Stochastic Scheduling with Availability Constraints in Heterogeneous Clusters

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1 Ths paper appeared the Proceedgs of the 8th IEEE Iteratoal Coferece o Cluster Coputg (Cluster 006), Sept Stochastc Schedulg wth Avalablty Costrats Heterogeeous Clusters Tao Xe Xao Q Departet of Coputer Scece Departet of Coputer Scece Sa Dego State Uversty New Mexco Isttute of Mg ad Techology Sa Dego, Calfora 98 Socorro, New Mexco 8780 xe@cs.sdsu.edu xq@cs.t.edu Abstract Hgh avalablty plays a portat role heterogeeous clusters, where processors operate at dfferet speeds ad are ot cotuously avalable for processg. Exstg schedulg algorths desged for heterogeeous clusters do ot factor avalablty. We address ths paper the stochastc schedulg proble for heterogeeous clusters wth avalablty costrats. Each ode a heterogeeous cluster s odeled by ts speed ad avalablty, ad dfferet classes of tasks subtted to the cluster are characterzed by ther executo tes ad avalablty requreets. To corporate avalablty ad heterogeety to stochastc schedulg, we troduce etrcs to quatfy avalablty ad heterogeety the cotext of ultclass tasks. A stochastc schedulg algorth SSAC (Stochastc Schedulg wth Avalablty Costrats) s the proposed to prove avalablty of heterogeeous clusters whle reducg average respose te of tasks. Experetal results show that our algorth acheves a good trade-off betwee avalablty ad resposveess.. Itroducto Stochastc schedulg s to vestgate the proble of schedulg a set of tasks wth rado features. Coo rado features such as task processg tes are usually odelled by specfyg ther probablty dstrbuto. Although a task's processg te s ot kow utl t s coplete, the probablty dstrbuto of task processg tes are assued to be kow by the syste as a pror. Stochastc schedulg could be preeptve or o-preeptve, coduct o oe or o ultple processors, ad be cocered wth varous optzato crtera. A heterogeeous cluster cossts of a array of dverse coputers, called coputg odes, whch are coected by a hgh-perforace etwork. To date heterogeeous clusters have bee eergg as popular coputg platfors for coputatoally tesve applcatos wth dverse coputg eeds. Schedulg algorths play a key role obtag hgh perforace parallel systes lke heterogeeous clusters []. The obectve of schedulg algorths s to ap tasks oto odes ad order ther executo a way to optze overall perforace. I schedulg theory the basc assupto s that all aches are always avalable for processg [7]. Ths assupto ght be ustfed soe cases but t s ot vald scearos where certa ateace requreets, breakdows or other costrats, whch ake the aches ot to be avalable for processg, have to be cosdered [7]. Exaples of such costrats ca be foud ay areas. For stace, coputatoal odes heterogeeous clusters eed to be ataed perodcally to prevet alfuctos [0]. I ths study avalablty s defed as the rato of the total te a coputg ode s fuctoal durg a gve terval to the legth of the terval. Thus, the avalablty of a heterogeeous cluster wll be degraded f oe or ultple odes are out of duty due to rado breakdow or prevetve ateace. O the other had, however, owadays ay hgh-perforace clusters eed a hgh avalablty [][0]. For stace, ltary applcatos, 4 7 healthcare applcatos, ad teratoal busess applcatos all dead a extreely hgh avalablty as severe daages or fatal errors could occur whe eve oly oe coputg ode becoes uavalable []. As such, a schedulg strategy for heterogeeous clusters has to factor avalablty to deal wth ateace actvtes ad uexpected falures. Ufortuately, covetoal stochastc schedulg algorths for heterogeeous clusters oly cocetrated o hgh throughput wth the /06/$ IEEE.

2 goal of reducg tasks average respose tes ad orally gored the avalablty requreets of the tasks. It s challegg, however, to acheve hgh throughput ad hgh avalablty sultaeously because they are two coflct obectves []. For exaple, t s uacceptable to assg a crtcal-task wth hgh avalablty requreet to a ode that provdes wth a hgh speed but low avalablty level. A feasble schee s to acheve a good trade-off such that tasks avalablty requreets ca be et whle average respose te s cofed to a deal rage. I ths paper we address the proble of schedulg dfferet classes of tasks wth avalablty costrats heterogeeous syste. We a at developg a stochastc schedulg strategy to prove avalablty of heterogeeous systes whle reducg average respose te of ult-class tasks. The schedulg algorth proposed ths paper ca be appled to heterogeeous systes where capacty ad avalablty costrats are kow a pror. The a cotrbutos of ths paper are: () a avalablty-latecy drve stochastc schedulg schee SSAC (Stochastc Schedulg wth Avalablty Costrats) for ultple classes of tasks o heterogeeous clusters; () a syste odel for quattatvely easurg avalablty of coputg odes; (3) two types of heterogeetes: coputatoal heterogeety ad avalablty heterogeety; (4) a sulated heterogeeous cluster where the SSAC strategy s pleeted ad evaluated. The rest of the paper s orgazed as follows. I the ext secto we brefly troduce related works. Secto 3 descrbes the syste odel, the task odel ad heterogeety odel. I Secto 4, we propose the SSAC schee for ultple classes of tasks rug o heterogeeous clusters. We preset Secto 5 experetal results based o sythetc becharks. Secto 6 cocludes the paper wth suary ad future drectos.. Related work I stochastc schedulg, a typcal scearo s that tasks have processg tes that are expoetally dstrbuted wth dfferet eas ad are to be processed by detcal coputg odes operatg parallel. I ths case zg the expected akespa (the te at whch all tasks are coplete) s a obectve fucto for a schedulg strategy dedcated to ths scearo. Extesve research has bee doe stochastc schedulg. Schopf ad Bera defed a stochastc schedulg polcy based o tebalacg for data parallel applcatos whose executo behavor ca be represeted as a oral dstrbuto [9]. Ca et al. studed the proble of fdg a dyacally optal polcy to process obs o a sgle ache subect to stochastc breakdows. The proble of schedulg custoers a ult-class G/G/ queue was addressed by Na ad Towsley [3] so as to ze a weghted su of the work-loads of the dfferet classes. However, lttle atteto has bee pad to schedulg tasks wth stochastc features ad hgh syste avalablty requreets. Recetly, Chakraverty proposed a co-sythess echas for geeratg gracefully degradg ultprocessor archtectures whch fulfll the dual obectves of achevg real-te perforace as well as esurg hgh levels of syste avalablty [6]. Over the last decade, heterogeeous clusters have becoe wdely used for scetfc ad coercal applcatos [8]. I recet years, the ssue of schedulg o heterogeeous clusters has bee addressed ad reported the lterature [7][4]. Doga ad F. Özgüer developed relable atchg ad schedulg algorths for tasks wth precedece costrats heterogeeous dstrbuted clusters [7]. Srvasa ad Jha corporated relablty cost, defed to be the product of processor falure rate ad task executo te, to schedulg algorths for tasks wth precedece costrats [3]. Raaweera ad Agrawal proposed a scalable schedulg schee called STDP for heterogeeous systes [6]. Schedulg algorths are of crtcal portace obtag hgh perforace varous coputg platfors [5][5]. The proble of schedulg ultple classes of tasks was otvated by a wde rage of dstrbuted applcatos lke scalable web server systes [9]. Sethuraa et al. proposed a optal stochastc schedulg strategy that ca ze a fucto of the per-class respose te varaces [0]. The schedulg algorth proposed ths paper dffers fro thers that our algorth corporates avalablty costrats to schedulg. I our prevous work, we studed securty-aware schedulg for clusters [5] ad Grds [6]. These schedulg algorths oly support hoogeeous systes, ltg ther applcablty to heterogeeous systes. Further, these algorths are ot sutable for ult-class tasks wth avalablty requreets. I cotrast, our algorth akes a tradeoff betwee avalablty ad resposveess.

3 Class Class Schedule Queue SSAC Avalabltyadaptve wdow Task allocato decso aker Local N N Avalablty defcecy Class N Fgure. Syste odel of the SSAC strategy Soe researches about provg avalablty of clusters were reported the lterature recetly. Solter ad Trpath preseted a protocol ad archtecture o the Su/spl trade/ Cluster syste for delverg cluster evets to a hgh-avalablty cluster []. Leagsuksu et al. proposed cocepts of tegratg hgh avalablty cluster echas wth a secure cluster frastructure []. Apo ad Wlbur desged a Advaced Mult Processor Network wth a hgh avalablty d []. Our approach of provg avalablty of a heterogeeous cluster s dfferet fro the ethods above. We tegrated tasks avalablty requreets to stochastc schedulg to acheve a good balacg betwee syste avalablty ad throughput easured as average respose te. 3. Matheatcal odels 3.. Syste odel I ths study, we cosder a queug archtecture of a -ode heterogeeous cluster whch heterogeeous odes are coected va a etwork to process depedet class of tasks subtted by users. Let N = {N, N,, N } deote the set of heterogeeous odes. The syste odel, depcted Fgure, s coposed of a task schedule queue, SSAC task scheduler, ad local task queues. The fucto of SSAC s teded to ake a good task allocato decso for each arrval task to satsfy ts avalablty requreet ad ata a deal perforace average respose te. A schedule queue s used to accoodate cog tasks. SSAC scheduler the processes all arrval tasks a Frst-Coe Frst-Served (FCFS) aer. After 3 beg hadled by SSAC, the tasks are dspatched to oe of the desgated ode N N for executo. The odes, each of whch atas a local queue, ca execute tasks parallel. The a copoet of the syste odel above s SSAC, whch s coposed of three odules: () Avalablty defcecy calculator; () Avalablty-adaptve wdow cotroller; ad (3) Task allocato decso aker. The avalablty defcecy calculator s used to calculate dscrepaces betwee a arrval task s avalablty requreet ad the avalablty value that each ode offers. The fucto of avalablty-adaptve wdow cotroller s to vary sze of the wdow to dscover a sutable ode for the curret arrved task so that () ts avalablty deads ca be well et; () the executo te ca be as sall as possble. To llustrate how avalabltyadaptve wdow cotroller works, we gve a exaple as below. I Fgure we assue that there are 8 odes the cluster. The frst row shows the executo te for a arrval task o the 8 odes secods. Note that the executo of each ode for a partcular task s a expected executo te. The secod row dsplays the avalablty levels that the 8 odes ca offer. The thrd row s a ode lst sorted by the task s executo te a o-decrease order. The sze of avalablty-adaptve wdow s 4, whch eas SSAC wll select a ode that ca delver the best avalablty wth the frst four caddate odes. If avalablty-adaptve wdow cotroller caot fd a dea ode ters of avalablty, t wll autoatcally elarge the wdow to expad the search rage. However, large wdow sze wll result a log executo te for the task a hgh probablty because the executo te creases whe the sze of the wdow elarges.

4 Executo te: Avalablty level: Node: Avalablty-adaptve wdow Fgure. Exaple sorted ode lst wth avalablty-adaptve wdow 4 After retrevg forato lke degree of avalablty defcecy o each ode ad the sze of avalablty-adaptve wdow for the curret task fro the correspodg odules, the task allocato decso aker wll decde whch ode wll be assged to the task. Each ode the syste odel above s heretly heterogeeous both coputato ad avalablty. Coputatoal heterogeety eas that for each task the executo te o dfferet odes s dstctve. Whle each task has a avalablty request, each ode offers the avalablty wth dfferet levels. The level of avalablty provded by a ode s oralzed the rage fro 0 to Tasks wth avalablty requreets For future referece, we suarze the otatos for avalablty Table. We cosder a heterogeeous cluster syste where arrval tasks are depedet of oe aother. There are classes of tasks subtted to the syste by users. Each class of tasks requres a coo avalablty level specfed by a user. Values of avalablty levels are oralzed the rage fro 0 to.0. For exaple, a crtcal task ay specfy avalablty level.0 ts request, eag that ths task should be assged to a ode that ca provde 00 percet avalablty. It wll take a rsk for beg dsturbed durg ts executo, otherwse. Suppose there are dfferet users ad each of the keeps subttg a class of tasks. The arrval patter of tasks class follows a Posso process wth rate (see Fgure ). Suppose there s a task T subtted by a user, T s odeled as a set of ratoal paraeters, e.g., T = (a, E, f, av ), where a ad f are the arrval ad expected fsh tes, ad E s a vector of expected executo tes for task T o each ode N, ad E = (,,, e ). Suppose T s requreet of avalablty s av. Sce arrval patters ad servce rates ca be estated by code proflg ad statstcal predcto e e 4 [3], t s assued ths study that the arrval patters ad servce rate s kow a pror. Notato Table. Notato of syste odel Explaato Nuber of classes of tasks Nuber of odes the syste Oe partcular class of tasks, p ρ φ φ ξ a δ Λ θ α A Oe partcular ode, Arrval rate of the th class of tasks Task arrval rate of the etre syste Probablty that a task of the th class s dspatched to ode Servce rate of tasks of the th class o ode Servce utlzato of all tasks of class Servce utlzato of ode Total servce utlzato of the syste Probablty that ode s avalable Avalablty requreet of tasks of class, 0 a Avalablty defcecy of ode Task arrval rate of the th ode Uavalable rate of ode A paraeter to cotrol the value of θ Syste avalablty d Dscrepacy betwee ξ ad a ES ES s TC Mea servce te of ode Mea-square servce te of ode Mea-square servce te of class o ode Expected respose te of tasks class

5 T Expected respose te of all classes Wthout loss of geeralty, we assue that tasks of the th class arrve accordg to a Posso process wth rate. All classes of tasks arrve at the syste at total rate of =. Let p = be the probablty that a task of th e th class s dspatched to ode, where. Th us, the task arrval rate of the th ode s coputed by = p. The servce rate of tasks of class o ode s deoted by, ad the correspodg ea servce te s gve by. The servce utlzato of class I s expressed [ ( )] ( ) = = as ρ = p p = p. Th e servce utlzato at ode s gve by φ ( ) = = p. The total servce utlzato of the syste ca be calculated by φ = φ. = Let ξ deote the probablty that ode s avalabl e for coputato. We deote a as avalablty requre et of class. To quatfy avalablty of a heterogeeous syste, we troduce the cocept of avalablty defcecy. Thus, the avalablty defcecy of ode s expressed by p δ = d = p d, () Λ Λ = = where Λ = p, 0, f a ξ d = = a ξ, otherwse Equato easures the dscrepacy betwee the avalablty of ode ad the avalablty requreets of tasks allocated to ode. Although the avalablty defcecy reflects a satsfacto degree avalablty, the avalablty defcecy s adequate to evaluate syste avalablty for all the classes of tasks durg ther executos. The avalablty of the syste for class s calculated by θ exp p, where = θ s the uavalable rate of ode. The uavalable rate s expressed as: θ = exp( α ( ξ ). Note that the rate odel s ust for llustrato purpose oly, ad t ca be replaced by ay uavalable rate odel or usg ay reasoable paraeter α. The syste avalablty ca be obtaed below A = θ exp p = =. () We odel each ode the syste as a sgle M/G/ queue. Hece, the average respose te of ode ca be calculated as TN where ES ad Λ ES = ES +, (3) ( φ ) ES are the ea ad ea-square servce te of ode, respectvely. They ca be calculated by the followg equato: p p ES = =, = Λ Λ = p ES = s = ( ) p s (4) = Λ Λ = Where s s the ea-square servce te of class o ode. Based o Equato 3, the expected respose te of all the classes s gve as follows T = TC, (5) = where TC s the expected respose te of class tasks. Now we forulate the stochastc schedulg proble as a trade-off proble betwee avalablty ad ea respose te. Thus, the obectve of the proposed schedulg algorth s to axze syste avalablty (see Equato ) ad to ze ea respose te of subtted tasks (see Equato 5) Heterogeety odel We descrbe two types of heterogeetes ths subsecto. The coputatoal weght of class o ode s defed as a rato betwee ts servce rate o ode ad the fastest servce rate the syste. That s, the coputatoal weght s expressed by w = ax ( ) k = k. The coputatoal het erogeety of the th class,.e. HC, ca be easured by the stadard devato of the coputatoal weghts. Thus, we have HC =, w w = (6) = = ( w w ) 5

6 where w s average coputatoal weght. The coputatoal heterogeety ca be expressed by HC = HC. = The heterogeety of avalablty a heterogeeous syste s wrtte as HA = ( ξ ξ ) = 4. The SSAC algorth, ξ = ξ. (7) = We ow propose the schedulg algorth, whch s teded to detere probablty {p }, a way to prove the syste avalablty ad reduce ea respose te. Our algorth reles o the followg proposto, whch ca be easly proved based o proposto. [0]. Proposto: Gve a -class M/G/ queue ad a - ode heterogeeous syste, class has arrval rate ad servce rate o ode. The schedulg polcy o. Sort ad label classes such that L ; = = =. for each class do 3. Italze avalablty defcecy ad respose te for class,.e., d, TC ; 4. create a set of odes N, where ode N f a ξ ; 5. for each ode N do 6. calculate avalablty defcecy of class o ode, d ; 7. calculate expected respose te of class, TC ; (see Equato 8) 8. f d < d or (d = d ad TC < TC) the 9. d d ; TC TC ; π ; 0. ed f. ed for. f the syste s balaced the 3. p π ; 4. allocate class to ode π; 5. else 6. Allocate class to the lghtly loaded ode; 7. ed f 8.ed for Fgure 3.The SSAC algorth ode that gves a hgher prorty to class over k wheever k zes the expected respose te T = TC (see Equato 5). = It s assued that the classes are labelled such that L. = = = Ths assupto s vald because the task classes ca be sorted ad relabelled the frst step of the algorth. For tasks of class, the expected respose te o ode ca be approxated by TC = W + = = ( l < p E ( s ρ )( l ) l, ρ ) pl where ρ l =. (8) l The SSAC algorth s depcted Fgure 3. The algorth as to prove avalablty whle atag low average respose te for ult-class tasks o heterogeeous systes. Frst, SSAC gves classes wth hgher servce utlzato hgher prorty. Thus, SSAC sorts ad re-labels all the classes a way that L (see = = = Step ). Step 4 detfes all odes that ca eet the avalablty dead of tasks of class. Steps 5-0 are at the core of the proposed algorth. I partcular, Steps 6 ad 7 leverage Eqs. ad 9 to estate the avalablty defcecy ad expected respose te of class o ode. Step 8 akes a effort to prove syste avalablty by reducg avalablty defcecy. I the case there s o way to further reduce the avalablty defcecy, Step 8 edeavors to ze the expected respose te of class. Whe the load of the syste s balaced, Steps 3 ad 4 allocate tasks of class to ode π, whch yelds the hghest syste avalablty. Iportatly, the average respose te s further reduced by the algorth through statc load balacg (see Steps ad 6). Theore. The te coplexty of SSAC s O(), where s the uber of odes, s the uber of task classes. Proof. The te coplexty calculatg avalablty defcecy ad respose te for ode s O() (Step 6 ad 7). Sortg the classes of tasks te a odecreasg order (Step ) wll take O(lg) sce we oly have classes. For other steps, they oly cosue O(). Thus, the te coplexty of the SSAC l 6

7 algorth s as follows: O()(O())+ O(lg)= O()+O(lg)= O(). 5. Sulatos Usg sulato experets based o sythetcally geerated workload, we evaluate ths secto the perforace of the SSAC algorth. Task arrval rate ad task executo te rage (ETR) are two portat workload paraeters (see Table ). We assue that task arrval tes abde by Posso dstrbuto ad task executo tes follow Ufor dstrbuto. We evaluate SSAC alog wth two exstg algorths uder a wde rage of syste workload codtos by varyg ad uber of odes. To reflect the heterogeety of the sulated dstrbuted syste, we traslated the executo te of each task fro a sgle value to a vector wth (uber of odes) eleets based o the heterogeety odel descrbed Secto 3. I purpose of revealg the stregth of SSAC, we copared t wth two wellkow schedulg algorths, aely, M-M ad Sufferage []. M-M ad Sufferage are opreeptve task schedulg algorths, whch schedule a strea of depedet tasks oto a heterogeeous dstrbuted coputg syste. They are represetatve dyac schedulg algorths for dstrbuted systes ad were successfully appled real world dstrbuted resources aageet systes such as SartNet. The two algorths are brefly descrbed below. () MINMIN: For each subtted task, the ode that offers the earlest copleto te s tagged. Aog all the apped tasks, the oe that has the al earlest copleto te s chose ad the allocate to the tagged ode. () SUFFERAGE: Allocatg a ode to a subtted task that would suffer ost ters of copleto te f that ode s ot allocated to t. Table. Characterstcs of syste paraeters Paraeter Nuber of stes Task arrval rate (Posso dst.) Task executo te rage (ETR) Value (Fxed) - (Vared) (6) (6, 3,64,8) (.0) (0., 0.4, 0.6, 0.8,.0) (, 500) secod Node avalablty level (Ufor dst.) (0..0) Task avalablty level (Ufor dst.) Coputatoal heterogeety.08 Avalablty heterogeety Sulato setup (0..0) Table suarzes the key cofgurato paraeters of the sulated dstrbuted syste used our experets. The perforace etrcs we used clude: Avalablty (see Equato ), Avalablty shortage (defed as the ea dscrepacy betwee avalabltes requested by tasks ad avalabltes provded by odes the dstrbuted syste), Node utlzato (defed as the percetage of total task rug te out of total avalable te of a gve ode), Average respose te (see Equato 5). 5.. Overall perforace coparsos The goal of ths experet s two fold: () to copare the proposed SSAC algorth agast the two heurstcs, ad () to uderstad the sestvty of SSAC to the task arrval rate. Fgure 4 shows the sulato results for the three algorths o a dstrbuted syste wth 6 odes. We observe fro Fgure 4a that SSAC sgfcatly outperfors the two heurstcs ters of Avalablty, whereas MINMIN ad SUFFERAGE algorths exhbt slar perforace. We attrbute the perforace proveet of SSAC over MINMIN ad SUFFERAGE to the fact that SSAC s a avalablty-adaptve scheduler ad udcously assgs a task to a ode ot oly cosderg ts coputatoal te but also ts avalablty deads. Slar observatos ca be ade fro Fgure 4b, where SSAC has a uch better perforace Avalablty shortage. The lower Avalablty shortage, the better perforace acheved avalablty satsfacto. As for the perforace of Average respose te (Fgure 4c), SSAC s slghtly worse tha the two exstg algorths by 5.7% o average. However, the perforace proveet of SSAC over MINMIN ad SUFFERAGE Avalablty s 73.3% o average. I addto, SSAC acheves a better perforace Node utlzato as well (Fgure 4d) Scalablty 7

8 Ths experet s teded to vestgate the scalablty of the SSAC algorth. We scale the uber of odes a heterogeeous dstrbuted syste fro 6 to 8. Fgure 5 plots the perforaces as fuctos of the uber of odes the sulated dstrbuted syste. The results show that the SSAC approach exhbts good scalablty. the syste. Ths s because wth a hgh probablty SSAC ca fd a ode that eets a task s avalablty deads well whe there are ore odes to be chose. For all the three algorths, ther perforaces prove ters of Average respose te (Fgure 5c). Ths ca be readly uderstood because ore odes result a low value for Average respose te. (a) (b) (c) (d) Fgure 4.Perforace pact of task arrval rate Fgures 5a ad Fgure 5b show the proveet of SSAC Avalablty ad Avalablty shortage over the other two heurstcs. It s observed fro Fgure 5a that the aout of proveet becoes ore proet wth the creasg value of ode uber. Ths result ca be explaed by the o-avalabltyawareess ature of MINMIN ad SUFFERAGE, whch erely select a ode for a task wthout cosderg the task s avalablty deads. Coversely, SSAC ca acheve a uch hgher perforace whe there are ore odes avalable 8 6. Suary ad future work I ths paper, we address the stochastc schedulg proble for heterogeeous systes wth avalablty costrats. Whle dfferet classes of tasks are characterzed by ther executo tes ad avalablty requreets, each ode a heterogeeous syste s odeled by ts speed ad avalablty. We troduce etrcs to quatfy avalablty ad heterogeety the cotext of ult-class tasks. To corporate avalablty ad heterogeety to schedulg, we have proposed a

9 stochastc schedulg. Our schedulg algorth s geared to ehace avalablty of heterogeeous systes whle reducg average respose te of ult-class tasks. Eprcal results show that the ovel algorth proves perforace avalablty over exstg schees for heterogeeous systes. I future Coputer Systes, Vol.9, No. 3, pp.83-33, Aug. 00. [3] T. D. Brau et al., A Coparso Study of Statc Mappg Heurstcs for a Class of Meta-tasks o Heterogeeous Coputg Systes, Proc. Workshop Heterogeeous Coputg, pp.5-9, Apr [4] X. Ca, X. Wu, ad X. Zhou, Dyacally optal (a) (b) (c) (d) Fgure 5. Perforace pact of uber of odes research, the heurstc wll be exteded to schedule parallel applcatos. Ths work ca be accoplshed by factorg precedece costrats aog tasks ad coucato avalablty. Refereces [] A. Apo ad L. Wlbur, ApNet - a hghly avalable cluster tercoecto etwork, Proceedgs IEEE Itl' Syp. Parallel ad Dstrbuted Processg, Aprl -6, 003. [] A.C. Arpac-Dusseau, Iplct Coschedulg: Coordated Schedulg wth Iplct Iforato Dstrbuted Systes, ACM Tras. o 9 polces for stochastc schedulg subect to preeptverepeat ache breakdows, IEEE Trasactos o Autoato Scece ad Egeerg, Vol., Issue, Aprl 005. [5] T.L. Casavat ad J.G. Kuhl, A Taxooy of Schedulg Geeral-purpose Dstrbuted Coputg Systes, IEEE Tras. Software Egeerg, Vol.4, No., pp.4-54, Feb [6] S. Chakraverty, Cosythess o ultprocessor archtectures wth hgh avalablty, Proceedgs 7th Iteratoal Coferece o VLSI Desg, pp , 004. [7] A. Doga ad F. Özgüer, Relable Matchg ad Schedulg of Precedece-Costraed Tasks

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