RAID-RMS: A fault tolerant stripped mirroring RAID architecture for distributed systems

Transcription

1 computers & security 28 (2009) available at joural homepage: -RMS: A fault tolerat stripped mirrorig for distributed systems Javad Akbari Torkestai a, *, Mohammad Reza Meybodi b,c a Computer Egieerig Departmet, Islamic Azad Uiversity, Arak, Ira b Computer Egieerig Departmet, Amirkabir Uiversity of Techology, Tehra, Ira c Istitute for Studies a Theoretical Physics ad Mathematics (IPM), School of Computer Sciece, Tehra, Ira article ifo Article history: Received 5 September 2006 Received i revised form 14 Jue 2008 Accepted 2 September 2008 Keywords: Disk mirrorig Reliability Data stripig abstract Disk arrays, or s, have become the solutio to icrease the capacity, badwidth ad reliability of most storage systems. I spite of its high redudacy level, disk mirrorig is a popular paradigm, because replicatig data also doubles the badwidth available for processig requests, improves the reliability ad achieves fault tolerace. I this paper, we preset a ew called -RMS i which a special hybrid mechaism is used to map the data blocks to the cluster. The mai idea behid the proposed algorithm is to combie the data block stripig ad disk mirrorig techique with a data block rotatio. The resultig improves the parallelism reliability ad efficiecy of the array. We show that the proposed is able to serve may more disk requests compared to the other mirrorig-based s. We also argue that a more balaced disk load is attaied by the give, especially whe there are some disk failures. ª 2008 Elsevier Ltd. All rights reserved. 1. Itroductio A Redudat Array of Idepedet Disks- system is composed of a disk array, ad a disk array cotroller. The cotroller s fuctio is to receive a operatio from the user of the disk array, ad to carry it out by performig a set of lowlevel operatios o specific disks. There are several s that are classified ito five levels (Patterso et al., 1988; Gibso et al., 1998). Differet s ca be distiguished based o their type of ecodig, mappig ad algorithms used to access data. I other words, each system ca be defied by these three compoets. The proposed i this paper carefully cosiders all the subjects above. The ecodig idicates the type of redudacy iformatio used to ecode the data. The mappig itroduces the patter used to place data ad redudat iformatio o the disk array. Algorithms used to access data ca be classified as ormal mode ad failed mode oes. I ormal mode, either there is o failure i the disk array or the cotroller kows about the failed disks, if ay. I failed mode, a disk failure has occurred i the middle of cotroller operatio. The cotroller the eeds to recover the error ad complete the operatio. This process is called error recovery. There have bee umerous reliability ad performace evaluatio studies of, sice the publicatio of Patterso et al. (1988). This paper focuses o the reliability ad badwidth, which are the mai reasos of formatio systems. Gibso et al. (1998), Thomasia ad Blaum (2006) ad Thomasia ad Blaum (2006), Thomasia (2006) preseted a reliability-based compariso amog some existig s, especially for those are based o mirrorig techique. There are several studies cosiderig ew disk mirrorig orgaizatios i which the icreasig disk loads due to the failures are balaced. For example, iterleaved * Correspodig author. Computer Egieerig Departmet, Islamic Azad Uiversity, Arak, Ira Tel.: þ ; fax: þ addresses: j-akbari@iau-arak.ac.ir (J. Akbari Torkestai), mmeybodi@aut.ac.ir (M. Reza Meybodi) /$ see frot matter ª 2008 Elsevier Ltd. All rights reserved. doi: /j.cose

2 computers & security 28 (2009) declusterig method-id (Tera data Corporatio, 1985), implemeted i the origial teradata database machie, partitios N disks ito c clusters ad the primary data o each disk is distributed evely amog the other disks i the cluster. Hsiao ad DeWitt (1993) itroduced a called chaied declusterig which is a improvemet over ID ad tolerates a larger umber of disk failures tha ID. I this, each disk is partitioed ito a primary ad secodary area, ad the primary data o each disk is replicated o the secodary area. Che ad Towsley (1996) proposed the group rotate declusterig techique i which similar to the basic mirrorig, disks are divided ito primary ad secodary disks. Data is striped ad the stripe uits of each primary disk are located i a rotatio maer o secodary disks. The s, based o their redudat data, provide differet reliability levels ad effective badwidth to access data. I spite of the high redudacy level i -1, due to the basic mirrorig techique, the caot balace the load icreased by disk failures ad so it reduces the reliability ad access badwidth for processig requests. To overcome this shortcomig, we propose a ew i which the data block stripig ad disk mirrorig techiques are combied. The former techique is used to balace disk loads ad improves the badwidth to access data ad the latter techique replicates the data blocks ad icreases the reliability of the array. The theoretical aalysis shows that the proposed outperforms the existig mirrorig-based s i ivestigated metrics ad the experimetal results completely cofirm it. It is show that the proposed is able to serve may more disk requests compared to the other systems whose s are based o disk mirrorig scheme. We also argue that a more balaced disk loads is attaied by the give model, especially whe there are some disk failures. The rest of the paper is orgaized as follows. I the ext sectio, we propose a ew, which is explaied i full detail i Sectio 3. The proposed is evaluated through theoretical aalysis i terms of the maximum badwidth, disk operatio cost ad reliability i Sectio 4, ad the compared to other similar s through simulatio i Sectio 5. The cocludig remarks are preseted i Sectio The proposed I this paper, we adopt the followig otatioal covetios to itroduce the proposed. Let N ad deote the block sequece umber i the memory address space ad the umber of disks i the cluster, respectively. M deotes the umber of blocks per disk, each of size S ad i ad j are idices to specify the horizotal ad vertical positios of a data or parity blocks, respectively. Formally, a redudat array of idepedet disks- ca be described by a quituple < ~ A; B ; R ; f B ; g R >, where ~ A ¼fa 0 ; a 1 ;.; a N g deotes the sequece of the data blocks, B¼fb ði;jþ j0 i m 1; 0 j 1g is the fiite set of data blocks i the disk array, R ¼ FWfr ði;jþ j0 i m 1; 0 j 1sg is the fiite set of redudat blocks which may be a ull set. It implies that a may provide o redudacy, like 0. Let x B ad x R be the cardiality of B ad R, respectively. The redudacy rate for a give ca be obtaied by x R /(x B þ x R ). f B :A / B is the block fuctio, which maps to each block sequece umber a N a two-dimessioal address b (i,j ) i the cluster. Let b deotes a give subset of B. g R :B / R is the redudat fuctio, which assigs a redudat block r (i,j ) to a give subset b. It gives rise to the s ca be easily studied. The basic idea behid the ew hybrid called -RMS 1 is to combie the data block stripig ad disk mirrorig techiques with the block rotatio to improve the access badwidth ad reliability of the array. To do so, the data blocks are divided ito two distict set of blocks: The primary data blocks ad the Mirrored (or Backup) blocks. Each disk is also partitioed ito a primary ad secodary area (Hsiao ad DeWitt, 1993) ad the former data blocks are distributed i the primary disk area ad the latter oes i the secodary. I this, Data is striped (Che et al., 1994) ad the primary data is distributed evely amog all the disks i the cluster, the the resultig primary data blocks o each disk are replicated amog the other ( 1) disks i a rotated maer fully described i the ext sectio. Now, if a sigle disk fails, a effectively balaced load ca be attaied at all survivig disks. So, this ca icrease the parallelism for processig requests, the reliability ad the effective badwidth to access data. It is show that the proposed is able to serve may more disk requests compared to the other systems whose s are based o disk mirrorig. Besides, such ca tolerate more disk failures ad decrease the rate of missig data due to the preseted data distributio. The disk failure may cause a egligible reductio to access data ad system performace compared to the other existig s (Akbari Torkestai ad Meybodi, 2005a; Akbari Torkestai ad Meybodi, 2005b; Akbari Torkestai et al., 2006; Akbari Torkestai ad Haghighat, 2003; Cortes, 1999; Stoebraker et al., 2000). The method proposed to distribute the data, forms the cluster so that each disk icludes both primary ad backup data copies. That is, the primary data blocks are located i the upper halves of the disks (i.e. primary area) ad their mirrored copies are located i the lower halves (i.e. primary area). The most importat issue which should be cosidered is desigig a efficiet data distributio algorithm for distributig the blocks i the maer metioed earlier. Such method descriptio is comprehesively preseted i the ext sectio. I this data distributio method the data blocks ad their backups are distributed by a right rotatio i the separated disks. Thus, less data will be lost after disk failures ad it ca be used as a data storig model for those systems i which data correctio, protectio ad security are really importat. Furthermore, i this model, while the system is i the recovery state to repair some failed disks or blocks, other blocks ad disks remai available ad this improves the system performace dramatically. 1 Rotatig-Mirrorig-Stripig (RMS).

3 42 computers & security 28 (2009) Descriptio of -RMS As metioed earlier, the proposed suggests a combiatio of the data block stripig ad disk mirrorig techiques with a data block rotatio to distribute the data i the cluster. I the remaiig of this sectio, the data distributio method proposed i this paper will be formulated ad described i detail. The formulas as show by (1) (3) provide two mappigs from the block sequece umbers to the primary data blocks i the cluster ad vice versa, as well as a mappig from the data blocks to their backup copies. I other words, the block fuctio f B :A / B ad redudat fuctio g R :B / R ca be realized by the metioed formulas. Sice the sequece block umbers i the memory space are addressed i a sigle-dimesio fashio, they must be trasformed to the two-dimesio addresses to be stored i the cluster. I our proposed array, each disk is partitioed ito a primary ad secodary area (Hsiao ad DeWitt, 1993). The data blocks are also divided ito two distict set of blocks: The primary data blocks ad the mirrored blocks. Let B (i,j ) s deote the primary data blocks which are located withi the upper halves of the disks, where 0 i 1ad 0 j m/2 1, adm (i 0,j 0 ) s deote the mirrored copies located i the lower halves, where m/2 i 0 m 1ad0j 0 1. Now, the data distributio method ca be described as follows: whe the cotroller receives a request to store a sigle or a set of data blocks, the followig steps should be take by the cotroller: Step 1. Data is striped (Che et al., 1994) ad the primary data is distributed evely amog all the disks i the cluster. The addresses i which the primary data blocks should be located are obtaied by (1). This formula defies the block fuctio f B :A / B for our method, where B deotes the primary data block. It s a mappig from the block sequece umber A N to the physical address (primary data block) of the cluster B (i,j ). i ¼ P N B ði;jþ ¼ R j ¼ P NR þðn mod Þ (1) mod Where 0 i m/2 1 ad 0 j 1. Let A N ¼ N for otatioal coveiece. Step 2. I this step, the primary data blocks o each disk are replicated i a rotated maer amog the other ( 1) disks modula- as stated by (2-a). It maps a mirrored block M (i 0,j 0 ) to each block sequece umber A N ad defies the redudat fuctio g R :B / R. ( i 0 ¼ P NR þ m=2 M ði0;j0þ ¼ h j 0 ¼ P ðnþ1þ i R þððnþ1þ mod Þ mod (2-a) Where m/2 i 0 m 1 ad 0 j 0 1. I the steps above, a right side rotatio techique is implicitly ivolved to fid the positio of data ad mirrored blocks withi disk array. For retrievig the missig blocks, the data blocks ad their backups eed to be immediately coverted, so (2-a) should be rewritte based o i ad j. Substitutig PN=R ¼ i ad j 0 ¼ j þ 1i (2-a) fially yields (2-b). i M ði0;j0þ ¼ 0 ¼ i þ m=2 j 0 ¼ðjþ1Þmod (2-b) Whe disk i fails, the correspodig backup copies of the missig primary data blocks, B (i,j ) s(for all j ¼ 0,1,.,m/2 1), ca be directly foud by (2-b) ad easily retrieved. The lost mirrored blocks M (i 0,j 0 ) (for all j ¼ m/2,.,m 1) ca be recostructed by iversely applyig (2-b). Besides, we represet a iverse-block fuctio i which the Cartesia coordiates B (i,j ) of the block-iterleaved data are mapped to the sequece block umber A N. ði Þþðj mod Þ i; A N ¼ ði þ 1Þþj i; i_j i j Where 0 i m/2 1ad 0 j Evaluatio ad compariso As metioed earlier, our proposed exploits the data stripig techique i order to balace the disk loads ad the disk mirrorig techique to retrieve the missig blocks. Therefore, it seems appropriate to implemet i those storage systems which hold huge amouts of critical data. I the remaiig part of this sectio, the preseted is theoretically aalyzed i terms of the maximum badwidth, disk operatio cost ad reliability ad its results are compared to those of the existig mirrorig-based s The maximum badwidth The s, based o their redudat data, provide differet reliability levels ad effective badwidth to access data. These are some criteria for evaluatig the effectiveess of the disk storage s. The access badwidth eeds to be cosidered whe the system is either i the ormal or failed modes to process the requests. Although the proposed, due to the block stripig techique, is able to access the total badwidth provided by all disks for processig both small ad large requests, the mirrorig-based s ad, cosequetly, the proposed replicate the data blocks o the secodary disks so the data blocks ad their backups would be ivolved for processig both small ad large requests. Therefore, all the s whose codig methods are based o the data mirrorig techique, ca efficietly exploit oly half of the total badwidth available to process large writigs. At first, we itroduce some cocepts upo which the ext discussios are based i the rest of the paper. Read/Write requests are those kids of disk operatios i which the whole or part of a data block is processed ad their scopes do ot exceed the give block at all. Therefore, such I/O operatios may ifluece the differet blocks of the same or differet stripes simultaeously (Corbett et al., 1993). Read/Write requests are those kids of disk operatios i which the several blocks of the same stripe or eve the differet stripes may be ivolved to process the requests. Note that, i most cases, the empirical results give i the literatures are ot as good as the theoretical results are. This is because the badwidth provided by the is cosidered i a maximum case ad so it is ot always reachable (Corme ad Kotz, 1993; Foster et al., 1997; Ho et al., 2000). (3)

4 computers & security 28 (2009) Let ad B be the total umber of disks i the arrays ad the maximum disk badwidth, respectively. As show i Table 1, the maximum badwidth provided by all give disk arrays to process the small requests is B. I spite of the high redudacy level i -1, due to the disk mirrorig techique, the effective badwidth provided by the model is limited to oly half of the badwidth available i the cluster. So whe a large is requested to process, the cotroller is able to process oly two cosecutive data blocks i parallel. The maximum badwidth provided by the other existig blockiterleaved s is B. I -5, to solve the bottleeck problem which is associated with modifyig the parity blocks i 4, the idividual parity disk is removed ad the parity blocks are distributed across the all disks. Sice the give parity blocks should be modified after processig the small or the large requests, the maximum badwidth available for processig small operatios is reduced to ( 1)/2 B ad for large operatios to ( 1) B Disk operatio cost Let N Totaldisk ad N Checkdisk be the total umber of disks ad the umber of check disks i the cluster, respectively. Let T R be the mea time to a give block ad L Data be the legth of a give request (i.e. the umber of blocks per file). As metioed before, i all s discussed i the previous sectios, idividual small requests ca be processed i parallel, where ¼ N Totaldisk. As show i Table 1, the average cost, due to processig the small operatios, usig such s is T R. We itroduce the followig formula to calculate the disk operatio cost eeded to process a request as log as L Data, where L Data is the umber of blocks eeded to be processed. This formula ca be applied for all s except -1. The resultig costs have bee show i Table 1. ðl Data T R Þ=ðN Totaldisk N Checkdisk Þ (4) The proposed ot oly does ot cause ay side effects o seek time ad disk cache hit, but it achieves better results tha the other disk arrays. I -5, the parity blocks, associated to the modified strips, should be updated after each small or large operatio. This process is described as follows: the modified data blocks ad the old parity block should be to obtai the ew parity block. The the ew oe is rewritte. Thus, as show i the last two colums of Table 1, each request has a additioal cost for ig the modified data ad the old parity blocks Reliability aalysis The more parallelism betwee requests ad the higher badwidth to access data, due to the striped data blocks, ad the higher reliability agaist disk failures due to the data mirrorig techique, are some of the advatages of the proposed. I this subsectio, the reliability of the proposed is evaluated i terms of the maximum disk failure coverage, which meas the maximum umber of disk failures that ca be tolerated by the disk array (Cortes, 1999; Aderso et al., 1996), ad the compared to those of the arrays metioed earlier. As metioed before, due to usig the data mirrorig techique i -1 ad -10 to backup the disk failures, the levels of the failure recovery provided by both give s are the same. Assume that two idepedet disks fail successively so that the secod failure occurs before the first oe ca be recovered completely. It implies that the rebuild process which is retrievig the first failed disk caot be completed before the secod disk failure. Sice the MTTR 2 is assumed to be much smaller tha the MTTF 3, the probability that the failed disk ca be retrieved ad the array retured to the origial state is close to uity. Therefore, the probability that each disk failure or missig data block ca be recovered by the give s is 1 (1/( 1)), where is the total umber of disks i the cluster. Despite their high redudacy level, because of the weak data distributio patter, these arrays caot tolerate the disks failures effectively. But, there is a special case, whe these s tolerate /2 successive idepedet disk failures (Corme ad Kotz, 1993; Foster et al., 1997; Harry et al., 1995; Howard et al., 1988; Hsiao ad DeWitt, 1990; Hu et al., 1999). -5 uses the distributed parity blocks to detect ad correct errors. I this, the cotroller checks the strips by xorig the data blocks ad parity block, ad recogizes the happeed failure, if ay. -5 ca oly tolerate the sigle disk failures ad detect the strips i which some failures happeed ad it is ot capable of exactly detectig the damaged data blocks. I the case that, the umber of failures happeed i a give strip is eve, the cotroller of such a array caot detect ay failures (Asami et al., 1999; Cabrera ad Log, 1991; Cao et al., 1994). As metioed earlier, -RMS uses a special hybrid mechaism to map the data blocks to the cluster. The mai idea behid the proposed algorithm is to combie the data block stripig ad disk mirrorig techiques with a data block rotatio to improve the parallelism, reliability ad efficiecy of the array. I this, the data is blockiterleaved ad the distributed i the other ( 1) disks modula-. The mirrored blocks are also replicated diagoally throughout the secodary area i a similar maer. Such a, whose data ad mirrored blocks are distributed diagoally, alleviates the effects of the both disk ad block failures. The results of the compariso betwee these s show that the proposed leads to cosiderably better results of both data block ad disk failure recoveries. Assume that two successive idepedet disk failures be happeed i the differet disks of the cluster so that the secod failure occurs before recoverig the first oe completely. I this case, the probability that the missig data blocks ca be recovered is 1 (1/( 1)( 2)). The system we cosidered i Sectio 4.1 to evaluate ad compare the give s, cocered the maximum badwidth provided by the models whe the system is i the ormal state. I this state, the cotroller does ot eed to perform ay special fuctios to support the system. I the remaiig part of this sectio, we cosider the maximum available badwidth of the s whe the system is i failed mode. I this 2 Mea time to repair. 3 Mea time to failure.

5 44 computers & security 28 (2009) Table 1 The theoretical results of the four s i terms of the maximum I/O badwidth, I/O rate ad recovery rate level Maximum badwidth -1 N B B/2 (/2) B (/2) B -10 B B (/2) B (/2) B -5 B ( 1) B ( 1)/2 B ( 1) B -RMS B B (/2) B (/2) B Read/ cost -1 R L/2 R W L W -1 0 R L/ R W L W/(/2) -5 R L R /( 1) R þ W L (R þ W )/( 1) -RMS R L/ R W L W/(/2) Recovery rate -1 ( 1) B B -10 ( 1) B (/2) B -5 ( 1) B ( 2) B -RMS ( 1) B ( 1) B state, the cotroller is recoverig the disk failures. First of all, the followig questios eed to be cosidered. 1 How much is the able to utilize the available badwidth after some disk failures? 2 How much is the system able to utilize the available badwidth of the cluster for retrievig the missig data? To aswer these questios, we describe the recovery process i detail. Whe a disk fails, rebuild processig is used to retrieve the cotets of the failed disk o a spare disk. Durig the recostructio process, the ormal fuctios of the system should be temporarily stopped. Therefore, to achieve higher performace, the recostructio iterval should be shorteed as much as possible. It improves the reliability of the array as the MTTR/MTTF ratio is reduced. Sice all the missig data blocks should be rewritte sequetially, the expected time to re a failed disk is the same for all s. So we cosider the expected time to do the ig process. I -1 ad -10, this process sequetially s the cotets of the mirrored disk ad the available badwidth to recostruct the failed disk is limited to oly the mirrored disk. I -5, this process ivolves the ig of successive blocks from the ( 1) survivig disks. Although these ig operatios ca be doe i parallel, but the metioed process should be repeated for all the missig blocks ad so here the expected time is also similar to those of the earlier s. The proposed ca ivolve the ( 1) survivig disks to the block-iterleaved backup copies simultaeously ad so provides the highest effective badwidth compared to the other s. As show i Table 1, after a sigle disk failure, the proposed model provides the most effective badwidth compared to the other s as we argued i Sectio 5.1. Furthermore, the proposed array ca tolerate all double disk failures whereas the other arrays will lose some data. I Table 1, let N total ¼, T R ¼ R, T W ¼ W ad L Data ¼ L for otatioal coveiece. 5. Experimetal results We coducted some simulatio experimets to study the performace of the proposed, ad compared the obtaied results to the other studied s i terms of the access badwidth, I/O rate ad reliability. We first experimeted the effective badwidth provided by the studied s to access data. The parallel s ad s are cosidered separately ad the large request size, for either or operatios, is set to 20 MB. The size of each block strip is set to 32 KB. This cofiguratio implies a high degree of stripig ad parallelism. The requests to access disks ad data are geerated with a uiform distributio. The measured access badwidth has bee show i Table 2 as a fuctio of the umber of cliet requests for parallel data accesses. The results summarized i all tables are averages over oe hudred rus. We cosidered both light ad heavy I/O traffic rates, ad varied the umber of cliet requests from 1 to 16 parallel cliet requests, while the umber of disks is fixed at 16. To reveal the parallel I/O capability of the disk arrays, the large ad the large are studied ad to test the idividual disk performace, the small or are cosidered. For a small, the access badwidth provided by -5 is very close to that of our proposed disk array ad -RMS performs oly slightly better tha -5, while it shows much better results tha -10. As the umber of cliet requests icreases, both -RMS ad -5 show higher scalability ad -10 lags behid. The simulatio results for large requests are very close to that for small requests. For parallel s of either a large file or a small block, the -RMS achieves the best scalability amog the other Table 2 Maximum badwidth compariso of -RMS, -10 ad -5 ad the effects of I/O rate (MB/S) of cliets RMS

6 computers & security 28 (2009) s with a highest 16 MB/s for 16 cliets. -5 scales slowly due to the bottleeck problem metioed earlier for modifyig the parity blocks. -10 scales slower tha our proposed, but very faster tha -5. To sum up, the -RMS, due to the full parallelism i accessig all data blocks i the upper half of the disk array, outperforms the others. Sice more disks i the cluster may satisfy more cliet requests, scalig of a disk array size may icrease the effective access badwidth. O the other had, it may also itroduce more cotetios. The effects of disk array size are very similar to the effects of the cliet request rate. I both cases, we cosider the saturated cases of accessig a large umber of cliet requests simultaeously. These experimets take ito accout the array size i the simulatios ad measure the access badwidth provided by the s metioed above, as the umber of disks icreases from 2 to 16 i array. The total umber of cliet requests is fixed at 16. The workload is fixed at 320 MB for large s or for large s, regardless of the array size. For small s or s, the fixed workload is set to 512 KB for 16 cliets. As show i Table 3, these experimetal results are slightly differet from those of the earlier oes, especially for operatios. For large or small s, the rakig give for previous experimets remais uchaged ad -RMS is raked above the other s ad -5 below. The differeces i access badwidth are attributed maily to the architectural characteristics of each disk array. The stregth of the -RMS lies maily i its superior performace i performig parallel operatios, regardless of the graularity. The I/O rates have bee show i Table 4 agaist the umber of disks i the cluster. I these experimets, the umber of cliet requests is fixed at 16, the umber of disks icreases from 2 to 16 ad each cliet requests to or 500 MB data o the array. The block results show that the -5 ad -RMS perform better tha -10. Especially, as the array size icreases to 16 disks, the proposed array ad -5 coverge to a output rate of aroud 4 MB/s. But the -10 speed lags far behid because it experieced more overheads. This overhead comes from a less aggressive mirrorig scheme o the -10. Table 4 also shows the results of the block experimets, where a 500 MB data is Table 3 Scalability of -RMS, -10 ad -5 for ad operatios uder a heavy I/O traffic coditio (MB/S) of cliets RMS Table 4 The I/O rates of the proposed, -10 ad -5 for ad operatios (MB/S) of cliets RMS writte to the disk array. The proposed ad -10 have the same output rate with a peak speed of 3.75 MB/s. This rate is almost idepedet of the disk array size. I -5, the overhead of excessive parity updates result i a lower output rate. I systems, the reliability of the s ca be also evaluated i terms of the maximum disk failure coverage, which meas the maximum umber of disk failures that ca be tolerated by the disk arrays. Amog the four s, -5 ca oly tolerate the sigle disk failures ad so it provides the lowest reliability. -1 ad -10, due to the duplicatio of all primary disks, ca tolerate up to /2 disk failures. -RMS, because of usig a diagoal data distributio algorithm, provides higher reliability agaist both disk ad data block failures. Therefore, we have coducted some simulatio experimets to compare the reliability of -RMS agaist the other mirrorig-based s, amely -1, -10 i terms of data recovery rate. But, sice -1 ad -10 have the same results, Table 5 oly shows a compariso betwee the proposed ad -10. These results express the probability with which the blocks of a failed disk ca be retrieved. I these experimets, the failures are geerated with a uiform distributio withi the disk arrays ad the data recovery rate is measured as the Table 5 The disk failures recovery rate of -RMS agaist -10 of disks of failures RMS

7 46 computers & security 28 (2009) umber of disks icreases from 3 to 16 ad the umber of failures icreases from 1 to /2 i each experimet. 6. Coclusio I this paper, we preseted a ew i which a special hybrid data distributio techique is used to locate the data blocks i the cluster. The mai idea behid the proposed algorithm is to combie the data block stripig ad disk mirrorig techiques with a data block rotatio to improve the parallelism, reliability ad efficiecy of the array. I such a system, if a sigle disk fails, a effectively balaced load ca be attaied at all survivig disks. It is show that the proposed is able to serve may more disk requests compared to the other existig mirrorig-based s. Besides, such ca tolerate more disk failures ad decrease the rate of missig data due to the preseted data distributio. So, this ca icrease the parallelism for processig requests, the reliability ad the effective badwidth to access data, especially after disk failures. The proposed i terms of the maximum badwidth, disk operatio cost ad reliability is theoretically aalyzed ad the obtaied results show that this outperforms the studied s i most of the ivestigated metrics ad the experimetal results completely cofirm the aalytic results. Fially, the give is appropriate to implemet i the distributed storage systems which hold huge amouts of critical data. Ackowledgemet The authors would like to thak the reviewers for their valuable commets ad costructive criticism of the origial mauscript. refereces Akbari Torkestai J, Haghighat AT. A ew redudacy algorithm for distributed eviromets. Operatig system & Security Coferece (OSSC), 2003, pp Akbari Torkestai J, Meybodi MR. A ew redudacy structure for usig i high reliable systems. Proceedigs of the Secod Iteratioal Coferece o Iformatio ad Kowledge Techology (IKT2005), 2005a. Akbari Torkestai J, Meybodi MR. A ew data mirrorig algorithm to ehace reliability ad fault tolerace. Proceedigs of the secod iteratioal coferece o iformatio ad kowledge techology (IKT2005), 2005b. Akbari Torkestai J, Izadi T, Meybodi MR., Implemetatio of a ew data security method for. Proceedigs of 11th aual CSI computer coferece of Ira, Fudametal Sciece Research Ceter (IPM), Computer Sciece Research Lab., 2006, pp Aderso T, Dahli M, Patterso D, Wag R. Serverless etwork filesystems. ACM Trasactios o Computer Systems 1996: Asami S, Talagala N, Patterso DA. Desigig a self-maitaiig storage system. Proceedigs of 16th IEEE Symposium o Mass Storage Systems, 1999, pp Cabrera LF, Log DE. Usig distributed disk stripig to provide high I/O data rates. Proceedigs of USENIX Computig Systems, 1991, pp Cao P, Lim SB, Vekatarama S, Wilkes J. The TickerTAIP Parallel Architecture. ACM Trasactios o Computer System 1994;12(3): Che SZ, Towsley D. A performace evaluatio of s. IEEE Trasactio o Computers 1996;45(10): Che PM, Lee EK, Gibso GA, Katz RH, Patterso DA. : highperformace, reliable secodary storage. ACM Computig Surveys 1994;26(2): Corbett P, Feitelso DG, Prost JP, Baylor SJ. Parallel access to files i the Vesta file system. Proceedigs of Supercomputig 93, Corme TH, Kotz D. Itegratig theory ad practice i parallel file systems. Proceedigs of DAGS 93 Symposium, 1993, pp Cortes T. Software ad parallel filesystems. I: Buyya Rajkumar, editor. High performace cluster computig s ad systems. Pretice Hall PTR; p Foster A, Kohr D, Krishaiyer JR, Mogill J. Remote I/O: Fast Access to Distat Storage, Proceedigs of the Fifth Workshop o I/O i Parallel ad Distributed Systems, 1997, pp Gibso G, Nagle D, Amiri K, Chag F, Gobioff H, Riedel E. A cost-effective, high-badwidth storage. Proceedigs of the 8th Coferece o Architectural Support for Programmig Laguages ad Operatig Systems, 1998, pp Harry M, Rosario JMD, Choudhary A. VIP-FS: a virtual, parallel file system for high performace parallel ad distributed computig. Proceedigs of the 9th Iteratioal Parallel Processig Symposium (IPPS 95), 1995, pp Ho R, Hwag K, Ji H. Desig ad aalysis of clusters with sigle I/O space,. Proceedigs of 20 Iteratioal Coferece o Distributed Computig Systems (ICDCS 2000), 2000, Taiwa, pp Howard JH, Kazar ML, Meees SG, Nichols DA, Satyaarayaa M, Sidebotham RN, West MJ. Scale ad Performace i a Distributed File System. ACM Trasactios o Computer System 1988;6(1): Hsiao HI, DeWitt D, Chaied declusterig: a ew availability strategy for multiprocessor database machies. Proceedigs of 6th Iteratioal Data Egieerig Coferece, 1990, pp Hsiao HI, DeWitt DJ. A performace study of three high availability data replicatio strategies. Joural of Distributed Parallel Databases 1993;1(1): Hu Y, Yag Q, Nightigale T. RAPID-Cache a reliable ad iexpesive cache for Disk I/O Systems. Proceedigs of the 5th Iteratioal Symposium o High Performace Computer Architecture (HPCA-5), 1999, pp Patterso DA, Gibso GA, Katz RH. A case for redudat arrays of iexpesive disks (). ACM SIGMOD, It. Cof. o Maagemet of Data, Jue 1988, pp Stoebraker M, Gerhard A, Schloss A. Distributed Raid a ew multiple copy algorithm. Berkeley, CA: Uiversity of Califoria; Tera data Corporatio. DBC/1012: database computer system maual, Release 2, Thomasia A, Blaum M. Mirrored disk orgaizatio reliability aalysis. IEEE Trasactios o Computers 2006;55(12): Thomasia. Shortcut method for reliability comparisos i. Joural of Systems ad Software 2006;79: