PFAS: A Resource-Performance-Fluctuation-Aware Workflow Scheduling Algorithm for Grid Computing

Transcription

1 PFAS: A Resource-Performance-Flucuaon-Aware Workflow Schedulng Algorhm for Grd Compung Fangpeng Dong and Selm G. Akl School of Compung, Queen's Unversy Kngson, ON Canada, K7L N6 {dong, akl}@cs.queensu.ca Absrac Resource performance n he Compuaonal Grd s no only heerogeneous, bu also changng dynamcally. However schedulng algorhms desgned for radonal parallel and dsrbued sysems, such as clusers, only consder he heerogeney of he resources. In hs paper, a workflow schedulng algorhm, called PFAS, s proposed and esed n he Grd envronmen. PFAS consders dynamc resource performance flucuaon n he Grd, and conducs he schedulng accordng o s knowledge of he flucuaon. Ths new algorhm works n an offlne way whch allows o be easly se up and run wh less cos. Smulaons show ha our approach can acheve beer schedules han he HEFT algorhm.. Inroducon The developmen of Grd nfrasrucures, e.g., Pegasus [], Grd Flow [2] and ASKALON [] now enables workflow submsson and execuon on remoe compuaonal resources. To explo he non-rval power of Grd resources, effecve ask schedulng approaches are necessary. In hs paper, we consder he schedulng problem of workflows whch can be represened by dreced acyclc graphs DAG) n he Grd. The ulmae goal gudng he mappng s o reduce he oal compleon me of all asks also known as makespan) n a workflow. As mos Grd resources are no dedcaed o Grd users, Grd resource performance s no only heerogeneous, bu also dynamcally changng due o he compeon among he uses. Therefore, some mechansms are nroduced o ry o capure relevan nformaon abou resource performance flucuaon nformaon e.g., performance predcon [4]), or ry o provde some guaraneed performance o users e.g., resource reservaon [], [6]) /07/$ IEEE These approaches make possble for Grd schedulers o ge relavely accurae resource nformaon pror o producng a schedule, hough resource performance flucuaon sll makes ask schedulng n he Grd more dffcul compared wh ha n radonal parallel and dsrbued sysems such as clusers, n whch resource performance s usually heerogeneous, bu sac for a user. In hs paper, we propose a workflow schedulng algorhm called PFAS for he argeed Grd envronmen. Bascally, PFAS s a ls heursc. Alhough PFAS works n an offlne manner, can be aware of resource performance flucuaon n he Grd, and adops a dynamc ask rankng mehod n he schedulng procedures and a look-forward echnque [7] o fnd proper ask assgnmens. Expermens show ha wh he help of hese wo echnques, PFAS ouperforms he well-known and frequenly referenced HEFT schedulng algorhm [8]. The res of hs paper s organzed as follows: n Secon 2, relaed work s nroduced; Secon presens he applcaon and resources model used by he proposed algorhm; Secon 4 descrbes he PFAS algorhm n deal; Secon presens smulaon resuls and analyss; fnally, conclusons are gven n Secon 6 2. Relaed Work The DAG-based ask graph schedulng problem n parallel and dsrbued compung sysems s an neresng research area, and algorhms for hs problem keep evolvng wh compuaonal plaforms, from he age of homogeneous sysems, o heerogeneous sysems and oday s compuaonal Grds [2]. Due o s NP-complee naure [], mos of algorhms are heursc based and can be classfed no hree caegores: ls algorhms, cluserng algorhms and ask duplcaon based algorhms. In ls algorhms, asks are assgned wh prory values and scheduled n he order of decreasng prory values. The HEFT algorhm [8] and he Dynamc Crcal

2 Pah algorhm DCP) [7] are ypcal examples of ls heurscs. Cluserng s a way o reduce communcaon delay n DAGs by cluserng asks heavly communcang wh each oher o he same subgraph, and hen assgnng a subgraph o he same processor. Cluserng algorhms have wo phases: he ask cluserng phase ha parons he orgnal ask graph no subgraphs, and a poscluserng phase whch can refne he clusers produced n he prevous phase and ge he fnal ask-o-resource map. Examples of hs knd of heurscs can be found n [] and [4]. The man dea of duplcaon based schedulng s ulzng resource dle me o duplcae predecessor asks. Ths may avod he ransfer of resuls from a predecessor o a successor, hus reducng he communcaon cos. In [] and [6], wo duplcaon-based schedulng algorhms are proposed for dsrbued-memory sysems wh homogeneous processors, and neworks of heerogeneous processors, respecvely. The problem of hese algorhms s hey ake he resource performance as a consan durng he execuon of he ob o be scheduled, whch s usually no he case n he Grd. The Exended Dynamc Crcal Pah algorhm xdcp) [7] enhances he DCP algorhm o adap o he dynamc and heerogeneous naure of Grd resources. Bu xdcp ddn use resource performance predcon explcly o refne he schedule. In [8], a DAG schedulng algorhm consderng background workload n mulclusers s proposed. In he argeed sysem, every resource has mulple processors and s own ndependen local scheduler, whch s smlar wh he resource model n hs paper. Bu assumes ha processors n he same resource cluser are homogeneous and share a local Frs-Come- Frs-Served queue, whch s no an assumpon of our approach. Anoher maor dfference s ha he scheduler works n an onlne manner, ha s, he Grd scheduler waches all queues of resource clusers and decdes where he nex schedulable ask should go dynamcally. Performance s Tme Workload Generaed by Reservaon Avalable Performance Fg. : Performance flucuaon resuled from advance reservaon on a resource along me. me slos s,,s k s nroduced. The processng capably of p n me slo s s denoed as c,, and we assume ha n a me slo, c, s a consan. In erms of communcaon delay, he communcaon cos of a daa un along a connecon l, s denoed as w, whch s also a consan along me, and w, = 0 f =..2 Applcaon Model We assume ha a workflow o be scheduled can be represened by a DAG G, as shown n he example of Fg. 2. A crcular node n G represens a ask, where v, and v s number of asks n he workflow. q v) s he compuaonal power consumed o fnsh. For example, n Fg. 2, q =. An edge e, ) from o means ha need an nermedae resul from, so ha succ ), where succ ) s he se of all mmedae successor asks of. Smlarly, we have pred ), where pred ) s he se of mmedae predecessors of. The wegh of e, ) gves he sze of nermedae resuls or communcaon for smplcy) ransferred from o ask. For example, he communcaon volume from o 2 s n Fg. 2. s k. Models and Defnons 4. Resource Model As menoned prevously, he dynamc performance flucuaon of processng nodes s consdered. In a resource managemen sysem supporng advance reservaon, avalable resource performance a a specfc me can be known by calculang he workload generaed by obs ha have reserved resources a ha me, as Fg. ndcaes. Thus, by referrng resource predcors or resource managemen componens supporng reservaon, he performance flucuaon can be caugh. Theorecally, f he me axe can be dvded no fne granular perods, he performance whn a perod can be approxmaed as a consan. Thus, o descrbe he flucuaon, a sequence of Fg. 2: A DAG depcng a workflow applcaon, n whch a node represens a ask, and a labelled dreced edge represens a precedence order wh a ceran sze of nermedae resul ransfer

3 When a feasble schedule s compued, he followng addonal resrcons apply: ) Only one ask can run on a processng node a he same me; 2) A ask canno begn unl ges all of s nermedae resul. Accordng o hs resrcon, we need o defne he earles sar me EST) of a ask on processng node p as: EST, p ) = max { CT ) + w e x, )} x PA ), pred ) x x Here CT x ) s he compleon me of x and PA x ) s he processor o whch x s assgned. All noaons used n he algorhm descrpon and her meanngs can be found n Table. 4. PFAS Algorhm The prmary obecve of PFAS s o assgn asks n a workflow o proper compuaonal resources o mnmze he makespan. To acheve hs goal n dynamc heerogeneous envronmens, he proposed algorhm has he followng feaures: ) I updaes he ranks of ask nodes n real me n each schedulng sep so ha he crcal pah can be recognzed dynamcally. 2) To avod a myopc opmzaon, looks forward along he curren recognzed crcal pah when selecng a resource for he curren ask node. ) To use dle me slos on a resource, can nser an unscheduled ask before a scheduled ask on he same resource f he nseron doesn volae precedence condons. 4. Task Node Rankng The crcal pah CP) of a ask graph s a se of nodes and edges, formng a pah from an enry node o an ex node, and all of he nodes called crcal nodes) on hs Table : Symbols and Defnons. Symbol Meanng Rank u ) Upward rank of ask Rank d ) Downward rank of ask Rank ) Toal rank of ask DCP Dynamc crcal pah a schedulng sep. PA ) The processor o whch ask s assgned EST, p ) The earles sar me of on processor p ECT, p ) The earles complee me of on processor p The esmaed execuon me of ask nodes EPTP, p, T) on pah P on p sarng from me T based on average performance of p. CT ) Complee me of afer s scheduled Execuon me of RT ) on he processor where s scheduled RQ The ready ask queue AVLT m) The earles avalable me of processng node p a he mh schedulng sep pah have he same maxmum rank value See Equaon 9)). As he schedulng proceeds, he CP of a ask graph mgh be changed because of he followng hree reasons: ) he communcaon cos beween wo conuncve ask nodes wll be se o zero, f hey are assgned o he same resource; 2) he execuon me and compleon me of a node can be esmaed afer s scheduled; ) he avalable me slos of a resource are o be changed once a ask node s assgned o he resource. So, nsead of usng a sac rank value compued a he begnnng of he schedule, PFAS adops a dynamc rankng sraegy, ha s, once a ask node s scheduled, he ranks for all of he oher nodes wll be updaed. A each schedulng sep, he scheduler chooses he unscheduled ask whch has he hghes dynamc rank. And sarng from hs node, he scheduler also consrucs a dynamc crcal pah DCP). To updae he rank of a ask node, average performance of processng nodes n feasble me slos s used. The feasble me AVLT of processng node p n he mh schedulng sep s defned by he followng Equaon: AVLT m) = mn{ EST, p )} RQ AVLT m) fnds he earles me when a processng node could run a ask n he ready queue n he mh schedulng sep. Tme slos afer hs me wll be consdered feasble and he correspondng performance whn hese slos wll be used o updae prores of ask nodes. For smplcy, we om m from all expressons, whou losng generaly. To evaluae he performance of a resource as accuraely as possble, he scheduler frs needs o esmae he number of me slos whch wll be used o complee he ob he value of parameer k n s,, s k ). In PFAS, an opmsc esmaon sraegy s used: The scheduler esmaes he seral processng me of he whole ob on each processng node respecvely, and chooses he smalles one. Ths sraegy s based on he expecaon ha he parallel processng, even n he wors case, s no worse han he bes sequenal one. To schedule a ask graph effcenly, s mporan o denfy he crcal asks o be scheduled a each sep. The delay of crcal nodes may resul n he exenson of he schedule lengh. Usually, he prory of a ask node can be obaned by fndng he maxmum dsance from hs node o he sarng nodes and exng node. Here, dsance means he sum of compuaonal and communcaon coss along a ceran pah. Unforunaely, due o he heerogeney and flucuaon of resource performance, s very dffcul o fnd how urgen a ask node really s due o he varaon of compleon mes of s successve asks on dfferen processng nodes and n dfferen me slos. To esmae he compleon mes of nodes n such a scenaro, several performance measuremen can be used, such as usng he medan [9] or average value of resource performance. In he followng dscusson, we use he

4 average performance value o demonsrae our algorhm. The average performance of p n dfferen slos, denoed by avg_c, s gven by Equaon ), where k s he number of me slos used o conduc he schedulng. avg _ c = c ), k AVLT AVLT k The average performance of all avalable compuaonal resources, denoed by avg_c, s gven by Equaon 2), where n s he number of processng nodes. avg_ c = avg_ c 2) n n Smlarly Equaon ) and 4) gve he average communcaon cos of p o all oher nodes avg_w, and he overall average communcaon cos avg_w, respecvely. avg_ w = w ), n n avg _ w = w 4) 2, n, n I s assumed ha he me requred o complee a ask on dfferen processors s unformly relaed o he performance of resources, ha s o say, f he performance of a processng node p s a consan c, wll fnsh ask whn me q / c. Followng hs assumpon, Equaon ) relaes compuaonal cos, resource performance and me for he performance flucuang scenaro: end c sar ss s s sar ) complee sc ) c + c + c ) q =, s, e, c u e= s+ u where s sar and s end are he sar and end of a me slo, u s he lengh of me slo, s sar and s complee are sar me and compleon me of, and s and c are ndexes of me slos n whch sars and complees, respecvely. Wh EST, p ) and he performance of p n dfferen mes slos, s sraghforward o ge he earles complee me of on p ECT, p ), accordng o Equaon ) where s sar = EST, p ) and s complee = ECT, p ). Now we can defne he prory of a ask node n G, whch s decded by s upward rank rank u and downward rank rank d. To recognze he crcal pah dynamcally, he rank of a node needs o be updaed n dfferen schedulng seps. rank u s compued recursvely from he ex node upward o he enry node. If a node s no scheduled ye, rank u ) s defned as: q ranku ) = + max e, ) avg _ w + ranku )) 6) avg _ c succ ) In hs case, snce s no scheduled, s execuon me and he delay of sendng nermedae resuls o s successors are gven by esmae usng average resource performance. If has been scheduled, he real run me of RT ) s known, bu a successor of mgh no scheduled ye. So n hs case rank u ) s defned as: rank ) = RT ) + u max TransTme, ) + rank succ ) u )) 7) e, ) wpa f s scheduled ), PA ) TransTme, ) = e, ) avg _ wpa ) oherwse If s scheduled, he nermedae resul ransfer me from o s known, oherwse, he average communcaon cos of he processng node of s used. Smlarly, rank d ) s compued recursvely from he enry node downward o he ex node. If has been scheduled, all of s predecessors have been scheduled oo. So, n hs case, rank d ) s defned as: rank ) = max { rank ) + RT ) + e, ) w } 8) d d PA ), ) ) PA pred Specally, for he enry node, rank d ) = 0. If has no been scheduled ye, we need o consder wheher s predecessors have been scheduled or no, so here are sll wo cases: rankd ) + RT ) + e, ) avg_ wpa ), scheduled rank ) = max q d pred ) rank ) + + e, ) avg_, oherwse avg_ c w d The rank of a ask node s defned as he sum of s upward and downward ranks: rank ) = rank ) + rank ) 9) u d 4.2 Processng Node Selecon Afer a crcal ask node s seleced, he scheduler needs o fnd an approprae me pon on a compuaonal resource o whch he ask node wll be assgned. To ulze dle me slos as much as possble, he scheduler uses an nseron-based mehod, whch can be formalzed by he followng rule. Rule: A ask can be nsered no processor p whch conans a sequence of asks {, 2,, }a me s, f n here s some m ha for every ask x n {,,, }, ECT, p ) EST,, p ), and for every ask 2 m x n {,,, }, ECT,, p ) y m m+ n EST, p ). y Rule saes ha a ask can be nsered on a processor only f here s are me slos large enough o accommodae whou delayng asks already scheduled or volang precedence orders among he asks. Inuvely, hgh prory asks should be assgned o resources whn her hgh performance me slos. The problem of selecng a processng node ha only gves he earles complee me for he curren ask s ha hs mehod s myopc and may fall no a local opmzaon. For example, can happen ha afer he ask a s assgned o a resource p x, s successors on he crcal pah P sarng from ask b also has o be assgned o p x because he nermedae resul ransfer beween a and b mgh delay he earles complee me of b oherwse. Bu acually, even b self s delayed on anoher resource, say

5 p y, s possble ha he execuon of remanng asks on P can make up hs delay because p y may have a faser compuaonal speed. So nsead of usng he smple myopc earles complee me sraegy, PFAS adops a look-forward approach o avod a based schedule ha only consders he curren ask and resource saus. To hs end, we frs defne a funcon EPTP, p, T) whch gves he esmae execuon me of a paral pah P on resource p, sarng a me T. q P EPT P, p, T) = c / k ), T T k Rule 2: If s he curren ask o be scheduled and s he drec chld of on he longes pah P measured by ask rank from o an ex node, hen should be scheduled o he processng node p x whch sasfes mn { PEST ) + EPT P, p, PEST y x, y n PEST ) = ECT, px ) + wx y ))}, e, ) 0) PEST ) s he earles me when a paral crcal pah P, sarng wh can possbly sar, and funcon EPT compues he esmaed execuon me of asks on P usng he average performance of each processng node afer hs me pon. So, Rule 2 saes ha nsead of only fndng he processng node ha can fnsh he earles, PFAS s ryng o fnd a par of processng nodes, p x and p y, so ha execuon me for he asks on he longes pah from o an ex node wll be mnmzed. Now we can presen he pseudo codes of he PFAS algorhm. The me complexy of PFAS wll be calculaed as wha follows: The whle loop on lne 4 wll run v mes o schedule every ask. In Selec_Processor, o fnd a longes pah for he curren ask node requres Ov) mes n he wors case, and he ouer for loops on lne 2 wll run n mes. To compue ECT of a ask, coss Ov*L), where L s he max node degree n ask graph G. The nner for loop wll also run n mes, and n each erae, wll cos a mos Ov) o compue he EPT funcon. To updae he avalable me of each processor, requres On*v) on lne 8. So, he oal cos of he Selec_Processor procedure s Ov+n*v*L+n 2 *v+ n*v) = On 2 *v). Back o Algorhm PFAS, o updae prores of unscheduled asks, coss On*k)+Ov), where On*k) s he cos o updae he avalable performance of each processor and Ov) s he cos o updae ranks of asks. So he oal complexy of PFAS s On 2 v 2 +nkv). PFAS Algorhm Inpu: A subgraph and a se of resources r,, r n. Oupu: ask node o resource mappng. Compue rank u and rand d for each ask usng average resource performance; 2. Se he prory of each ask as he sum of s rank u and rand d ;. Inal he ready queue RQ wh he enry ask; 4. Whle here are unscheduled nodes){. Selec he hghes prory ask n RQ; 6. Call Selec_Processor) o assgn ask ; 7. Updae prores of all asks; 8. } Process Selec_Processorask ). Fnd he longes pah P from o an ex node. 2. For all avalable processors p {. Compue ECT, p ); 4. For all processors p. Call EPTP, p, ECT,p )+w, *e,)) 6. } 7. Inser o p ha sasfes Rule 2; 8. For all avalable processors p, updae avalable me of p AVLT and feasble performance. An example llusrang he PFAS algorhm s gven below, whch akes daa n Table a) and b) as resource performance and communcaon cos respecvely, and schedules he ask graph gven by Fg. 2. I s also compared wh oher wo schedulng mehods: he HEFT algorhm and a performance flucuaon aware algorhm whou he look-forward sraegy called NLF). In Table 2, ranks of asks a each schedulng sep are gven, and n Table, he avalable average performance of each compuaonal resource s gven. In he frs sep, s seleced as s he hghes rank ready ask and he curren dynamc crcal pah s DCP = {, 4,, 7, 8 }. Accordng o Rule 2, assgnng o p wll gve he mnmum value Table: a) A able showng he performance flucuaon of compuaonal resources n 2 me slos. b) Communcaon cos of un daa ransfer beween resources gven n a). p p 2 p s 2 s 2 2 s 2 2 s s 8 8 s s s 8 8 s 9 4 s 0 6 s 4 s avg_c 4 avg_c 4 a) p p 2 p p 0. p p. 2 0 avg_w b)

6 Table 2: Task Node ranks and he dynamc crcal pah of each schedulng sep n shadng cells). Seps ,8 +2/ 4+/ +/4 Lengh P P2 P P P2 P 2 +2/ 4 2+2/ 4 2+2/ +/ +/ /24 4+/4 2 4+/6 6 +9/ /2 7 6+/ / 8 7+7/ /4 8 9+/2 Lengh a b / / 0 Lengh P P2 P 4 +/8 4+7/ /7 8 c Table : Feasble average performance of compuaonal resources n each schedulng sep. Seps p p 2 p Avg. Inal / 8/4 87/ / 2/20 87/ / 024/69 87/ / 707/28 87/ / 602/ 87/ / 602/ 87/ /27 602/ 87/ of Expresson 0) wh p x = p and p y = p 2, he value s 6.784, wh p x = p y =, he value s , wh p x = 2, p y = 2, he value s 7.079). In he begnnng of he second sep, he ranks of asks are updaed as he fnsh me of s already known and avalable me slos on resources have changed. Now 4 s n he ready queue wh he hghes prory, and DCP 2 = { 4,, 7, 8 }. Agan, Rule 2 s called o fnd he bes nseron whch s processor 2 wh p x = p y =, he value s , wh p x = 2, p y = 2, he value s ). Evenually, PFAS wll gve a schedule as he Gan char n Fg. a). Fg. b) and c) gve he resuls of he wo compared mehods. I s obvous ha PFAS gves he bes scheduled n erm of makespan.. Expermens To evaluae he effecveness of PFAS n he Grd crcumsances, comparave expermens are done o smulae s performance. Three dfferen schedulng algorhms are esed n he expermens: ) PFAS, 2) PFAS whou look-ahead along he dynamc crcal pah NLF), and ) HEFT algorhm. The performance merc we used for he comparson s he Scheduled Lengh Rao SLR), whch s he rao of real makespan o he heorecal lower bound of any possble schedulng, whch equals he execuon me he longes pah measured n Fg. : Gan chars of he dfferen schedule approaches for he example: a) PFAS; b) PFAS whou look-ahead NLF); c) HEFT. compuaon cos on he fases resources whou any communcaon delays.. Expermenal Sengs In he expermens, hree resource clusers are used. Each cluser consss of 0 processng nodes conneced by a LAN. The resource clusers are conneced by a WAN. The opology and nal parameers such as processng capacy, communcaon cos, and load of each processor are generaed usng a oolk named GrdG.0 [0]. In erms of npu ask graphs, a ask graph generaor called Task Graph For Free TGFF) [] s used o generae ask graphs submed o he Grd. TGFF has he ably of generang a varey of ask graphs accordng o dfferen confguraon parameers, such as average number of ask nodes of each graph, average ougong and ncomng degrees for each node n a graph, and compuaonal and communcaon cos for each ype of ask nodes and edges. To es he adapve ably of our schedulng approach o dfferen ask graphs and resource sengs, he followng parameers are consdered n he expermen: The average number ask nodes n a graph v; The rao of he average degree of a ask node o he oal number of asks n a graph Edge densy n a graph); The compuaon-o-communcaon rao CCR) of a ask graph. CCR s he average rao of compuaon cos o communcaon cos. A hgh CCR value means a ask graph s compuaon-nensve. Resource performance flucuaon facor whch decdes he percenage ha he performance of a compuaonal resource can ncrease or drop n dfferen me slos. The communcaon heerogeney facor whch decdes how dfferen communcaon coss beween dfferen compuaonal resources are.

7 .2 Smulaon Resuls Wh respec o he number of nodes n a ask graph, dfferen average values are appled: 20,, 60, 80 and 00. For each of hese values, 2 graphs are generaed. Fg. 4 a) llusraes he average performance of he schedulng algorhms. Frs, can be observed ha, as he number of ask nodes ncreases, he performance of all of hese hree algorhms decreases. The explanaon for he performance drop s ha: he ncreasng of ask nodes number wll resul n more accumulae error n ask node rankng. Second, PFAS acheves he bes performance among he hree algorhms. NLF whch only consders he performance flucuaon ouperforms HEFT by a small margn. Ths mples ha he benef brough by only updang he ask node ranks dynamcally s lmed. The edge densy s an mporan characer of a graph, whch decdes he communcaon volume among asks. To descrbe he edge densy, he rao of he average degree of each ask node o he oal number of nodes n a graph s used n our expermens. Fve dfferen sengs are esed: 0.0, 0., 0.2, 0. and 0.4. For each seng, 2 dfferen graphs are generaed as well. As Fg. 4 b) ndcaes, as he degree of ask nodes ncreases, he SLR of PAFS frsly drops and hen keeps seady, and s he overall bes. The SLR of NLF and HEFT frsly ncreases and hen drops. Increasng he degree of asks mples ncreasng of he oal communcaon volumes, so he makespan s exended due o more communcaon delay. The neresng pon s afer he rao s greaer han 0., SLR of all of he hree algorhms drops agan. The explanaon o hs phenomenon s ha, as he oal number of ask nodes s fxed, ncreasng he average degree of nodes has he effec of reducng he lengh of he crcal pah and ncreasng he breadh when a ask graph s generaed by TGFF. So, as he degree ncreases, he possbly of hgh parallelsm also ncreases, whch mgh shadow he ncrease n communcaon volume. Ths also explans why he performance PAFS s worse han HEFT a he begnnng: when he crcal pah s longer, here are more errors n he look-head procedure whch reles on he esmae o he fnsh me of he crcal pah. The oher parameer conrbung o characerscs of a ask graph s he CCR. In he expermen, he rao ncreases from 0. o 0. As Fg. 4 c) ndcaes, as he rao ncreases, he SLR of PFAS and NLS slghly drops and hen ncrease, and he one of PFAS s he lowes. The drop of SLR a he begnnng s brough by he decreasng communcaon o compuaon cos rao. Bu as compuaon cos of a ask node ncreases, s execuon me on dfferen resources a dfferen me becomes more dfferen, whch mples ha he esmae o execuon me depars from he real suaon furher. To es he adapveness of he hree schedulng SLR SLR SLR PAFS HEFT NLF Number of Task Nodes a) Degree/Node Number b) Compuaon/Communcaon Rao c) Fg. 4: Expermen resuls of dfferen parameer sengs. a) Dfferen number of asks n a Grd Workflow. b) Dfferen average node degree n a ask graph. c) Dfferen compuaon o communcaon rao n a ask graph. mehods o compuaonal power flucuaon, fve dfferen values are assgned o he performance flucuaon facor: 20%, %, 0%, 60% and 80%, each denong he maxmum allowed percenage of full compuaon power drop n dfferen me slos. As Fg. a) shows, as resource performance becomes more flucuang, he SLR of all mehods ncreases whch s brough by he more dffculy o ge accurae esmae. PFAS, followed by NLF, s he bes among he esed algorhm. The oher resource relaed parameer nvolved n he smulaon s he communcaon cos heerogeney rao. In he expermen, he rao s assgned dfferen values also: 0.2, 0.4, 0.6, 0.8 and.0, whch gves he maxmum percenage of he communcaon cos of a connecon beween wo resources can dfferen from he average cos

8 SLR 0 20 SLR Performance Flucuaon Facor 60 0 a) Communcaon Heergenesous Facor b) Fg. : a) Dfferen performance flucuaon facors. b) Dfferen communcaon cos facors. value. As Fg. b) ndcaes, he SLR of he hree mehods ncreases as he nework connecon becomes more heerogeneous whch brngs more errors o ask node ranks. The SLR of PFAS s sll he lowes, followed by NLF and HEFT, whch means PFAS s more adapve o he nework heerogeney han he oher wo mehods. 6. Conclusons In hs paper we propose a resource performance flucuaon aware workflow schedulng algorhm PFAS for he Grd. Insead of usng a sac ask rankng approach whch s usually conduced once a he begnnng of a DAG schedulng algorhm, PFAS updaes ask ranks and consrucs he crcal pah dynamcally n he schedulng procedure accordng o he change n performance of avalable resources. PFAS also adops a look-ahead approach o assgn a crcal ask. Ths allows o overcome myopc decsons made by he earles complee me creron whch s used by many oher schedulng algorhms. Expermens show ha he schedulng performance, measured n makespan, benefs from boh echnques. Smulaon resuls also show ha PFAS s adapve o dfferen ask graphs and resource opology sengs. Is overall performance s much beer han ha of he HEFT algorhm, whch s a powerful DAG schedulng algorhm desgned for heerogeneous compuaonal envronmens. The curren mplemenaon of PFAS does no consder he possbly of wrong performance predcon, whch s lkely n he real suaons. Ths s he problem on whch we are currenly workng. The smulaons also show ha esmang ask ranks by average resource performance leads o an accumulaon of esmae errors when he crcal pah s long or resources are more heerogeneous, so beer and more complex ways mgh be nroduced n he fuure for mprovemen. The algorhm s also gong o be esed by realsc workflows n he Grd. References [] E. Deelman, J. Blyhe, e al. Pegasus: Mappng Scenfc Workflows ono he Grd. In he Proc. of Grd Compung: Second European AcrossGrds Conference AxGrds 2004), pages:- 26, January [2] J. Cao, S. A. Jarvs, e al.. GrdFlow: Workflow Managemen for Grd Compung. In Proc. of he rd CCGrd, pages:98-20, Tokyo, Japan, May 200. [] M. Weczorek, R. Prodan and T. Fahrnger. Schedulng of Scenfc Workflows n he ASKALON Grd Envronmen. In ACM SIGMOD Record, Vol.4, No., pages: 6-62, Sepember 200. [4] L. Yang, J. M. Schopf and I. Foser. Conservave Schedulng: Usng Predced Varance o Improve Schedulng Decsons n Dynamc Envronmens. In Proc. of he 200 Supercompung, pages: -- 46, November 200. [] K. Aggarwal and R. D. Ken. An Adapve Generalzed Scheduler for Grd Applcaons. In Proc. of he 9h Annual Inernaonal Symposum on Hgh Performance Compung Sysems and Applcaons HPCS), pages: - 8, May 200. [6] G. Maeescu. Qualy of Servce on he Grd va Measchedulng wh Resource Co-Schedulng and Co- Reservaon. In Inernaonal Journal of Hgh Performance Compung Applcaons, Vol. 7, No., pages: , 200. [7] Y.K. Kwok and I. Ahmad. Dynamc Crcal-Pah Schedulng: an Effecve Technque for Allocang Task Graphs o Mulprocessors. In IEEE Trans. on Parallel and Dsrbued Sysems, Vol. 7, No., pages: 06-2, May, 996. [8] H. Topcuoglu, S. Harr and M.Y. Wu. Performance- Effecve and Low-Complexy Task Schedulng for Heerogeneous Compung. In IEEE Trans. on Parallel and Dsrbued Sysems, Vol., No., pages: , [9] H. Zhao and R. Sakellarou. An Expermenal Invesgaon no he Rank Funcon of he Heerogeneous Earles Fnsh Tme Schedulng Algorhm. In Proc. of Euro-Par 200, Sprnger-Verlag, LNCS 2790, pages: 89-94, Klagenfur, Ausra, Augus 200. [0] D. Lu and P. Dnda. Synheszng Realsc Compuaonal Grds. In Proc. of ACM/IEEE Super-compung 200, Phoenx, AZ, USA, 200. [] R.P. Dck, D.L. Rhodes and W. Wolf, TGFF Task Graphs for Free, Proc. of he 6h. Inernaonal Workshop on

9 Hardware/Sofware Co-desgn, 998. [2] F. Dong and S. G. Akl. Grd Applcaon Schedulng Algorhms: Sae of he Ar and Open Problems. Techncal Repor No , School of Compung, Queen's Unversy, Canada, Jan [] H. El-Rewn, T. Lews, and H. Al. Task Schedulng n Parallel and Dsrbued Sysems, ISBN: 09926, PTR Prence Hall, 994. [4] J. Lou and M. A. Pals. A Comparson of General Approaches o Mulprocessor Schedulng. In Proc. of he h Inernaonal Symposum on Parallel Processng, pages:2-6, Aprl 997. [] T. Yang and A. Gerasouls. DSC: Schedulng Parallel Tasks on an Unbounded Number of Processors. In IEEE Trans. on Parallel and Dsrbued Sysems, vol., no. 9, pages: , 994. [6] S. Darbha and D.P. Agrawal. Opmal Schedulng Algorhm for Dsrbued Memory Machnes. In IEEE Trans. on Parallel and Dsrbued Sysems, vol. 9, no., pages: 87-9, January 998. [7] R. Baa and D. P. Agrawal, Improvng Schedulng of Tasks n A Heerogeneous Envronmen. In IEEE Trans. on Parallel and Dsrbued Sysems, Vol., no. 2, pages: 07 8, February [8] T. Ma and R. Buyya. Crcal-Pah and Prory based Algorhms for Schedulng Workflows wh Parameer Sweep Tasks on Global Grds. In Proc. of he 7h Inernaonal Symposum on Compuer Archecure and Hgh Performance Compung, pages: 2-28, Ocober 200. [9] L. He, S. A. Jarvs, D. P. Spooner, D. Bacgalupo, G. Tan, G. R. Nudd. Mappng DAG-based Applcaons o Mulclusers wh Background Workload. In Proc. of he h IEEE Inernaonal Symposum on Cluser Compung and he Grd CCGrd'0), pages: 8-862, May 200. and a co-auhor of Parallel Compuaonal Geomery Prence Hall, 992). Dr. Akl s edor n chef of Parallel Processng Leers and presenly serves on he edoral boards of Compuaonal Geomery, he Inernaonal Journal of Parallel, Emergen, and Dsrbued Sysems, and he Inernaonal Journal of Hgh Performance Compung and Neworkng. Bographes Fangpeng Dong receved hs B.Sc from he Deparmen of Compuer Scence and Technology, Pekng Unversy, Beng, Chna n 2000 and M.E. from he Insue of Compung Technology, Chnese Academy of Scences, Beng, Chna n 200. He s now a Ph.D. suden n he School of Compung, Queen's Unversy a Kngson, Onaro, Canada. Hs maor research neress nclude Grd compung and oher parallel and dsrbued sysems. He s also an IEEE suden member. Selm G. Akl receved hs Ph.D. degree from McGll Unversy n Monreal n 978. He s currenly a professor of Compung a Queen's Unversy, Kngson, Onaro, Canada. Hs research neress are n parallel compuaon. He s auhor of Parallel Sorng Algorhms Academc Press, 98), The Desgn and Analyss of Parallel Algorhms Prence Hall, 989), and Parallel Compuaon: Models and Mehods Prence Hall, 997),