Reliability-Driven Reputation Based Scheduling for Public-Resource Computing Using GA

Transcription

1 2009 Intrnatonal Confrnc on Advancd Informaton Ntworkng and Applcatons Rlablty-Drvn Rputaton Basd Schdulng for Publc-Rsourc Computng Usng GA Xaofng Wang #, Ch Shn Yo*, Rakumar Buyya* 2, Jnshu Su # 2 #Collg of Computr, Natonal Unvrsty of Dfnc Tchnology Changsha, 40073, Hunan, Chna {xf_wang, ss 2 }@nudt.du.cn *GRIDS Laboratory, Dpartmnt of Computr Scnc and Softwar Engnrng Th Unvrsty of Mlbourn, VIC 300, Australa {csyo, ra 2 }@css.unmlb.du.au Abstract For an applcaton n publc-rsourc computng nvronmnts, provdng rlabl schdulng basd on rsourc rlablty valuaton s bcomng ncrasngly mportant. Most xstng rputaton modls usd for rlablty valuaton gnor th tm nflunc. And vry fw works us a robust gntc algorthm to optmz both tm and rlablty for a workflow applcaton. Hnc, n ths papr, w propos th rlablty-drvn (RD) rputaton, whch s tm dpndnt and can b usd to valuat a task s rlablty drctly usng th xponntal falur modl. Basd on th RD rputaton, w also propos Knowldg-Basd Gntc Algorthm (KBGA) to optmz both tm and rlablty for a workflow applcaton. KBGA uss hurstcs to acclrat th voluton procss wthout gvng nvald solutons. Our xprmnts show that th RD rputaton can mprov th rlablty of a workflow applcaton wth mor accurat rputaton, whl th KBGA can volv to bttr schdulng solutons mor quckly than tradtonal gntc algorthms. Kywords rlablty, rputaton, workflow schdulng, gntc algorthm, hurstc. Introducton Publc-rsourc computng whch combns lmnts of Pr-to-Pr (P2P) and Grd computng s an mportant tchnology, and s usd n many applcatons such as SETI@Hom and BOINC [3]. Usually, publcrsourc computng comprss a larg numbr of unsuprvsd rsourcs whch hav no pror trust and ar mor suscptbl to unrlablty. Hnc, many factors may lad to falurs for an applcaton. For xampl, a rsourc may b ovrloadd, slow connctd, msconfgurd or malcous. Thus, n publc-rsourc computng, th schdulng of an applcaton must also account for rlablty, bsds xcuton tm (makspan) whch s normally consdrd. To nabl rlabl schdulng, two mportant ssus nd to b consdrd: () how to valuat a rsourc s rlablty and () how to prform rlabl schdulng basd on th rsourc s rlablty nformaton. Rputaton systms ar commonly usd to valuat a rsourc s rlablty [,2,9,,3]. But, most xstng rputaton systms hav two problms. Frstly, from th rsourc prspctv, most rputaton modls [,2,9,] valuat a rsourc s rputaton accordng to ts rato of succssfully compltd tasks. Thy do not consdr th nflunc of th task s runtm (sz). For xampl, pr A has a hghr task falur rat (task falurs pr unt tm) than pr B, so pr B should hav a bttr rputaton. But, tradtonal rputaton modls wll nstad prdct a bttr rputaton for pr A whn pr A xcuts mor short runtm tasks and pr B xcuts mor tasks wth longr runtm. Ths s bcaus pr A may complt mor short tasks succssfully than pr B. Scondly, from th task prspctv, xstng rputaton modls assgnd th sam rlablty (succss probablty) [,3] to all th tasks on a rsourc basd on th rsourc s rputaton. But, th longr a task runs on an unrlabl rsourc, th lowr succss probablty t should hav. Gvn th rsourc rlablty nformaton, t s known to b a NP-hard problm to optmz both makspan and rlablty for a workflow applcaton wth task dpndncs [9]. Svral lst hurstcs hav bn proposd for ths problm n non-gntc algorthms [7,5,6]. Usually, gntc algorthms (GAs) can provd bttr qualty solutons than lst hurstcs [6,2]. Although GA s mor tm consumng, t s accptabl for applcatons wth long runtm. Morovr, th spd of GA can b acclratd by adoptng paralll gntc algorthm tchnology [4]. Currntly, b-obctv gntc algorthm (BGA) [7] s th only GA that w know can gv both makspan and rlablty optmzd schdulng solutons for workflow applcatons. But BGA may gv nvald solutons whch volat th dpndnc btwn tasks. In addton, most GAs [8,0,7] volv th schdulng solutons randomly, whch may lad to slow convrgnc of th algorthm. In ths papr, w propos th novl rlablty-drvn (RD) rputaton modl for rsourc rlablty valuaton. RD rputaton consdrs th runtm of tasks by usng th rsourc s task falur rat (task falurs pr unt tm) X/09 $ IEEE DOI 0.09/AINA

2 to dfn th rputaton. It also provds a ral tm rputaton that can b usd to valuat a task s rlablty drctly usng th xponntal falur modl. Basd on RD rputaton, w thn dfn th rlablty-drvn schdulng problm and two schdulng hurstcs whch am to optmz makspan and rlablty for a workflow applcaton. Fnally, w dsgn th knowldg-basd gntc algorthm (KBGA) to provd schdulng solutons. KBGA volvs th task xcuton ordr accordng to th task s mportanc valu, so that th schdulng wll not volat th dpndncy btwn tasks. Th mutaton of KBGA has two oprators namly swappng mutaton and rassgnng mutaton whch volv th solutons ntllgntly basd on our hurstcs. Th rmandr of ths papr s organzd as follows. Scton 2 ntroducs rlatd work. Scton 3 prsnts th schdulng systm modl. Scton 4 dfns th RD rputaton and ts calculaton algorthm. Scton 5 dfns th schdulng problm and two hurstcs, whl KBGA s prsntd n Scton 6. Exprmntal rsults ar prsntd n Scton 7, followd by th conclusons n Scton Rlatd Work Th ral tm rsourc rlablty can b montord by th rsourc s rputaton, whch can b dfnd as th probablty that th rsourc can dlvr th xpctd utlty srvc [2]. For P2P systms, two popular rputatons EgnTrust [9] and PowrTrust [] wr dsgnd. Thy comput th local trust valu basd on th normalzd numbr of succssful transactons btwn two partcpants. For publc-rsourc computng systms, Sonnk t al. [] calculatd a workr s rlablty as th rato of corrct rsponss. Nthr th normalzd numbr nor th rato of corrct rsponss consdrd th tm nflunc. Song t al. [3] usd fuzzy logc to valuat th rputaton. Although task runtm s ncludd n thr modl, thy dd not spcfy how th task runtm affcts th rputaton. Th tm rlatd prformanc can also b valuatd by th rsourc avalablty [4]. But t focusd on th hardwar analyss, not ncludng th task lvl bhavour analyss. Morovr, most xstng works dd not gv mthods or algorthms to prdct th ral tm task falur rat for a rsourc, whch s ndd for task schdulng. Howvr, our rlablty-drvn rputaton s spcally dfnd to b tm dpndnt, and our rputaton calculaton algorthm can provd a ral tm falur rat valuaton for a rsourc. Optmzng both makspan and rlablty for a workflow applcaton s known to b a NP-hard problm. Many lst hurstcs hav bn proposd [7,5,6]. Dongarra t al. [5] provd that tasks should b schduld to th nod wth th mnmum multplcaton valu of th nstructon xcuton tm γ and rlablty λ. Mark t al. [7] proposd a gnral b-crtra schdulng hurstc whch dvds th schdulng nto prmary and scondary schdulng. Gnrally, a gntc algorthm can gv bttr schdulng solutons than lst hurstcs [2]. Dogan t al. proposd a b-obctv gntc algorthm (BGA) for workflow applcatons [7]. BGA volvs th schdulng solutons randomly whch may gv nvald solutons volatng th dpndncy btwn tasks. Wang t al. [0] rprsntd a schdulng soluton as two strngs: th task-rsourc assgnmnt strng and th task xcuton ordr strng. Although ths mthod can solv th nvald soluton problm, thy dd not consdr rlablty. Most xstng GAs [8,0,7] also volv th schdulng solutons randomly, whch may lad to slow convrgnc of th algorthm. In contrast, our KBGA volvs th task xcuton ordr accordng to th task s mportanc valu and mutats a soluton basd on our two hurstcs. Thus, our KBGA can volv th schdulng solutons ntllgnt wthout gvng nvald solutons. 3. Modls and Assumptons In th typcal publc-rsourc computng modl [] as shown n Fg., thr s a cntral srvr whch assgns obs submttd by th clnts to th rsourc provdrs. W modl a workflow ob as a Drctd Acyclc Graph (DAG): Job = ( V, E). V s th st of nods v ( n) whch dnots th tasks of th workflow ob. E s th st of dgs (, )( < n) whch rprsnts th dpndnc btwn tasks v and v, v s th parnt task and v s th chld task. For ach task nod v, ts wght v s th numbr of nstructons of ths task whch s assumd to b known usng complng tchnology [5]. Th lngth of a path n th DAG s th sum of th wghts of all nods along th path. Fg.. Systm Modl. Thr ar som rsourc voluntrs n th systm, whch ar not cntrally controlld and wll on or lav th systm dynamcally. Lt R = { r, r 2 r m} b th m rsourcs avalabl n th systm. Each rsourc r s assocatd wth two valus: rdr, th rsourc s RD rputaton and γ, th rsourc s computng spd 42

3 llustratd by untary nstructon xcuton tm (.. th tm to xcut on nstructon). Gvn th rsourc s nformaton, th cntral srvr can schdul th workflow ob. Lt M : V R dnots th mappng functon, and thn M ( ) = r mans task v s assgnd to rsourc r. W assum that th cntral srvr can only schdul at most on task to on rsourc at any tm. W also assum that th cntral srvr can montor th task xcuton, hnc f a task succssfully fnshs or fals bfor complton, th srvr can dtct t and snd a rputaton rport. Svral tchnologs hav bn proposd to dal wth ths problm such as chckpont and quzzs vrfcaton [8]. 4. Rlablty Evaluaton as Rputaton In publc-rsourc computng, many dscrt vnts may lad to falurs of an applcaton such as nonavalablty of rqurd srvcs, ovrloadd rsourc condtons and malcous actvts. All ths vnts ar ndpndnt and may happn randomly, hnc w us th commonly usd Posson Dstrbuton [5,6,7] to modl th falur of a rsourc provdr. Th falur dnsty functon s λt f ( t) = λ ( t 0), whr λ s th falur rat of a rsourc. Lt num_fals b th numbr of falurs wthn a rsourc durng th ob runtm prod of run_tm. W can comput th falur rat by Equaton whch s th nvrs of Man Tm To Falur (MTTF). num _ fals λ = = = x x dx MTTF run _ tm λ. () λ 0 To nabl rlabl schdulng, th rsourc s ral tm falur rat should b montord. Although tradtonal rputaton systms can b usd to montor th rsourc s rlablty, thy nthr prdct th falur rat for a rsourc drctly nor consdr th tm nflunc. Hr, our tm dpndnt rputaton s drctly rlatd to th falur rat, whch can b dfnd as: Rlablty-Drvn (RD) Rputaton ( rdr ) of a rsourc r s th gnrally sad or blvd probablty of task falur pr unt tm, wth whch th rsourc provdr wll fal to complt th tasks assgnd to t. 4. Calculaton of Ral tm RD Rputaton A rsourc s RD rputaton rprsnts ts ral tm falur rat λ ntroducd abov. To mantan th RD rputaton, w dvd th succssv tm nto tm ntrvals whch last a wndow tm T wndow. For ach tm ntrval, th srvr mantans a rputaton statstc rpu _ sta = ( s, f, runtm, c ) for ach rsourc r. Th varabls s and f ar th start and fnsh tms for an ntrval rspctvly, runtm s th total CPU tm that rsourc r donats for task xcuton n th ntrval, and c s th numbr of falurs xprncd by tasks. Algorthm shows th RD rputaton calculaton algorthm. It bgns wth ntalzng ach rsourc s rputaton statstc rpu _ sta for th frst tm ntrval (ln ~6). Lt us assum that th algorthm coms to tm ntrval t for rsourc r. Aftr a task v assgnd to rsourc r succssfully fnshs or fals, th srvr gvs a rputaton rport tstmony = ( s, f, c ), whr s and f ar th start and fnsh tms of task v rspctvly, and c s th numbr of falurs durng ths task. If a task fals, w smply assgn c to b, othrws t s 0. Th srvr uss ths rport to updat th rputaton statstc rpu _ sta ( ln 9~). Aftr ach updat of th rputaton statstc rpu _ sta, a ral tm statstcal falur rat statstc λ for rsourc r can b computd usng Equaton. Hr, th whol lngth of th currnt tm ntrval s f s. Durng th runtm of th rsourc s donatd task xcuton tm n th currnt ntrval, th rsourc has c task falurs. Durng th rmanng tm f s runtm n th currnt ntrval, th rsourc s assumd to work wth a rputaton obsrvd n th last tm ntrval t. Thus th assumd numbr of task falurs for th rmanng tm n th currnt t ntrval s rdr t ( f s runtm ), whr rdr s th rcordd RD rputaton for rsourc r n th last tm ntrval t. And w can gt th ral tm statstc falur rat by: t statstc c + rdr ( f s runtm ) λ =. (2) f s Th rputaton should dcay ovr tm, thus th ral tm RD rputaton for rsourc r n th currnt tm ntrval t can b dfnd as: t statstc rdr = α rdr + ( α ) λ, (0 α < ) (3) whr α s th dcay factor. If α s zro, th ral tm RD rputaton wll b qual to λ statstc, whch mans t s totally dcdd by th currnt statstcal falur rat. 43

4 At th nd of th currnt tm ntrval t, th ral t tm RD rputaton rdr s rcordd as rdr for rsourc r (ln 6), and th srvr starts anothr rputaton statstc for th nxt tm ntrval t + (ln 7~9). For th ntal tm ntrval, w assum that th RD rputaton 0 ntal rdr for ach rsourc r s rdr (ln ntal 2). rdr s th ntal RD rputaton for all th rsourcs. It should b st to a rlatvly hgh falur rat. In ths way, t gvs rsourc provdrs ncntvs to supply good qualty srvcs to mprov thr rputaton. Algorthm RD Rputaton Calculaton Algorthm for ach rsourc r do 2 0 ntal rdr = rdr = rdr 3 t 4 s = f = currnt_ tm 5 runtm 0; c 0 6 nd for 7 whl thr s a rputaton rcord tstmony do 8 f ( f < s + Twndows) thn //currnt ntrval 9 c c + c 0 runtm runtm + ( f s ) f max( f, f ) 2 Rmov th rcord tstmony 3 Comput λ statstc by Equaton 2 4 Comput rdr by Equaton 3 5 ls //nxt ntrval 6 t rdr rdr 7 t t + 8 s = f = s + Twndows 9 runtm 0; c 0 20 nd f 2 nd whl 5. Rlablty-Drvn Schdulng Problm In ths scton, th rlablty-drvn schdulng problm basd on RD rputaton s formalzd frst. Thn two hurstcs ar dfnd for gntc algorthms to mprov th schdulng solutons. 5. Problm Rprsntaton In a workflow applcaton, ach task could b xcutd only aftr all ts parnt tasks hav bn compltd. Thus th avalabl start tm for a task v s: aval t = max t, (4) (, ) E whr t s th nd tm for task v. If task v has no parnt tasks, ts avalabl startng tm s 0. Lt functon dl( r ) b th tm whn rsourc r s dl. Thn th bgnnng and ndng tms of task v can b dfnd as: whr M () b t t b aval = max{ t, dl( M ( ))}, (5) = t + v γ whr M() = r s th rsourc to whch task v s assgnd, r. Lt t b and γ s th nstructon spd of rsourc s th tm whn rsourc r fnshs all th tasks assgnd to t n schdulng S, whch can b dfnd as: t s = max M ( ) = r { t }. (6) Th rlablty of a workflow applcaton s th probablty that all ts tasks complt succssfully. It can b gvn by th probablty that all th rsourcs rman functonal untl all th tasks assgnd to t ar compltd [5]. Snc rdr rprsnts th falur rat for rsourc r, th probablty that rsourc r can succssfully complt all ts tasks n schdulng S s t s rdr R s =. Thus th succss probablty R s for an applcaton n schdulng S can b computd as th product of all R s, whch s llustratd n Equaton 7. W can s that to maxmz th rlablty, w nd to m mnmz th falur factor fal ( S ) = t rdr. m m ts rdr R s = Rs = =. (7) = Th rlablty-drvn schdulng of a workflow applcaton s to maxmz th rlablty and mnmz th makspan for th applcaton wthn th tm constrant of th dadln D. Thrfor th schdulng problm can b formalzd as: m Mnmz fal( S) = ( ts rdr ) = Mnmz tm( S) = max( ts ). (8) r R Subct to tm( S ) < D 5.2 Hurstc ruls To maxmz th rlablty, Hurstc can b appld [5]. It has bn provd that to maxmz th rlablty, th task should b schduld to th rsourc wth mnmal γ rdr whnvr t s possbl. Hurstc = s 44

5 Lt S b a schdul whr all th tasks ar assgnd to a rsourc wth mnmum γ rdr. Thn any schdul S S wth rlablty of R s s such that R s < Rs. To mnmz th makspan for an applcaton, w should gv hghr prorty to tasks that can start arlr and to tasks that hav a bggr nflunc to th makspan of th applcaton. Thus th scond hurstc can b dfnd as: Hurstc 2 Lt th mportanc of a task v b th lngth of th longst path bgnnng from th task n th DAG graph, whch can b dnotd as: v, (, ) E mpt( ) =. (9) v + max mpt( ) othrws (, ) E And th task v s prorty p () s: aval p( ) = E( γ ) mpt( ) max( t, dl( M ( ))), (0) whr E(γ ) s th man nstructon spd of all rsourcs. Thn, f thr ar two tasks schduld to th sam rsourc, th on wth th hghr prorty should b schduld frst. 6. Rlablty-drvn Schdulng usng Gntc Algorthm For th schdulng problm of workflow applcatons, a GA can usually gv bttr solutons than lst hurstcs [2]. A typcal GA conssts of th followng stps: () crat an ntal populaton consstng of randomly gnratd solutons whch ar also calld chromosoms; (2) valuat th ftnss of ach soluton and rmov poor solutons from th populaton; (3) gnrat a nw gnraton of solutons by applyng two voluton oprators, namly crossovr and mutaton; and (4) rpat stp 2 and 3 untl th populaton convrgs. In ordr to mak a GA convrg to bttr solutons mor quckly wthout gvng nvald solutons, w dsgn th knowldg-basd gntc algorthm (KBGA). KBGA volvs th task xcuton ordr accordng to th task s mportanc valu. It also optmzs th typcal GA by applyng two nw mutaton oprators basd on our two hurstcs. Th dtals of KBGA ar prsntd n th followng sctons. 6. Chromosom Encodng and Crossovr For workflow applcatons, a chromosom s a data structur nto whch a schdulng soluton s ncodd. W us a two-dmnsonal ncodng strng [8] to rprsnt a schdulng soluton. As llustratd n Fg. 2c, on dmnson of th strng rprsnts th ndx of rsourcs, whl th othr dmnson shows th ordr of tasks on ach rsourc. Th two-dmnsonal strng can b convrtd nto a on-dmnsonal strng accordng to th rsourc s ndx and task s ordr. Th ondmnsonal strng comprss a lst of ordrd pars (, ), also calld a gn. Th par (, ) dnots task v s schduld to rsourc r. Th ordr btwn tasks n th on-dmnsonal strng only maks sns whn tasks ar schduld to th sam rsourc. v 0 v v 3 r v 0 v v 2 v 4 a) workflow xampl 2 r 2 v r 3 r 4 v 4 v 2 tm b) ral schdul Two-dmnsonal strng bfor crossovr r :v 0 -v 3 - r 2 :v - (0,)(3,)(7,)(,2)(6,2)(5,3)(4,4)(2,4) r 3 : r 4 :v 4 -v 2 (3,)(4,2)(5,2)(0,3)(,3)(7,3)(2,4)(6,4) aftr crossovr On-dmnsonal strng (0,)(3,) (5,2) (,3)(7,3) (4,4)(2,4)(6,4) (0,)(3,)(7,) (,2)(6,2) (5,3) (4,4)(2,4) (3,)(7,) (,2)(4,2)(6,2) (0,3)(5,3) (2,4) c) chromosom strngs d) crossovr opraton Fg. 2. Encodng and Crossovr Exampl. Th crossovr opraton crats nw chromosoms by randomly xchangng part gns of th xstng chromosoms. As llustratd n Fg. 2d, our algorthm prforms th crossovr opraton on th on-dmnsonal strng as follows: () Two chromosoms ar randomly chosn from th currnt populaton, and two random gns ar slctd from on of th chromosoms; (2) All th gns btwn th slctd two gns ar chosn as crossovr gns, and th rsourc allocaton for all th tasks rlatd to th crossovr gns ar xchangd btwn th slctd two chromosoms; and (3) For ach rsourc n th two nw chromosoms, th tasks assgnd to t ar rschduld n th dscndng ordr of thr mportanc valu mpt (). In ths way, th parnt tasks ar always schduld bfor thr chld tasks, thus avodng th nvald soluton problm [7]. Aftr crossovr, two nw offsprng ar gnratd by combnng task assgnmnts takn from th two parnts. 6.2 Mutaton Typcally, a mutaton opraton changs som of th gns n a chromosom randomly, whch causs th algorthm to sarch randomly around th good solutons. W obtan two nw mutaton oprators, namly rassgnng mutaton and swappng mutaton. Thy us th two dfnd hurstcs to hlp th algorthm volv mor drctly to th good solutons. Th rassgnng mutaton mprovs th rlablty for a schdulng usng Hurstc. Frst, t chooss a task n on schdulng soluton randomly. Thn t rassgns th task to a rsourc wth a lowr γ rdr, and schduls th 45

6 task ordr accordng to ts mportanc valu mpt (). In Fg. 3a, task v6 s orgnally schduld to rsourc r 2 whos γ rdr s 2. Th rassgnng mutaton rassgns t to rsourc r wth a lowr γ rdr of as shown n Fg. 3b. Hnc th rlablty of th workflow applcaton has bn mprovd, although th makspan rmans th sam. Th swappng mutaton mprovs th makspan for a schdulng accordng to Hurstc 2. It randomly chooss a rsourc n on schdulng, and compars th prorty of two succssv tasks on th rsourc. It swaps th xcuton ordr of th two tasks f th prcdng task has a lowr prorty. In Fg. 3a, task v 4 s schduld bfor v 2 bcaus t has a hghr mportanc valu, but has a lowr prorty. Thrfor th swappng mutaton xchangs thr xcuton ordr. Fg. 3c shows th nw schdulng whr th makspan of th applcaton has bn rducd. γ =, rdr = γ 2 =, rdr2 = 2 v 0 v 3 v v 4 v 2 h( 4) = h( 2) =.5 v v 0 v 3 v 2 v v 4 v 0 v 3 Fg. 3. Mutaton Opraton. 6.3 Evaluaton In th volutonary-basd optmzaton mthods, ftnss functons ar usd to masur th qualty of a soluton accordng to th optmzaton obctvs. As our goal s to optmz th rlablty and makspan for a workflow applcaton undr th tm constrant, th ftnss valu f (s) for a schdulng soluton S can b dfnd as: fal( s) mnfal tm( s) mntm f ( s) = ω + ω maxfal mnfal 2 maxtm mntm. () + f ( s) ( ω + ω = ) pnalty 0 f tm(s) < D whr f pnalty ( s) = f tm(s) > D Hr, maxfal and mnfal ar th maxmum and mnmum falur factors for th solutons n th currnt populaton rspctvly, whl maxtm and mntm 2 v 4 v 2 ar th maxmum and mnmum makspan rspctvly. Th frst two lmnts of f (s) ncourag th algorthm to choos th solutons wth mnmum falur factor and mnmum makspan. Both ths two obctvs ar assgnd a wght accordng to th usr s trad-off rqurmnt. Th thrd lmnt f pnalty (s) s to handl th tm constrant. If th makspan of a schdulng xcds th tm dadln D, th functon wll gv a pnalty to ts ftnss valu. 7. Exprmnts W us GrdSm [5] to smulat a publc-rsourc computng nvronmnt for our xprmnts. Thr ar 200 rsourc provdrs n th systm. Thy donat varous numbrs of CPU cycls whos spd s unformly dstrbutd n [ 5 0 4,0 3 ] mllsconds pr nstructon. Th actual falur rats for rsourc provdrs ar assumd to b unformly dstrbutd from 0 3 / h ψto 0 4 / h [7]. Th structur of a workflow applcaton can b catgorzd nto balancd and unbalancd [8]. Lk othr prvous works [8,6,7], w us a random DAG gnrator to smulat th applcaton. Our smulatd workflow applcaton conssts of 300 tasks. Th man outdgr for a task nod s 2. Th 3 task s sz s chosn unformly btwn 5 0 Mllon 5 nstructons (MI) and 72 0 MI. Th rputaton dcay factor s 0.2, whl th ftnss valuaton wght ω andω 2 ar both st to b 0.5 so that th algorthm gvs th sam prorty to both rlablty and makspan. a) RD rputaton compard wth tradtonal rputaton: Th tradtonal rputaton modl uss th rato of succssfully compltd tasks as a rsourc s rputaton. To compar th dffrnc btwn RD and tradtonal rputatons, w tst th two rputatons undr svral xtrm condtons: th sz of all th tst tasks n th systm ar {2,24,36,48,60,72} 0 5 MI rspctvly, th rsourc provdr has a hgh falur rat of 0 3 / h or a low falur rat of 0 4 / h, and th rsourc provdr donats rsourcs of a fast spd of 000MIPS or a slow spd 500MIPS. To facltat th comparson, w drv th task falur probablts for a mdum-szd task basd on th tradtonal and RD rputaton. Fg. 4 shows th two falur probablts normalzd by th standard task falur probablty basd on th rsourc s actual falur rat. Th task falur probablts basd on RD rputaton rman consstntly clos to th standard task falur probablty. Th tradtonal rputaton basd task falur probablty gts clos to th standard task falur probablty only whn th tst tasks n th systm also hav th mdum task sz. Othrws, th falur probablty also ncrass as th sz of th tst tasks ncrass. And whn th rsourcs hav a fastr spd (Fg. 4a) or lowr falur 46

7 rat (Fg. 4b), th task falur probablty basd on tradtonal rputaton wll hav a gratr dvaton from th corrct on. Ths s bcaus th normalzd falur probablty basd on tradtonal rputaton obys a ngatv xponntal functon. Th lowr falur rat and fastr spd wll contrbut to a smallr xponnt whch rsults n gratr dvaton. b) RD rputaton s nflunc to schdulng: To compar th schdulng rsults basd on tradtonal and RD rputaton, half of th rsourcs n th smulaton hav th actual falur rat, whl th othr half of th rsourcs hav thr RD rputaton basd falur rat or tradtonal rputaton basd task falur probablty. Fg. Normalzd Falur Probablty RD_Fast RD_Slow Tradtonal_Fast Tradtonal_Slow Task Sz (E+5 MI) 5 shows both th tradtonal rputaton basd schdulng and RD rputaton basd schdulng hav almost th sam makspan undr varous condtons. Th RD rputaton basd schdulng also has a consstntly lowr falur probablty, whl th tradtonal rputaton basd schdulng has a hghr falur probablty, spcally whn th rputatons ar computd undr condtons whn th task s sz s vry small or vry larg. Ths s bcaus undr such condtons, th tradtonal rputaton gvs a dffrnt rsourc falur rat from th standard on, and tasks ar schduld to mor unrlabl rsourcs. Normalzd Falur Probablty RD_Hgh RD_Low Tradtonal_Hgh Tradtonal_Low Task Sz (E+5 MI) a. Varyng Rsourc Spd b. Varyng Rsourc Falur Rat Fg. 4. Normalzd falur probablty of a mdum-szd task basd on tradtonal rputaton and RD rputaton. Falur Probablty RD_Low Tradtonal_Low RD_Hgh Tradtonal_Hgh Task Sz (E+5 MI) Task Sz (E+5 MI) Fg. 5. Falur probablty and makspan of a workflow applcaton basd on tradtonal rputaton and RD rputaton. Normalzd Makspan RD Tradtonal Makspan (Sconds) Thousands BGA KBGA BGA 0.65 KBGA Numbr of Itratons Numbr of Itratons Fg. 6. Makspan and rlablty gvn by BGA and KBGA n trms of tratons. Rlablty 47

8 c) KBGA s prformanc: W compar KBGA wth BGA [7] whch also optmzs makspan and rlablty for an applcaton by volvng solutons randomly. Th avrag makspan and rlablty of all th solutons ar computd aftr ach traton. Fg. 6 shows KBGA mprovs th makspan and th rlablty for an applcaton mor quckly than BGA. Aftr som tratons, t bcoms vry dffcult for BGA to fnd a bttr soluton by randomly volvng solutons, whl t s asr for KBGA to volv wth hurstcs. At th nd of th algorthm, KBGA can gv a bttr qualty soluton than BGA, n partcular, th hurstcs of KBGA can optmz rlablty mor than makspan. 8. Conclusons In ths papr, w studd th rlablty-drvn schdulng problm n publc-rsourc computng nvronmnts. W proposd th tm-dpndnt RD rputaton for rsourc rlablty valuaton. Th RD rputaton uss th falur rat to dfn a rsourc s rputaton so that t can b usd to valuat a task s rlablty drctly usng th xponntal falur modl. Our RD rputaton calculaton algorthm can also montor th ral-tm changs of th rputaton dynamcally. Basd on th RD rputaton, w dfnd th rlablty-drvn schdulng problm and two hurstcs that am to optmz makspan and rlablty for a workflow applcaton. W proposd th KBGA to volv th schdulng solutons ntllgntly usng th hurstcs. KBGA addrsss th nvald soluton problm by volvng th ordr btwn tasks accordng to thr mportanc valu. Smulaton rsults show that th RD rputaton modl can mprov th rlablty of a workflow applcaton wth mor accurat rputaton. Th KBGA algorthm also outprforms th typcal GA n volvng schdulng solutons. Acknowldgmnts Xaofng s vst to th GRIDS Lab at th Unvrsty of Mlbourn s supportd by th Chns Scholarshp Councl. W thank Marco A. S. Ntto and Sungn Cho for thr commnts. Rfrncs [] J. Sonnk, A. Chandra, and J. Wssman. Adaptv Rputaton-Basd Schdulng on Unrlabl Dstrbutd Infrastructurs. IEEE Transactons on Paralll and Dstrbutd Systms, 8():5-564, [2] A. Jøsang, R. Ismal, and C Boyd. A Survy of Trust and Rputaton Systms for Onln Srvc Provson. Dcson Support Systms, 43(2):68-644, [3] I. Fostr, and A. Iamntch. On Dath, Taxs, and th Convrgnc of Pr-to-Pr and Grd Computng. 2nd Int l. Workshop on P2P Systms, [4] D. Kondo, G. Fdak, F. Cappllo, A.A. Chn, and H. Casanova: Charactrzng rsourc avalablty n ntrprs dsktop grds. Futur Gnraton Comp. Syst. 23(7): , [5] A. Sulsto, G. Poduval, R. Buyya, and C. Tham, On Incorporatng Dffrntatd Lvls of Ntwork Srvc nto GrdSm, Futur Gnraton Computr Systms (FGCS), 23(4):606-65, [6] X. Wang, R. Buyya and J. Su, Rlablty-Orntd Gntc Algorthm for Workflow Applcatons Usng Max-Mn Stratgy, 9th IEEE Intrnatonal Symposum on Clustr Computng and th Grd, [7] M. Wczork, S. Podlpng, R. Prodan, and T. Fahrngr. B-crtra Schdulng of Scntfc Workflows for th Grd. IEEE Symposum on Clustr Computng and th Grd, May, [8] J. Yu, M. Krly, and R. Buyya, Mult-obctv Plannng for Workflow Excuton on Grds, IEEE/ACM Confrnc on Grd Computng, [9] S. Kamvar, M. Schlossr, and H. Garca-Molna, Th Egntrust Algorthm for Rputaton Managmnt n P2P Ntworks, ACM World Wd Wb Conf. (WWW 03), May, [0] L. Wang, H. J. Sgl, V. P. Roychowdhury, t al., Task matchng and schdulng n htrognous computng nvronmnts usng a gntc-algorthm-basd approach, J. Paralll Dstrb. Comput. 47():8-22, 997. [] R. Zhou and K. Hwang, "PowrTrust: A Robust and Scalabl Rputaton Systm for Trustd Pr-to-Pr Computng, IEEE Trans. on Paralll and Dstrbutd Systms, 8(5): , [2] T. D. Braun, H. J. Sgl, N. Bck t al, A comparson of lvn statc hurstcs for mappng a class of ndpndnt tasks onto htrognous dstrbutd computng systms, J. of Paralll and Dstrbutd Computng, 6(6):80-837, 200. [3] S. Song, K. Hwang, and Y.K. Kwok, Rsk-Rslnt Hurstcs and Gntc Algorthms for Scurty-Assurd Grd Job Schdulng, IEEE Trans. on Computrs, 55(6):703-79, [4] D. Lm, Y. Ong, Y. Jn, B. Sndhoff, B. L, Effcnt Hrarchcal Paralll Gntc Algorthms usng Grd computng, Futur Gnraton Computr Systms, 23(4): , [5] J. Dongarra, E. Jannot, E. Saul, and Z. Sh. Bobctv Schdulng Algorthms for Optmzng Makspan and Rlablty on Htrognous Systms. ACM Symp. on Paralllsm n Algorthms and Archtcturs [6] M. Hakm, and F. Butll, Rlablty and Schdulng on Systms Subct to Falurs. Intrnatonal Confrnc on Paralll Procssng(ICPP), Spt [7] A. Dogan and F. Ozgunr. B-obctv Schdulng Algorthms for Excuton Tm-Rlablty Trad-off n Htrognous Computng Systms. Th Computr Journal. 48(3):300-34, [8] S. Zhao and V. Lo, Rsult Vrfcaton and Trust-basd Schdulng n Opn Pr-to-Pr Cycl Sharng systms, IEEE Confrnc on Pr-to-Pr Systms, Spt [9] R. Duan, R. Prodan, and T. Fahrngr, Prformanc and Cost Optmzaton for Multpl Larg-scal Grd Workflow Applcatons, ACM/IEEE Confrnc on Suprcomputng, Novmbr,