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組合せ最適化問題に基づいた 低消費電力タスク・スケジューリング
情報処理学会第 74 回全国大会 4M-4 !"#$%&'()*+,./01234564789:;<=6>?@;AB CD EF†! GH IJ‡ KLKMKMNOPMQRSOPMTU† KLKMOPMVOPW4XBMS‡ !" #$%&! ! YZ[\]^_`abcde)fg/012 ahij'(klmn,gopa-q/012 rstugvwlxyjz{|}n,gopa ~•€\]^_`a•‚ƒ„…r.†‡#gˆ k • / 0 1 2 r s t u g DVFS (Dynamic Voltage Frequency Scaling)k,‰Š‹rŒ•Ž -34564789:;<=xyj••‡}n ,g[1,2]o‘’•“./0123456478 9:;<=r345)•‚ƒ„…r”•–ng !"#$%&'(kŽnk|{[345=—˜ r™…a345š)›”Ž[œ345š)›• žŸyr%•ugˆk•$% r¡¢ugxy r••ugo345=—˜r ETF l£J¤¥l 4789:;<=6>?@;AB•4789: ;<=Ž-¦§) DVFS r%•Ž-¨"a$% r¡¢ugˆkr©¥kugo '" ()! ! DVFS k“\]^_`a•‚ƒ„…k•‚1 ªa!•«‡}g P-State r[\]^_`a•‚ ~)•¥)¬-ugˆk•/012rstug Š‹•®g[3]o‘’•“ AMD ¯°a Athlon64 3000+\]^_`rŒ•ugoˆa\]^_`) “ P-State j 3 ±²•³‡}n,goP-State r ¬-‡#gˆk•[\]^_`a•‚ƒ„…r 1/2 ´•.†‡#[/012r 1/4 ´•stug ˆkj•µgo¶ 1 )·r¸uo=—˜a¹º j»¼½¾[¿ºj/012r«Žn,go(b) •“(a)f•€\]^_`a»¼ÀÁj 1/2 kl •»¼½¾j 2 Â)lgj[/012“ 1/4 •® goŽ-jmnÃ_ÄV›aÅÆ[ulÇÈ/ 012ÉrÊËugk(b)aÌjÍlÎlgoŽ -jmnÏн¾)ÑÒj®g¨"[DVFS ) f•(b)aÓÔ•\]^_`r•‚‡#-ÌjÕ Öj×,oDVFS r•,-./0123456 4789:;<=“[œ345aÏн¾rz {[P-State a¬-jØcl345rÙÚugˆ k•/012Érstugo *" +,-./! ! e•ÛÜ-f‰)[\]=—BÝÞa»¼½ ¾rhi‡#l,f‰œ345) P-State r”• –n[/012rstugaj[./034 564789:;<=a©¥•®go345… Fig.1 Power Consumption and execution time r n[P-State a…r P kugkˆa ß¾“ Pn kl•[345…jhiugk$% ràq gˆkjáâ•®go‘’•“ˆa'(rœ3 45)$%l P-State r”•–ng!"#$%& '(kz{go!"#$%&'(k“[ãKl ¡¢Éräå'(rstugæ[´-“çèr é-uê'(r Έk•$× ràqg'( • ® g [4] o ë ) ˆ a ' ( • “ [ ® g 3 4 5 ) DVFS r%•ugkìaíÎa345)paî ïrðñua•[J¤¥l!"#$%&'(a yr%•ugˆkjâŽ,o ! ‘’•“ãKl¡¢Érstug-q345 =—˜ròåæa345š)›”Ž[›”Ž345š)óŽn!"#$%&'(a*‘ôõ aJå•®g›•žŸyr%•ug>\]:Ä rö•ugo›•žŸyk“[pa'(a†÷ øùe÷ør›•çèkŽnúŸŽ[paçè )"Çl,û3:<“üýugˆk•¡¢Ér stugxy•®g[5]o‘>\]:Ä•“[PState r%•Ž-kµ)\]=—BÝÞaþÿ½ ¾jhiŽ-¨"û3:<rüýugk,‰› •çèr•,go ! 345=—˜r,Îåæa345š)›”Ž[ ¡¢ugˆk•¡¢Éastj!"•µgj[ 345ša#$)“%³j&'•®go®g3 45š(a DVFS a%•jìa345š)îï r){l,f‰l345›”jÿ*+j[,» ¥)“âŽ,o®g345) P-State r%•Žˆk•»¼½¾j-. [ìa345a»¼/0 ½¾j1Îlm-kugoˆakµ/0½¾j 1Îlm-345)%••µg P-State j[/0 ½¾j1Îlg2kLv•®gkµ[ˆ}|a 345“34“Žn,gj DVFS %•)fgî ïjÍlÎêa345škŽn56)óþ•µ gkz{|}go7)þÿ"Ƚ¾r89 ug 1-467 Copyright 2012 Information Processing Society of Japan. All Rights Reserved. 情報処理学会第 74 回全国大会 !"#$%&[1,2]' DVFS ()*+,-./0 1234567 2 8!"#$%&*9-:;6 7<*#$% n3=n7 '>?@ABC-DEFG6 ;FHAIJKLBC-MNOPQRSTU/ FGS;Q6R*S/=!"#$%& A *#$ % n1=n2 '#$% n2=n3 C8VW;Q>?@A BC-XY;Q6ZE=!"#$%& B U[\ ]8#$% n5=n6 C=n6=n7 C*>?@ABC -XY;Q6!"#$%&U'>?@ABCXY3^GQE_=!"#$%&8`3^GQ Gabc*#$%8 DVFS -()3ES/=X Y3^GQ>?@ABCTde;QE_=+, T./GSfgQ6 !" #$%&'(! ! hi*jkl-fm3Enopqr$stu vwxyz{|}w~•-h€8•‚Q6ƒ„ *#$%8…3^ DVFS -()3ES/=†# $%* P-State T‡ˆ3E‰Š‹=!"#$%& S3^Œ•3^GQ‰Š=RbŽ-#$%&S 3^•!•‘;Q6R*•!•‘-’#$%U J5RSU=G0“c*”•#$%&S=–* #$%S[•!•‘ObFc—E˜”•#$% &-™š;Q6ZE=›”•#$%&8…3^ œ•=DVFS -()3E‰Š* P-State -žŸ 3=\]* ¡-J56R*S/=†*”•# $%&8`3^GQ#$%T¢£S3^¤¥3 E‰Š=¦*”•#$%&S§Š-J56¨© 8˜”•#$%&8…3^˜”•#$%&8` 3^GQ<Uª«T¤¥3^GQ#$%-#$ %&S3=DVFS -()3E‰Š* P-State žŸ3¢£T¤¥3E‰Š=•!•‘3=†* ”•#$%&8`3^GQ‰Š'§Š;Q6¨ ¬-8•!•‘ObFc—E#$%-’^=# $%&S3^”•#$%&*®“8;Q6hi * ¡8¯°±²*”•#$%&8”•3=” ³´µ¶-();QRSU·*™š-J56 )" *+,-! ! ¸I¹U'”³´µ¶-)G^º»¼¶*½ ¾ ¿ À - J 5 6 Á  u à Á Ä v x 8 ' AMD Athlon64 3000+ÅÆÇÈÉT 8 ƒÊËObEÉ vÌžŸÍ-ε;Q6$stuvwxy…Ï S3^ STG (Standard Task Graph set)[6]cŽ ”³´µ¶UžŸÐ¾F#$%² 20 *#$%y ÑÒ 180 ÓÔ-¡Œ3^Õ);Q6STG U'ª « Ö $ × ' Ø µ O b ^ G F G E _ CCR (Communication to Computation Ratio)[7] * 0.1 -Õ);Q6CCR 'ª«>?*ÙÚU4° 0.1 U'ª«TeFGÛÜSµÝOb^GQ6h i*ÁÂuÃÁÄvxÛÜ- Intel Xeon E5430 2.5GHz=Þßw 8GB * Linux àv%$ávÁ Fig.2 Connection Task Group ! Tabel 1 Experimental results žŸâ•[sec] opqrã[W*ut] ”³´µ¶ º»¼¶ 32835.38 728656 235.07 728656 Äxi8äå3E6 ! #$%”•-JHa8”³´µ¶-)GQ‰ ŠS=º»¼¶-)GE‰ŠU=¦*žŸBC S·S3^æŽbE¨çopqrã-èé;Q6 ÁÂuÃÁÄvx*§ê-ë 1 8:;6I¹§ ꯰=”³´µ¶Sº»¼¶UæŽbE¨ç opqrãT®ì3^GQRST”cQ6#$ %”•-JHFG”³´µ¶U'¨(·TžŸ U/Q*U=º»¼¶U[¨(·T™šU/^ GQRST”cQ6ZE=º»¼¶*žŸBC 'í 1%SF—^GQ6;‚^*#$%-”³´ µ¶U·0*U'F0=±²*#$%&8”• 3ERSU>?â•Tîi3ESRST”cQ6 ." /012! ! DVFS ()8¯Q¨(·™š{|}w~•8 “G^•‚E6¿ÀI¹*§ê=º»¼¶U[ ¨(·T™šU/=>?â•*îi-ïð;Q RSTU/E6ñ©*òkS3^=”•#$% &*#$%²T 20 -ógQSžŸ8ô.FBC TccQE_=¯°./G#$%²*#$%y ÑÒU*žŸõ¶-f»;Qö÷T4Q6 3456! 1. øù®ú,ûüý®,þÿ!":”#$%•#^{|}w~ •8$‘Qopqr%d*E_* DVS()#$%&' Í ä ”, ( 8 ) * + , - . / Ò0vÑ• FIT2009,Vol.1,pp.157-164 (2009). 2. øù®ú,ûüý®,þÿ!":”1|2zÅÆÇÈÉ ÛÜ 8$‘QDVS-)GEopqr%d{|}w~•*ä å”,q3-4567C , Vol.131,No.4,pp926-933 (2011). 3. Hisa Ando:”ÅÆÇÈÉ-8gQ./ –ê^3F0$9 v:-;<;Q=> ”,?@4A./¿5A (2011). 4. ñBC ,DEFG:”H²žI¶SJŠP¨(ˆ ”,K,. !šLA (1982). 5. MNOP,QERS:”JŠP¨(ˆ –Þ#TU-<VS 3^-“,ûüWX (2001). 6. T.Tobita and H.Kasahara:”Performance Evaluation of Minimum Execution Time Multiprocessor Scheduling Algorithms Using Stndard Task Graph Set”,Proc.of 2000 Int’l.Cong. on Parallel anad Distibuted Processing Techniques and Applications (PDPTA),pp745-751 (2000). 7. O.Sinnen:”Task Scheduling for Parallel Systems”,Wiley-Interscience (2007). 1-468 Copyright 2012 Information Processing Society of Japan. All Rights Reserved.