystemModel 2 . 1 O bjects Ad i s t r i b u t e ds y s t e mi scomposedo fm u l t i p l eo b j e c t s . Eacho b j e c色 oi sane n c a p s u l a t i o no fd a t aandac o l l e c t i o no fm e t h o d s .l nぬi sp a p e r, weassumemethods a r es y n c h r o n o u s l yi n v o k e dbyu s i n gt h er e m o t ep r o ・ c e d u r ec a l l . Onr e c e i p to far e q u e s tm e s s a g em w i t h opi sp己r f o r m e dont h eo b j e c 七o .Then, amethodop, t h er e s p o n s em e s s 8 0 g ew i t hむh e r e s u l もo fopi ss e n tba . c k . u 凶h ermorei nv o k emethodson Themethodopmayf o t h e ro b j e c旬 ,. ie .i n v o c a t i o no fopi sn e s t e d . Am e s s 8 0 g emis8 0 no1'ph. a ni f fm i sr e c e i v e db叫 no も s e n ti nt h es y s もe m.A c o n s i s t e n tg l o b 8 o lc h e c k p o i n ti s d e f i n e d七obeonewhereもh e r ei snoorphanm e s s a g e[ 2 ] . t h esystemi sreferredω 剖 ~essage-based s i n c e H e r e, 8 o t i o ne a . chm e s s a g ec 8 o r i ti sn o td i s c u s s e dwhati n f o r m r i e s .I nF i g u r e1 , 8 0p a i r o fo b j e c も So ia nd0; t a k el o c a l ', r e s p e c t i v e l y , ando is e n d sames c h e c k p o i n t sc '叩 dc s a g em も0 句・ l nF i g u r e1 ( 2 ), ag l o b a lc h e c k p o i n t( c ', d)i si n c o n s i s もe ntb e c a u s em i s叩 o r p h a n . , 2 . 2 Typeso fmethods L e to p (s )denote8 0脚 色 eo b t a i n e d byp e r f o r m i n g8 0 methodopon8 0s t a t e so f8 0 no b j e c to .o p l a O P 2m e 8 0 n s t h 8 0 t8 0methodOP2 i sp e r f o r m e da f t e rDpl c o m p l e t e s . Ap 8 0 i ro fmethodsOPl and叩 2o f8 0 no b j e c t0 a r ec omp a t i b l eπ i OPl。 明 ( s ) OP200Pl( s )f o re v e r ys t 8 0 t eS o f o n f t i c ti f fもhey8 0 r en o tcomp 8 o t i b l e . o[ 4 ] .Dpl刷 物 c 色os u p p o r t stwok i n d so fmethods , . ie :8 0 n Ano b j e c u p d a t emethodwhichc h a n g e st h e 's t a t eo f0 and8 0 non-upd . a t eo newhichd o e sn o tchange色hes t a t eo fo . -73ー , , = F o rex 田n p l e, d e p o s i to faB a n l co b j e c ti sanupdate h e c l ci sanon-updateo n e .I nt h i sp a p e r, method嗣 dc we槌 sumet h a tt h et y p e so ft h emethodsa r es p e c i f i e d w i t ht h ec o n f l i c t i n gr e l a t i o namongt h emethodsi nt h e b j e c t . d e f i n i t i o no fもheo 吋i c i po . t e si name もh od01'i fm i sa A messagem pa r e q u e s to rr e s p o n s eo f0 1 ' .L e tOp(m)d e n o t eamethod i nwhichm p a r t i c i p a t e s .Ano b j e cも0 s e n d sar e q u e s t もh e ro b j e cも0 ;・Onr e c e i p to fmltO P 2 mlo fop2もoano i sp e r f o r m e don町 ・ L e top~ d e n o t e細 川αnceo fa methodO1'~, i .e .computationo fOPc Ii nOh・Theo b j e c t 句 s e n d sar e s p o n s em2o fo~ t o0. ,Here, mlandm2 p a r t i c i p a t ei n。 局 ,i . e .Op(ml) Op(向)=例. 0 ; 4 O 1 ' l ι1. , 弓 官 , 向 0 . ; ・-c O3 . o i . J u t = 3 d t i m e F i g u r e2 :P o s s i b l ec 旬. h e c k p o i n 色i me ( 1 )C o n s i s もe n t ..( 2 )I n c o n s i s t e n t 同:c h e c k p o i n t F i g u r e1 :M e s s a g e b a s e dc h e c k p o i n t s . 3 O-consistentCheckpoints Wed i s c u s swhatt y p e so fc h e c k p o i n t scanbet a k e ni n t h eo b j e c t b a s e ds y s t e m . 3 . 1 Message-basedsystem , Ano b j e c t0 t a k e sal o c a lc h e c k p o i n tc 'wheret h es t a t e ss t o r e di nt h el o g1( i 1 , , . n).If七heobject o f0 i o ii sf a u l もあ向 i sr o l l e dbackt ot h el o c a lc h e c k p o i n も c 'byr e s t o r i n gt h es t a t es t o r e di nt h el o g Then, o t h e ro b j e c 旬 h avet ober o l l e dbackt ot h ec h e c k p o i n t s i ft h e y hadr e c e i v e dm e s s a g e ss e n もb yO i . Ag l o b a l sat u p l e( c1, . . . , ♂ )ofthel o c a lc h e c k c k e c l c p o i n tci p o i n t s . Fromh e r e, atermc h e c l c p o i n tmeansag 1 0 6o . 1 o n e .I fano b j e c tois e n d samessagem b e f o r eもa k i n g c 'b u ta n o t h e ro b j e c t句 r e c e i v e sm a f t e rt a k i n gc ', m h e c k p o i n tci sc o n s i s t e n tぜ t h e r e i sanorphan. Thec tc .T h i sd e f i n i t i o ni sr e f e r r e dも0 剖 i snoorphan問 a message-basedc o 悶 i s t e n 古c h e c l c p o i n t .I nF i g u r e1 ( 1 ), t h ec h e c k p o i n t( c ', c 1 )i sc o n s i s t e n tw i t ht h em e s s a g e もi o n .I nF i g u r e1 ( 2 ), ( c "c 1 )泊 i s i n 。 c ∞nsis色旬e 町 加n b a s e dd e f i n i b e c a u s em i sano r 抑制・ P a p e r s[ 1 3, 9 , 1 1 ]d i s c u s show t o同 k ec o n s i s t e n tc h e c k p o i n t si n出 emessage-bωed s y s t e m . , ,= . i ' nF i g u r e2 . . . , o~ ,} i . 町(叩~, c { )={OE恥 We d i s c u s sw rn h e t h e ro o te a c hc h e c k p o i n t( 4, d , . )canbetakenintheobject・b踊 edsystem. The もc も cmayb c o n s i s t e n h e c k p o i n 0・ ei n c o n s i s t e n tw i t h もh 回 e em e s s a g e b dd 七 i o n .F o rexample, e f i n i ec h e c k 七h p o i n t s( d a )and(c 4, , l ~)釘e message-basedIncons i s t e n ti i g u r e2 .I sn nF f場 i o n u p d a t e, もh e伽 旬 d e n o t e dby~. i st h esamea s~ and~. Thati s, ( c 1, 伽 a n d s h o w t h e t e s a m e 倒 的 , Th c { ) ( 弓 , ~) ~)・ c h e c k p o i n t( sc o n s i s t e n t wi 七ht h em朗 s a g e 弓 , ~) i b a s e dd e f i n i t i o nb e c a u s eもh e r ei snoo r p h a n . Hence, t h eo b j e c t0 a nber e s t a r t e d合omanyo ft h el ;c o c a l c h e c k p o i n t s~ andd.tぜ句 c a nb er e s t a r t e dfrom~. A 1 c h e c k p o i n tc ( , . cn)i so b j e ct c -6 t lc o n o i o t e n t , tUe ・c o n s . i dent)i v e r yo f fe b j e c to ( 0 a nber o l l e dbackもo ic t h el o c a lc h e c k p o i n tc nc 'and出e a nb e目 前a r t e dfrom i o b j e c tp cfrom七h o i n to fv i e w .( c 1, ~) and , ~) : c も areO ・c o n s l s e n t . I f叫 i sanupdateもype, ( c sn o t0・c o n s i s t e n t , l ~) i b e c a u s eO~ mayh a v echangedt h e脚 色ea td H i s 0 ; a . r o l l e dback色oc su n d o n e .Supposet h a t0 a k e s ;t i, O 1 ' ii w h e r e i s 剖 p a r t i a l l y p e r f o r m e d s h o w n i n F i g u r e o~ ~ 2 . 叫 旭 町u i r e dt obea b o r t e dw h i l eo t h e rmethods b e i n gp e r f o r m e da t~ mayn o th a v et obeu n d o n e . = < 4 同町 C1 ー ~.,~ c 2 ~.,~ 4 4 4 3 . 2 0b j e c t -basedsystem Supposeamethodo p li nano b j e c t町 i n v o k e s停 2 h b j e c t0 a n o t h e ro ;・Figures2showsapairofpossible b j e c t s h e c k p o i n t s4andc obet ' l o c a lc a k e ni nもheo ht e s p e c t i v e l y . Here,let 可(~戸, c nd0 e t ;,r 1 )beas o ia o fmethodswhich • p r e c e d eザ and • s h e c k p o i n tc 1o u c c e e dal o c a lc ra r eb e i n gp e r ・ 七c formeda 1i n句、. C o n d i t i o n s 叫 sn o n u p d a t e . 停~ i i s ' n o n u p d 蹴 . ~ 句 m 駒 d ) Mch i d i哨田 , 式d n s巧 o h n m o a d i d ( hm ws sn o n u p d a t e . ~,~. I 坐 i T a b l e1 O D s i s t e n tchec~points f o rF :0・c i g u r e2 . y p e so fl o c a lc Therea r e色wot h e c k p o i n t s i . e . com, i p l e t eand初 c o m p l e t eo n e s . Al o c a lcheckpoin~ c i s o .methodb 旬 i comple e r ei sn fもh e i n gp e r f o r m e da tci • n c o m p l e t e .F 0もh si o rexample, e r w i s e, c 'i si n c o m c~ i upp08eぬeo p l e t ei i g u r e2 nF .S b j e c t .0 sr o l l e dback ;i 同e c o n s i n tc h e c k p o i n tc t oan0・ sc o m p l e t e, k :If i -74- c t t h es t 抗 eo f句 i sj u s tr e s t o r e dfrom出 el o g . .I f~ i s もh emethodsb e i n gp e r f o r m e da t~ h a v e i n c o m p l e t e, t a t ei sr e s t o r e d .However, no t ob ea b o r t e da f t e r出 es methodi nv o k e dbyぬemethodsa b o r t e di sr e q u i r e d t ob er o l l e dbacks i n c et h emethodsa r en o n u p d a t e . ec h e c k p o i n t( e i, d a )whend ai si n L e tu sc o n s i d e rもh r er o l l e dbackもoc land c o m p l e t e .SupposeOiand句 a , 4 t respectively. Sinceo~ i sa b o r t e donr o l l i n gb a c k t od g,匂 i sf i n a l l yr o l l e dbackもoas t a もed e n o t e dby~. (ι~) i sc o n s i s t e . n t . Hence, ( c i, d g )i s0・c o n s i s 悦n t . (c~ , t 4 )and( c 1, G )arealso0・consi凶 ent. L e tu sc o n s i d e rcheckpoi附 (C~ , ~), (c~ , ~), and (c~ , ~) w hicha r em e s s a g e b a s e di n c o n s i s t e n t .I f叩 4 i sn o n u p d a t e, ~ d e n o t e st h esames t 抑 制 Gs i n c e 例 doesnoも changethe叫 a t e . Hence ,(c~ , ~) i s0・ c o n s i s t e n ts i n c e(c~ , G )i sm e s s a g e b a s e dc o n s i s t e n t . H e r e, s u p p o s et h a t~ I sr e a .dandt h e r ei ssomew r i t e 叫 h preceding叫 卸dfollowingc { . 。 品 readsdata c {deno七e sas 七a t ed i f f e r e n t w r i t t e nby喝 h・ Hence, .Ifnomethodfollowingc {andpreceding叫 fromG c o n f l i c旬 w i t h0品 , o~ sendsthesameresulteveni f 叫 i sp e r f o r m e db e f o r e叫 1 ・H ence, i f場 i sn o n u p d a t eandc o n f l i c t sw i もhn omethodi nt h eseも宥J(O~ , c i )ofreq印 刷 ,(c~ , c { )i sO c o n s i s t e n t . (c~ ,~) i s a l s oO c 。 ∞nsi 泊 s も 旬 e 町 加n 乱 l i n c o m p l e t e . Ta b l e 1summarizes 出 h eme 伺s 回s 胞a 伊 g e b 踊 e 吋d i n 。 c ∞n 悶s i 泊 s s 七 同 e 叫 n も b 叫 u も 1 泊 O -c ∞ o n 四 s i 恒 s t 旬e 叫 n も l 凶 c h e c k p o i n 旬 , w herec h e 侃c k p o i n 色 旬 m a 釘 r . r k e ♂ dキ 釘 卸ei n c o “ 凹 [ Def 貧 i n 耐i 託 悩 t i 加 。 叩 n ] 阿Su即 p p。s 田 卿 e色出 h 加 伽 a 叫 も 叩叫~ s e n d samessagem t o op~ i nano b j e c t0 ; .・L e tc 'b eal o c a lc h e c k p o i n tmost t 1ytakenbyt h eo b j e c t0 & . Them essagem i si n r e c e n f l u e πt ia . li f fo n eo ft h ef o l l o w i n gc o n d i もi o n si ss a t i s f i e d : 1 .I fm i sar e q u e 凶 me 嗣 ,g e, amethodOp(m)(= 叩 , 1 )i su p d a t e . Op(m) (=叫)i s 2 .l fm i sar e s p o n s emessage, d )conflicts u p d a t eo rsomemeもhodin向 (Op(m), w i t hOp(m). I famethodop;.i sa b o r t e d, o n l ymethodsr e c e i v i n gi n r er e q u i r e dt obea b o r t e d . f i u e n t i a lm e s s a g e sfromOPia c o n F o l l o w i n gt h ee x a m p l e sd i s c u s s e dh e r e,O 七sa r ed e f i n e d槌 f o l l o w s . s i s t e n tc h e c k p o i n c1,. . . , ♂ )i s [ D e f i n i t i o n ]A g l o b a lc h e c k p o i n tc=( o b j e c t b a s e dc o n s i s t e n t(0 ・c o n s i s t e n t )i f f七h e r ei sno i n f i u e n t i a lorphanmessage叫 c .口 , . . co)i sassumedt obec o n s i s 加 l t .A f t e rs e n d i n g andr e c e i v i n gm e s s a g e s, 0 &t a k e saf i r s tl o c a lcheck~ p o i n tc i . Thus, t a k e st h et t hl o c a lc h e c k p o i n tc ; a f t e rt a k i n g七he( t 1 ) t hl o c a lc h e c k p o i n tC i l( t>0 ) . Thecommunicationbetween 1andc~ i sr e f e r r e dt o 栂 c k e c k p o i n t飢 t e r va .l1 ; 1 'Int h ei n t e r v a l, ; 1 0;.sends andr e c e i v e sm e s s a g e s .H e r e, tdenotesacheckpoint numbero fc~. Thec h e c k p o i n tnumberi si n c r e m e n t e d byo n ee a c ht i m eal o c a lc h e c k p o i n ti sもa k e n .Suppose Oi a 叫o nomouslyt a k e sas u c c e e d i n gl o c a lc h e c K p o i n t c~ a f t e r同 k i n gc~_l ・ Then, o n l yi fもh e r ei sam e s s a g e m wh i c h0 s e n d sもoano も h e ro b j e c t0;, mi smarked c h e c k p o加 t e d .Bys e n d i n gm, t h eo b j e c t0 &n o t i 貴e st h e a k e sc~. Thus, Oi d e s t i n a t i o no b j e c t so fm t h a t0;. t d o e sno 色s e n 4anya d d i t i o n a lc o n t r o lm e s s a g eもor e ・ q u i r eo t h e ro b j e c 胞 もot a k el o c a l .c h e c k p o i n t s .H e r e, s u p p o s et h a tal o c a lc h e c k p o i n t~-1 i st a k e ni nt h e o b j e c t0 ;andac h e c k p o i n t( c L 1 1~-1) i sc o n s i s t e n t . Onr e c e i p to ft h ec h e c k p o i n t e dm e s s a g em from0 "the a k e sal o c a lc h e c k p o i n t~ a twhich0 ;s a v e s o b j e c t匂 t もh es t a t ewhichi sj u 同 b e f o r er e c e i v i n gm. I ti s .c l e a r t h ec h e c k p o i n t (c~ , ~) i sc o n s i s も e n tfromt h ed e f i n i t i o n .Then, s u p p o s e0 ;s e n d sam e s s a g em't o叩 o t h e r sa l s omarkedc k e c k p o i n t e d .Onr e c e i p 七 o b j e cもOle・m'i o fm, O l et a k e sal o c a lc h e c k p o i n ti n出 es 剖n eway回 0 ; .Thus, e a c ho b j e c t同 k e sal o c a lc h e c k p o i n toni t s 叫i n g吐l ec h e c k p o i n t i n gp r o c e d u r eo rar e c e i p to f i n i t i ac h e c k p o i n t e dm e s s a g e . " 0 c : _ , 4 . 2 O-consistentcheckpoints Ano b j e c t0 &m anipula もe sv a r i a b l e sC P l, ・ , C]Jn 色。 i d e n もi f yal o c a lcheckpoinも c~. Eachv a r i a b l ei si n i t i a l l yO .I f0 t a k e sc~ , t h ec h e c k p o i n tnumbercp i s i n c r e m e n t e dbyo n e, i .e .C P i: =C P ; .+1andt=C P i .A m e s s a g em wh i c h0 s e n d st o0; a f t e r同 k i n gc 1c a r r i e s av e c 旬ro fc h e c k p o i n tnumbersm.cp=(m.cpl'・ , m.cp π ), wherem.cp 1 : C P : 1( k 1 , . , n). Onr e c e i p to fam e s s a g em fromano もh e ro b j e c t 句 , a no b j e c t0 c h a n g e sav a r i a b l eC .町i.e . CPj := m . c p j・Thus, i nt h eo b j e c 七, i O cp showsacheckpoint a k e smo 同r e c e n もl yand明 showsa numberwh i c h0 t newes もc h e c k p o i n tnumbero fa n o t h e ro b j e c 色町 w h i c h 0 k nows( j= 1, . , n, j: f ;i ) .・ I 'ha もi s, 0 k nows 抗 ( C ! p l '.,. c.~pJ i sac u r r e n tc h e c k p o i n t .I fm . c p j t h >. c p ;i n0 " 0 findsむhat0 hasもakenasucceeding c h e c k p o i n tc ' uwhereu m.cp;. A checkpointc~ i s i d e n t i f i e dbyac h e c k p o i n tv e c t o r(C~.CP1 , ・.', c~.cPn) w h e r ec 1 . c p ;s howsav a l u ew h i c hc p ;h a st a k e nwhen c~ w ω 胞 ken( j 1, . ,n ) . Al o c a lc h e c k p o i n tc~ h槌 abitmapc~.BM (BM , t , . . B Mn). Supposeanobject0& i n i 七i a t e sac h e c k p o i n t i n gp r o c e d u r ea f t e rt a k i n gC 1 1andもhen, 0 , , , = , , , , , , = = = , , = , 4 CheckpointingProtocol Wed i s c u s sanωynchronousp r o もo c o lf o rt a k i n gc h e c k p o i n t samongo b j e c t s . 4 . 1 Basicprotocol l nt h ea s y n c h r o n o u sp r o もo c o l,e a c ho b j e c t0 ; .i s舗 sumedt oi n i t i a l l yt a k eal o c a lc h e c k p o i n tc~ wheret h e ; .i s t a k e n . Ani n i t i a lc h e c k p o i n t( c a, i n i t i a ls t a t eo f0 -75- c h e c k p o i n t i n gp r o t o c o li n i t i a t e dbyasameo b j e c t . [ D e f i n i t i o n ]Ap a i ro il o c a lc h e c k p o i n t sc~ and~ a r e i nt h esamegenerationi ic~.BM nct.BM= Fゆand c~ . c p l : ~. c p l :f o re v e r yo b j e c t01 cs u c h色h a tc~.BM1c ct.BM l : 1 . ロ S i n c ei ti sc l e a rt ha . tもh e r ei snoorphanm e s s a g ei n t h esameg e n e ra . t i o nc h e c k p o i n t, t h ei o l l o w i n gt h e o r e m h o l d s . [Theorem]A c h e c k p o i n tcomposedo isameg e n e ra . t i o nl o ca . lc h e c k p o i n t si sc o n s i s t e n t .ロ Eacht i m eano b j e c t0 s e n d sam e s s a g em, as e q u e n c enumbers qi si n c r e m e n t e dbyo n e .I n a d d i t i o n, as u b s e q u e n c enumbers s q ;i si n c r e m e n t e dbyo n ei fm i ss e n tt oano b j e c t0 ;( j= 1, . . ,. n).Themessagem e q u e n c enumberm .sqandav e c t o ro ft h e c a r r i e sもhes s u b s e q u e n c enumbersm . s s q=( m . s s q l, , . m.ssqn . ) . Ano b j e c t0 ;m a n i p u l a t e sv a r i a b l e sr s q l, ・ , rsq. nand r s s q1!・ , rssqntoreceive.messages.Onreceiptofm from0 "O jr e c e i v e sm i fm .ss 町 =r s s q +1 . Th a . t 0 ;de 1 iv e r sm e s s a g e sf o re a c ho b j e c ti nt h es e n d i n g i s, s s 前 +1a ndr s q :=m . s q . o r d e r . Then,何時:=r s q showas u b s e q u e n c enumberands e r s s q iandr q u e n c enumbero fm e s s a g ewhich0 ;h a smos もr e c e nt 1 y i , r e s p e c t i v e l y . r e c e i v e dfromO も Them e s s a g em a l s oc a r r i e sav e c t o ro ft h er e c e i p s e q u e n c enumbersm.r q=( m .r q l, ・ , m.rqn . )wh e r e m . r q1 c r s q l c( k 1, . ,n ) . Here, m.rq1 cs howsa s e q u e n c enumbero fm e s s a g ewhich0 r e c e i v e s告om 0 ;j u s tb e f o r et a k i n gt h el o c a lc h e c k p o i n tc~ andt m.cp ( k 1, ・ ・ ・ ,n ) . Onr e c e i p もofmf rom0 "t h eo b j e c も0 ;c o l l e c t sas e も 崎 o fm e s s a g e smj1J . , m;l;whichο;hassentもoOi a f t e rt a k i n gt h ec u r r e n tl o c a lc h e c k p o i n t~-1 and0 h a sr e c e i v e db e f Q r et a k i n gc~. Here, mjh・ s q: 5m.r町 [ F i g u r e3 ] .MessageswhichO js e n d sa f t e rt a k i n g~-1 a r es t o r e di nt h es e n d i n gl o go f0 ; .Suppose0 ;r e c e i v e s I fm.cPi>C 1 ' i ,0 ; ac h e c k p o i n t e dm e s s a g em fromO j・ knowst h a to it a k e sanewc h e c k p o i n 色c l .0 ;c o l l e c t s e n ta f t e r~-1 and e v e r ym e s s a g em'which句 h舗 s m ' . s q<m.rs 匂 ・ M;i sas e to ft h em e s s a g e sc o l l e c t e d h ed e f i n i t i o n, i もi sc l e a rf o rt h e h e r e .A c c o r d i n g七ot f o l l o w i n gtheoremt oh o l d . = = = , = , ,= , 0 句 ( 5, 3, 8 ) t i m e F i g u r e4 :C y c l i cc h e c k p o i n t s . = , C t D2 , , , = Thec o n d i t i o no ft h et h e o r e mi sr e f e r r e dtoω 飢i f l 包e n t i a l . m e s s , og e(1M)cond~tio_n_. I fatle~t oneoithe m e s s a g e smjl, . , mj';i sd e c i d e dt obei n f l u e n t i a la c c o r d i n gt o色h e .1Mc o n d i t i o n s, もh e o b j e c t0 ;泊 k e sa 1 0 ω 1checkpoint.~ s h o w i n gas t a t eo fj u s tb e f o r er e e r w i s e, O jd o e sn o t同k eal o c a lc h e c k c e i v i n g .m.0もh . m;; ,a r eo r p h a n ss i n c eもhey p o i n te v e n .i fm j 1 ', h e c k p o i n t~, t h e a r en o ti n f t u e n t i a l . If 匂 ~akes ac si n c r e m e n t e dbyo n ei n0 ; . c h e c k p o i n tnumber明 i M e s s a g e swhich0 ;s e n d sa f t e rt a k i n g~ a . r emarked c h e c / c p o i n t e dωpresentedh e r e . O j ~-1 4 . 3 C y c l i ccheckpointing Supposet h e r ea r et h r e eo b j e c 旬 0 1, 0 2, and0 3w h e r e C P 1, C P 2, c 拘)i s( 4, 2, 7 )i ne a c h ac h e c k p o i n tv e c t o r( も[ F i g u r e4 ] .Supposetheo b j e c t0 1t a . k e sal o c a l o b j e c c h e c k p o i n tc l .0 1s e n d sac h e c k p o i n t e dm e s s a g em1 2 , 7 )t o0 2a f t e r色a k w i t ht h ec h e c k p o i n tv e c t o r( 5, hgc i .句 t a k e sal o c a lc h e c k p o i n tc lonr e c e i p もo f mlw h e r ec ; . c p= ( 5, 3, 7 ) . Then, 0 2s e n d sac h e c k p o i n t e dm e s s a g ef f l 2w i 凶作, 3,7 )t o句・ Onr e c e i p も ofm ゎ0 3t a k e s~ ands e n d sac h e c k p o i n t e dme 蹴 g e 3, 8 )もo0 1・ H e r e, e v e ni f0 1r e c e i v e sm3, m3w i t h( 5, 0 1d o e sno もn e e dt oもa k eal o c a lc h e c k p o i n もb e ca . u s ea c h e c k p o i n t(c~ , c l, c~) もaken a l r e a d yi sc o n s i s t e n t .I f , t h eo b j e c t s0 1, 0 2, 叩 d0 3c a n n o tt e r 0 1t a k e sc Ah e r e ec h e c k p o i n t i n gp r o c e d u r e .T h i si sac y c l i c m i n a t eもh c h e c / c p o i n t i n g . Wed i s c u s showt or e s o l v e出 e _ c y c l i cc h e c k p o i n t i n g . I nF i g u r e4, t h eo b j e c t0 1s e n d s句 ac h e c k p o i n t e d C P ( 5, 2 , 7 )andm1・ BM= m e s s a g emlw i t hm1・ ( 1, 0, 0 )a f t e rCP1 i si n c r e m e n t e dand凶 k i n gc~. On 色o fm1, c p ( 5, 2, 7 )i n0 2・Then, 0 2s e n d s r e c e i p m2w i t hm2・ op ( 5, 3, 7 )andm2.BM ( 1, 1 , 0 )t o 0 3a f t e rt a k i n gc~. Onr e c e i p to fmぁ o atakesalocal c p ( 5, 3, 8 ) c h e c k p o i n tc landt h e ns e n d sm3w i t hm3・ andm3.BM ( 1, 1 , 1 )も0 01・ When0 1r e c e i v e sm3, 0 1 : k nowst h ec h e c k p o i n t i n gp r o c e d u r eW~ i n i t i a t e dby0 1 m 3 . C P l= 5b e c a u s ec h e c k p o i n t si d e n t f f i e d s i n c eC P 1= 2, 7 )and( 5, 3, 8 )a r ei n七h esameg e n e r a : もi : e m. by( 5, Onr~~eipt o fa _che~pointed m e s s a g em froman ・ o t h e ro b j e c t0 ;, ぬeo b j e c toi d o e sn o tt a k eal o c a l checkp~nt i fm.cps~ow~ a .Ba~e g e n e r a t i o nc h e c k p o i n t a s0. ,Here, o im a n i p u l a t e sもh ec h e c k p o i ntv e c t o rc p andもh ebitmapB M槌 f o l l o w s : l :: =max(cpl :t m .cp l : )i fm.BM 1 c=1 . • C P = = = d u = t i m e F i g u r e3 :I n f l u e n t i a lm e s s a g e s . [Theorem)Am e s s a g emjhi nM;i si n f t u e n t i a li ft h e f o l l o w i n gc o n d i t i o n s h o l d : 1 .m;h卯 i su p d a t ei fT J : I . jh .i sar e q u e 凶 , o r 2 . m;h・ opi su p d a t eo rc o n f l i c t sw i t hsomeu p d a t e m j h・ op , ~-1) ぜ m;h. i sar e s p o n s e . methodi n巧 ( 口 -76ー = = O a c 02 内 a宮a 01 a c i a • B M:=B MU m.BM. Thec h e c k p o i n tv e c t o rcpandt h ebitmapB Ma r e s a v e di nぬel o go n l yぜ色,heya r eu p d a t e d . 4 . 4 Mergeo fcheckpoints Next, s u p p o s et h e r ea r ef o u ro b j e c 旬 01, O~h 03, and 0 4剖 showni nF i g u r e5 . Here,e v e r yo b j e c th剖 a c h e c k p o i n もv e c t o r( 4, 3 , 7 , 2 ) .Suppose出 品 t h eo b j e c t s 0 1 and0 4i n i t i a t e七h ec h e c k p o i n t i n gp r o c e d u r e . 0 1 s e n d sac h e c k p o i n t e dmessagem1a f t e rもa k i n gal o c a l c h e c k p o i n tC lwithcp (5, 3, 7, 1 )andB M ( 1, 0, 0, 0 ) . Onr e c e i p to fml, o:a凶k e sal o c a lc h e c k p o i n t C~ andt h e ns e n d sac h e c k p o i n t e dmessagem2w i t h cp ( 5, 4, 7, 1 ) andB M ( 1, 1 ,0,0). Onもhe o t h e rh剖叫 0 4t a k e sal o c a lc l 悶 k p o i n tc~ w i t hc p= ( 4, 3, 7, 2 )andB M ( O, 0, 0, 1 )andt h e ns e n d sa c h e c k p o i n t e dm essagem4t o0 3・Theo b j e c to atakes al o c a lc h e c k p o i n tC~ w i t hCp ( 4, 3, 8, 2 )andB M ( 0, 0, 1 , 1 )andt h e ns e n d sm3も002・Theo b j e c t0 2 r e c e i v e sm3wi 七hC p ( 4 , 3, 8, 2 )andB M ( 0, 0, 1, 1 )from句 a f t e rt a k i n gc ;w i t hcp ( 5, 4, 7, 1 ) .0 3 r e c e iv e sm2wi もhc p ( 5, 4, 7, 1 )andB M ( 1, 1 , 0, 0 )a f t e rt a k i n g~ wi 七hc p ( 4 ,3, 8, 2 ) . Onewayi s 七h a も0 2and句 ぬkel o c a lc h e c k p o i n t sC~ w i t hcp ( 4, 5, 8, 2 )andB M ( 0, 1 , 1 , 1 )組 dc~ w i t hcp ( 5, 4, 9, 3 )andB M ( 1, 1 ,1, 0 ) . Byu s i n gぬi smethod, もh eo b j e c t s01, 02, 03, and0 4t a k eもwocl 悶 k p o i n t s(c~ , c i, d,c;)and(c;,Ci,ci,ci).Here,suppose出 品 04 sr o l l e dback七oc~. i sf a u l t y叩 di I no r d e rt or e d u c et h enumbero fc h e c k p o i n t st a k e n we凶 k e s叩 approachもomergingm u l i n出 esystem, b j e c t0 2 t i p l ec h e c k p o i n t st oo n e .I nF i g u r e丸 山eo r e c e i v e sac h e c k p o i n t e dmessagem3a f t e r同 k i n gt h e twoc h e c k p o i n t s( c A,c~) l o c a lcheckpoint~. Here, w i t h( 1, 1 ,0,0) and (C~ , c~) with (0,0,1,1 )町 e l, 4,c~) with(1,1, mergedi n t oonec h e c k p o i n t(c~ , c 1, 1 ) . [Mergeofcheckpoints]A f t e rano b j e c t向 同k e sa "r e c e i v e sac h e c k p o i n t e dmessage l o c a lc h e c k p o i n tc~ , 0 m. 1 .I fac h e c k p o i n tdeno 旬 db ym.cpi sn o ti nt h esame = c:~ ,,, 1 c e <4 3 8 2> = = timc = F i g u r e5 :C h e c k p o i n t s = o . " : 3 Oi = = = = = = = generationω C~ , ・ c t . c p: =m.cp i f =1. J , : J , : c~.BMJ,: ~-1 = = = d ‘ 品 = = =0andm.BM c 1 ・ ~.BM :=c~.BM Um.BM. 2.0 出e r w i s e, cl.BM:=c~.BM U m.BMandC1.CPl : =max(c~.叩1c, m.cpJ,:) f o rk=1 , , . n, kp :i .ロ [Theorem]A s e to fl o c a lc h e c k p o i n 旬 wh i c hb e l o n g も ot h esameg e n e r 抗i o ni s0・c o n s i s 七e n t . 刊 もh etheorembyc o n t r a d i c t i o n .A s [ P r o o f ]Wep r o e r ea r etwol o c a lc h e c k p o i n t s~ and~ sumet h a tもh whichb e l o n gt o叶l esameg e n e r a t i o n .anda r en o t0・ c o n s i s t e n t, i .e . 世l e r ee x i s t sani n f l u e r 凶i a lmessagem sr e c e i v e db e f o r ec ![Figwhichi ss e n ta f t e rc~ andi u r e6 ] . Here, i f町 s e n d sm t o0 ;, mi smarkedc h e c k p o i n t e d .Onr e c e i p to fm, 0 ;同 k e sal o c a lc h e c k p o i n t ~-1 j u s tb e f o r er e c e i v i n gm i fm i si n f l u e n t i a l .Othe r w i s e, o ;d o e sno もt a k eal o c a lc h e c k p o i n t .Thus, t h e checkpoin旬 c~ a nd& , .neverbelongt osameg e n e r a もi o n . T h i sc o n t r a d i c t st h ea s s u m p t i o n .ロ F i g u r e6 :Sameg e n e r 剖i o nc h e c k p o i nt s 5 R estartingProtocol I fano b j e c to ii sf a u l t y , もh er e s t a r t i n gp r o もo c o li si n i ,詰 r o l l e dback加もhel o c a lc h e c k t i a t e d .Theo b j e c t0 p o i n tc :whichi smostr e c e n t l y同 k e nby~. I no r d e r t ok e e pt h es y s もem0・c o n s i s t e n t, o b j e c 旬 w hichhave f t e r同 k i n g r e c e i v e di n f l u e n t i a lm e s s a g e ss e n tby0 a t h el o c a lcheckpoin色 c~ a r er e q u i r e dt ober o l l e db a c k . Therea r e七woc 卸 e s, onec a s ei st h a t0 "r e c o r d sm e s s a g e swh i c hOi s e n d si n七hel o gandt h e0もh e rc a s ei s t h a tOi d o e sn o tt a k el o gs i n c e. i tt a k e st i m e七or e c o r d , weぬk e eachmessages e n ti nt h el o g .I nt h i sp a p e r t h ef i r 凶 a p p r o a c h .Theo b j e c t0 s e n d sa -r o l l b a c kr e ・ que 前 m essageR・Reqt oe v e r yo b j e c も句 w hicho ih鎚 s e n tm e s s a g e sa f t e rt a k i n g Then , 0c a nr e s t a r tt h e computation幽 y n c h r o n o u s l yw i t ho t h e ro b j e c t s . b j e c t sR-Reqもob e I no r d e rt od e c i d eもowhicho s e n _ t, e a c ho b j e c t0 r e c o r d sd e s t i n a t i o no b j e c t si nal o g SL~. When~ t a k e sc~ , SL~ i si n i t i a t e dもobee m p t y . Eachもime0 s e n d sani n f t u e n t i a lmessagem も0飢 ・ 0もh e ro b j e c t0 ;a f t e rc t,SL~ SL~ U {Oj}. Here,m n f l u e n t i a la c c o r d i n gt ot h ei n f l u e n ・ i sd e c i d e dぬ bei t i a lm e s s a g e( I F )c o n d i t i o n s, I no r d e rt or e d u c eもh e o v e r h e a d色ow r i t e七hel o g ,SL~ i sw r i t t e n色ot h el o g o n l yi fSL~ i sc h a n g e d .I f0 i sr o l l e db a c k主ot h el o c a l ch~ckpoint c l, 0s e n d sR-Reqt oe v e r yo b j e c t0 ;i n SL~. H ere, R・Reqc o n t a i n st h ef o l l o w i n gi n f o r m a t i o n : • Ac h e c k p o i n tv e c t o rc p ( C P 1 '・ ・ ・, cPn) o fもh e "i sr o U e db a c k . l o c a lc h e c k p o i n tc~ 七o which0 仰11. , rvn)whereeach • Ar o l l b a c kv e c t o r問 =( T町 i s1i fo iknowsOlc i sr o l l e db a c k . 0七h e r w i s e, r vJ,: O . Onr e c e i p to fR-ReqfromOi, ano b j e c tOj d i s c a r d s Reqi fR R e q . r v ; 1s i n c e0 ;h a sbeena l r 句 dyr o I l e d R・ -77- , , c : . , , = , , • = = = , b a c ki nt h i sg e n e r a t i o n .O t h e r w i s e, r V : l:=max(r, V : l R・R e q . r V k )( k=1 , . . ,. n)・句 looksforanoldestlocal ' uwhereC P i=R・R e q ' C P i 'I f0 ;f i n d ss u c ha c h e c k p o i n tc l o c a lc h e c k p o i n t~, c ' ui sr e f e r r e d色0 剖 r o l l btJc kp o i n t o f0 O t h e r w i s e, t h emostr e c e r i tc h e c k p o i n tw h e r e C P i: <R-Req.cPibecomesarollbaclcpoint. Then, 0 ; c o l l e c 旬 a8 e tRVo fm e s s a g e swhich0 ;h a sr e c e i v e d fromo ia f t e rt a k i n g~. I f 色h e r ei ssomei n f t u e n t i a l m e s s a g ei nR V, 句 i sr o l l e dbackt ot h er o l l b a c l cp o i n t c i .句 sendsR-ReqもoeveryOlc inSL~ wiもhR-Req.rvj : 三 1a . n dr VI := 1 .I f o ;h剖 n o tr e c e i v e danyi n f t u e n t i a l "0 ;d i s c a r d s R・Reqs i n c e0 ;i sn o t m e s s a g efrom0 r e q u i r e dt ob er o l l e db a c k . e C h e c k p o i n t i n gandC o n c u r r e n tR o l l b a c kf o rR c o v e r yi nD i s t r i b u t e dS y s t e m s- , AnO p t i m i s t i c Approach, "Proc. 0 1IEEE SRDS-7,pp.3・12, 1 9 8 8 . ・・ , 0 <0, 0, 0> C i <1, 0, 0> <0, o .0> Oj <0.o .0> [ 2 }Ch 卸 d y ,K.M.andLamport,L.“ ,Di山 ibuted 旬 D e t e r m i n i n gG l o b a lS t a t e so fD i s Snapsho t r i b u t e dS y s t e m s " ,AOMTOCS, Vo l .3, No・1 , p p .6 37 5, 1 9 8 5 ; . M .J ., G r i f f e t h, . N .D ., a n d . L y n c b, N .A ., [ 3 ]F i s c b e r, “ G l o b a lSも叫e so faD i s t r i b 凶e d. System, "IEEE 7rtJ n s .01 1 .S 0 β切 tJr eE n g i n e e r i n g , Vo l .SE -8, N o . 3, pp.19ι202, 1 9 8 2 . 間G a r c i a -Mo1 i na ,H., “Using Semantics Knowl- a n s a c t i o n P r o c e s s i n gi naD i s t r i b u t e d e d g ef o rTr D a t a b a s e, "Proc.olAOMSIGMOD, Vo l .8, N o . 2, p p .1 8 8 ・2 1 3, 1 9 8 3 . 0 " [ 5 ]H i g a k i,H ., Sima ,K.,Tanaka,K.,Tacbik a . wa , T .叩 dTa 凶 awa , M. “ ,CheckpointandRollback i nAsynchronousD i s t r i b u t e dSyste~ ," P r o c .0 1 lEEEINFOOOM'97, p p .1 0 0 0 1 0 0 7 , 1 9 9 7 . c f c ; . and Ta . ki z a w a ,M., “Checkpoint・ [ 6 }H i g a k i,H Rec o v e r yPro もo c o lf o rR e l i a b l eM o b i l eS y s t e m s, " P r o c .0 1IEEESRDS-17, p p . 9 3 ・ 9 9, 1 9 9 8 . . 叩 d Toueg,S ., “Checkpoi凶 ngand [ 7 ] Koo,R " R o l l b a c k R e c o v e r yf o r D i s t r i b u t e dS y s t e m s, lEEE 宝Mn6. 01 1 .C omputers, Vo l .C 1 3, N o .1 , p p .2 3 3 1, 1 9 8 7 . t i m e F i g u r e7 :R e s t a r t i n gp r o c e d u r e . S u p p o s et h a t 叫ueeo b je c t s0 " 0 ;,and 01 : t a k e c h e c k p o i n t s剖 showni nF i g u r e7 .H e r e, i f0 becomes , 0 i sr o l l e db a c kt ot h ec h e c k p o i n 色C iwhicbi s f a u l t y もr e c e nt 1yもakenby0・ ,O is e n d sani n f t u e n t i a lm e s mos s a g e7 ' l ' 1 ¥ もoOj a f t e rc l .向日nds句 i nSL~ s i n c eT n ii s 0 s e n d sR-Reqt o0; w i t bv e c t o r s i n f l .u e n t i a l . Then, C p ( 1, 0, 0 )and刊 =( 1, 0, 0 ) .Onr e c e i p もo fR・Req 丘omoi, 句 f i n d sano l d e s もl o c a lc h e c k p o i n tc {wbere C p 1b e c a u s eR R e q .C!pi 1 .S i n c ef f l ii nRL'i si n 句 i sr o l l e db a c kt o~. R-Req・川 1 .Then, f t u e n t i a l, 句 s e n d sR~Req t oOJ :i fm;i si n f l u e 凶 a l .Onr e c e i p むd R・ReqfromO j, 01 :i sr o l l e db a c k初七hec h e c k p o i n tc~ i fm;i si n 到u e n t i a l .0むb e r w i s e, OJ :j u s td i s c a r d sR-Req andc o n t i n u et h ec o m p u t a t i o n . , = , = [ 8 ]L i n,L . andAhamad, M.“ ,Cbeckpointingand R o l l b a c k R e c o v e r yi nD i s t r i b u t e dO b j e c tB錨 e d S y s t e m s, "Proc.0 1IEEESRD5 . ・9 , p p .9 7 1 0 4, 1 9 9 0 . , [ 9 ]Leong, H .V .andAgrawal, D . “ ,UsingMessage S e m a n t i c st oReduceRo l l b a c ki nO p t i m i s 色i cMe s s a g eL o g g i n gR e c o v e r ySchemes, "P r o c .ollEEE p p . 2 2 7 2 3 4, 1 9 9 4 . IODOS-14, , = = 6 ConcludingRemarks . and S i n g h a l,M., “A Low[ 1 0 ] Manivannan,D 回 i Overtead R e c o v e r yT e c h n i q u eU s i n g Qu ~~I!chronous C h e c k p o i n t i n g, "P r o c .0 1 IEEE ICDOS ・ 1 6, p p . 1 0 0 1 0 7, 1 9 9 6 . [ 1 1 ] Ra manathan, P .andS h i nK .G . “ ,Checkpoinレ s i n gandR o l l b a c kR e c o v e r yi naD i s t r i b u t e dSy temUs i n gCommonTimeB踊 e , "Proc.0 1IEEE ・7 , p p .1 3 2 1, 1 9 8 8 . SRDS . and T a k i z a w a ,M., “Distributed [ 1 2 ]T, 卸aka,K " C h e c k p o i n t i n gBased onI n f l . u e n t i a lM e s s a g e s, P r o c .ollEEEICPADS'96, p p .4 4 0 4 4 7 , 1 9 9 6 . Weh a v ed i s c u s s e dhowもot a k eo b j e c t b u e dc o n s i s t e n t ・c o n s i s t e n t )c h e c k p o i n t sw h i c hc a nb e _t a k e nfrom (0 も i o np o i n to fv i e wbutmaybei n c o n s i s t h ea p p l i c a t e n twi 七ht h et r a d i t i o n a lm e s s a g e b a s e d d e f i n i 色i o n .We h a v ed e f i n e d加: j l u e n t i t J lmeS6tJg e 6ont h eb回 i so fもh e s e m a n t i c so fr e q u e s 旬 a ndr e s p o n s e swhereもbem e t h o d s町 en e 凶e dandもh emethodsa r ep e r f o r m e dbyt h e r e m o t ep r o c e d u r ec a l l . Onlyo b j e c t sr e c e i v i n gi n f l u e n t i a lm e s s a g e sa r er o l l e dbacki f出 es e n d e r so f出 e i n f l . uen もi a lm e s s a g e sa r er o l l e db a c k .The0・c o n s I 8 t e n t h .e c c 1 p o i n ti so n ewhereもh e r ei snoorphani n f l u e n t i a l c m e s s a g e .Weh a v ep r e s e n t e dぬe創 刊c h r o n o u sp r o も 0・ c o lf o rt a k i n g0・c o n s i s t e n tc h e c k p o i n旬. [ 1 4 ]Wang , . Y .M.andF吋 叫 W. K .“ ,Optimistic Mess 暗号 L o g g i l ! gf ? r I~depend<<mt C h e c k p o i n t i n g1 n _M e s s a g e P 剖 s i n gS y s 旬 ms , "P r o c .ollEEE ・1 1, p p .1 4 7 ・1 5 4, 1 9 9 2 . SRDS References [ 1 5 ] Weikum , G., " P r i n c i p l e sandR e a l i z a t i o nS t r a t e g_ie~_ :.o~ ~_u!ti!c:v~l . 'þ'~_n8action M anagement, " ACMTODS, Vo l .1 6 , N o .1 , p p . 1 3 2 1 8 , O 1991 . [ 1 3 ]Tanaka ,K.,Higaki,H.,and Takizawa,M., “ O b j e c t ・B舗 e dC h e c k p o i r i t si nD i s t r i b u 旬 dS y s "J0. 1 品 r n a l0 1ComputerSystemsS c i e n c e. a nd tems, E n g i n e e丙n 9, V o l .1 3, N o . 3, p p .1 2 5 1 3 1, 1 9 9 8 . [ 1 }Bhargava ,B. and Lian,s .R.,"Independent -78-