High Availability with Diagonal Replication in 2D Mesh (DR2M) Protocol for Grid Environment

Transcription

1 High Availability with Diagoal Replicatio i 2D Mesh (DR2M) Protocol for Grid Eviromet Rohaya Latip (Correspodig author) Faculty of Computer Sciece ad Iformatio Techology Uiversiti Putra Malaysia Tel: rohaya@fsktm.upm.edu.my Hamidah Ibrahim, Mohamed Othma, Md. Nasir Sulaima, Azizol Abdullah Faculty of Computer Sciece ad Iformatio Techology Uiversiti Putra Malaysia Tel: hamidah, mothma, asir, azizol@fsktm.upm.edu.my The research has bee supported by Malaysia Miistry of Sciece, Techology ad Iovatio (MOSTI) uder the Fudametal Grat No: FR. Abstract Replicatio is a useful techique for distributed database systems ad has bee implemeted i EU data grid ad HEP i CERN for hadlig huge data access. Replica selectio i their prototypes still ca be ehaced to provide high availability, fault tolerat ad low i commuicatio cost. This paper itroduces a ew replica cotrol protocol, amed Diagoal Replicatio i 2D Mesh (DR2M) for grid eviromet ad compares its performace with the previous protocols. The performace i this paper is data availability for read ad write operatio, which are compared to the Read-Oe Write-All (ROWA), Votig (VT), Tree Quorum (TQ), Grid Cofiguratio (GC), Three Dimesioal Grid Structure (TDGS), ad Diagoal Replicatio o Grid (DRG). This paper discusses the protocol of replicatig data for grid eviromet, puttig the protocol i a logical 2D mesh structure by employig the quorums ad votig techiques. The data file is copied i a selected replica from the diagoal sites i each quorum. The selectio of a replica depeds o the diagoal locatio of the structured 2D mesh etwork where the middle replica is selected because it is the shortest path to get a copy of the data from most of the directio i the quorum. The algorithm i this paper also calculates the optimized umber of odes to be grouped i each quorum ad how may quorums are eeded for the umber of odes, N i a etwork. DR2M protocol also esures that the data for read ad write operatios are cosistet, by esurig the quorum must ot have a oempty itersectio quorum. To evaluate the DR2M protocol, we developed a simulatio model i Java. Our results prove that our protocol improves the performace of data availability compared to the previous data replicatio protocol, amely Read-Oe Write-All (ROWA), Votig (VT), Tree Quorum (TQ), Grid Cofiguratio (GC), Three Dimesioal Grid Structure (TDGS), ad Diagoal Replicatio o Grid (DRG). Keywords: Data replicatio, Grid, Data maagemet, Availability, 2D Mesh protocol 1. Itroductio A grid is a distributed etwork computig system, a virtual computer formed by a etworked set of heterogeeous machies that agree to share their local resources with each other. A grid is a very large scale, geeralized distributed etwork computig system that ca scale to iteret size eviromet with machies distributed across multiple orgaizatios ad admiistrative domais (Krauter, 2002; Foster, 2002). Esurig efficiet access to such a large etwork ad widely distributed data is a challege to those who desig, maitai ad maage the grid etwork. The availability of a data i a large etwork ad replicatig data at a miimum commuicatio cost are also some of the issues (Ragaatha, 2001; Lamehamedi, 2002; Lamehamedi, 2003; Lamehamedi, 2005). EU data grid ad HEP i CERN used Reptor as the prototype to maage replica i grid (Guy, 1997; Kuzst, 2003). Figure 1 shows the mai compoet of the Replica Maagemet System, Reptor was implemeted for EU Data Grid. I our work, we ivestigate o the replica selectio for optimizig ad improvig data accessig by usig replica cotrol protocol i distributed database to the grid eviromet. Distributed computig maages thousads of computer systems ad it has a limited memory ad processig power. O the other had, grid computig has some extra characteristics. It is cocered to efficiet utilizatio of a pool of 95

2 Vol. 1, No. 2 Computer ad Iformatio Sciece heterogeeous systems with optimal workload maagemet utilizig a eterprise's etire computatioal resources (servers, etworks, storage, ad iformatio) actig together to create oe or more large pools of computig resources. There is o limitatio of users or origiatios i grid computig. Eve though miimum umber of odes for grid is oe but for DR2M protocol the best miimum umber of odes should be more tha five to suite the large etwork size such as grid eviromet. Quorums improved the performace of fault tolerat ad availability of data (Mat Deris, 2003; Mat Deris, 2004; Yu, 1997). Quorums reduce the umber of copies for readig or writig data. To implemet quorum, a protocol must satisfy two costraits which are total of quorum for read, q r ad write quorum, q w must be larger tha the total umber of votes, v assiged to the copies of the data object ad the quorum for write, q w is larger tha v/2 (Mat Deris, 2001). For votig approach, every copy of replicated data object is assiged a certai umber of votes ad a trasactio has to collect a read quorum of r votes to read a data object, ad a write quorum of w votes to write a data object. To address the availability, DR2M replicates data o the middle ode of a quorum of read or write i the logical structured of 2D mesh topology etwork. The term replica meas the selected odes that have the copy of the data file. Java is used to ru this replicatio protocol. The paper is orgaized as follow: i Sectio 2, DR2M protocol ad its algorithm are itroduced. I Sectio 3, we preset the previous replica cotrol protocols. This sectio icludes the formulatio for read/write availability for the previous protocols i distributed database ad grid computig. Sectio 4 describes the simulatio framework ad Sectio 5 discusses the simulatio results. Brief coclusios ad future works are discussed i Sectio Diagoal Replicatio i 2D Mesh (DR2M) Protocol I DR2M protocol, all odes are logically orgaized ito two dimesioal Mesh structure. We assume that the replica copies are i the form of text files ad all replicas are operatioal meaig that the copies at all replicas are always available. The data are replicated to oly oe ode of the diagoal site which is the middle ode of the diagoal site i each quorum. This protocol uses quorum to arrage odes i cluster. Quorum is groupig the odes or databases ito small cluster to maage the replica for read or write operatios. Figure 2 illustrates how the quorums for etwork size of 81 odes are grouped by odes of 5 x 5 i each quorum. Nodes which are formed i a quorum itersect with other quorums. This is to esure that each quorum ca commuicate or read other data from other odes which is i aother quorum. The umber of odes grouped i quorum, R must be odd so that oly oe middle ode from the diagoal sites ca be selected such as the black circle i Figure 2, which reduces the commuicatio cost. Example, s(3,3) i Figure 2 is selected to have the copy of data. 2.1 The correctess This sectio shows that DR2M protocol is accessig the updated ad cosistet data. From the defiitio 2.1 ad proof shows the quorums itersect with each other ad follow the two coditios of makig sure that the data are cosistet. Defiitio 2.1: Assume that a database system cosists of x odes that are logically orgaized i the form of two dimesioal grid structure. All sites are labeled s(i,j), 1 i, 1 j. D(s), is the diagoal sites, D(s) = s(i,j), where i = j = 1, 2,, for each quorum. For example, Figure 2 has 81 odes where the size of the etwork is 9 x 9 odes. For q1, the diagoal site D(s) is {s(1,1), s(2,2), s(3,3), s(4,4), s(5,5)} ad the middle ode s(3,3) has the copy of the data file. Figure 2 has four quorums where each quorum actually overlaps with each other. Example ode e i q1 is actually ode a i q2 ad ode a i q3 is actually ode e i q4. Sice the data file is replicated oly o oe ode i each quorum, thus it miimizes the umber of database update operatios. The selected ode of data file is assiged with vote oe ad the rest of the odes will have vote zero. A vote assigmet o grid, B, is a fuctio such that, B(s(i,j)) {0, 1}, 1 i, 1 j where B(s(i,j)) is the vote assiged to site s(i,j). This assigmet is treated as a allocatio of replicated copies ad a vote assiged to the site results i a copy allocated at the selected ode. That is, 1 vote 1 copy. Let L B = B(s(i,j)), s(i,j) D(s) where L B is the total umber of votes assiged to the selected ode as a primary replica i each quorum. Thus L B = 1 i each quorum. Defiitio 2.2: Let q r ad q w deote the read quorum ad write quorum respectively. To esure that read operatio always gets the updated data, q r + q w must be greater tha the total umbers of copies (votes) assiged to all sites. To 96

3 make sure the cosistecy is obtaied, the followig coditios must be fulfilled (Mat Deris, 2004). i. 1 q r L B, 1 q w L B ii. q r + q w = L B +1. These two coditios esure that there is a oempty itersectio of copies betwee read ad write quorum. Thus, these coditios esure that a read operatio has the most recetly updated copy of the replicated data. Let S(B) be the set of sites at which replicated copies are stored correspodig to assigmet B, the, S(B) = {s(i,j) B(s(i,j)) = 1, 1 i, 1 j } From Figure 2, q r = {s(3,3) from q1, s(3,3) from q2, s(3,3) from q3, s(3,3) from q4} L B = 4 for the whole etwork ad i DR2M protocol q r = q w the q w = {s(3,3) from q1, s(3,3) from q2, s(3,3) from q3, s(3,3) from q4} L B = 4 for the whole etwork. Defiitio 2.3: For a quorum q, a quorum group is ay subset of S(B) where the size is greater tha or equal to q. The collectio of quorum group is defied as the quorum set. Let Q(B,q) be the quorum set with respect to assigmet B ad quorum q, the Q(B,q) = {G G S(B) ad G q} For example, from Figure 2, let site s(3,3) be the primary database of the master data file m. The diagoal site are s(1,1), s(2,2), s(3,3), s(4,4), ad s(5,5). Cosider a assigmet B for the data file m, such that B(s(1,1)) = B(s(2,2)) = B(s(3,3)) = B(s(4,4)) = B(s(5,5)) = 1 ad L B = B(s(3,3)). Therefore, S(B) = {s(3,3)}. For simplicity, a read quorum for data file m, is equal to write quorum. The quorum sets for read ad write operatios are Q(B,q1), Q(B,q2), Q(B,q3) ad Q(B,q4) as i Figure 2, where Q(B,q1) ={s(3,3)} i q1, Q(B,q2) = {s(3,3)} i q2, Q(B,q3) = {s(3,3)} i q3, ad Q(B,q4) = {s(3,3)} i q4. Therefore, the umber of replicated data file m is equal to 4. Theorem 2.1. The DR2M protocol is accessig cosistet data. Proof. The theorem holds o coditio that the DR2M protocol satisfies the quorum itersectio properties for the read-write properties ad write-write properties by Defiitio 2.2. The availability of a read (A DR2M,R ) ad write (A DR2M,W ) operatio is calculated as i Eq. (1) ad Eq. (2) respectively, where is the grid colum or row size, example is 7, for 7 x 7 odes of grid etwork size ad p is the probability of data available which is betwee 0 to 1, qr ad qw are the umber of quorums for read ad write operatios respectively. Thus, the formulatio for read availability for DR2M, A DR2M,R is as give i Eq. (1) A DR2M,R = i i ( p (1 p) ) (1) qr i ad the formulatio for write availability, A DR2M,W is as give i Eq. (2) A DR2M,W = i i ( p (1 p) ) (2) qw i As the etwork size grows bigger, the more quorums are idetified. The umber of colums ad rows i each quorum must be odd, to get the middle ode. If the iput of odes, is ot odd the the simulator will create virtual empty odes to the last row ad colum of the 2D mesh. By selectig oly oe middle ode i each quorum has miimized the commuicatio cost. The algorithm for this DR2M protocol is show i Figure 3. It illustrates how the algorithm was desiged ad implemeted. 3. Related Work There are few protocols to replicate a data i distributed database ad grid computig as discussed i the followig subsectios: 3.1 Read-Oe Write-All (ROWA) Protocol ROWA is a simple ad straightforward protocol (Ozsu, 1996). It requires all copies of all logical data items that are updated by a trasactio be accessible for the trasactio to termiate. Failure of oe site may block a trasactio ad 97

4 Vol. 1, No. 2 Computer ad Iformatio Sciece reduce database availability. I ROWA, a read operatio eeds oly oe copy, while a write operatio eeds to access the umber of copies. Therefore, the availability for a read operatio ca be represeted as oe out of (Jai, 1991), ad for a write operatio as out of. Thus, the formulatio for read availability for ROWA, A ROWA,R is as give i Eq. (3) A ROWA,R = p i (1 - p) -i (3) 1 i ad the formulatio for write availability A ROWA,W is as give i Eq. (4) A ROWA,W = p i (1 - p) -i (4) i where p is the probability that a copy is accessible ad p is from 0.1 to 0.9. ROWA reduces the availability of the database i case of failure sice the trasactio may ot complete uless it reflects the effects of the write operatio o all copies. Therefore, there have bee a umber of algorithms that have attempted to maitai mutual cosistecy without employig the ROWA protocol (Ozsu, 1999). 3.2 Votig (VT) Protocol I VT approach, every copy of replicated data object is assiged to a certai umber of votes ad a trasactio has to collect a read quorum of r votes to read a data object, ad a write quorum of w votes to write the data object. Quorum must satisfy two costraits which are r + w must be larger tha the total umber of votes, v assiged to the copies of the data object ad w > v/2, where the total of write quorum of w votes must be larger tha half of the total umber of votes, v. For replicas, VT protocol allows choices for the read ad the write quorum. It starts from (read 1, write ) to (read, write 1). To avoid the read availability becomes expesive, the read quorum k is selected where k is smaller tha the majority quorum. From Mat Deris (2001), the formulatio for read availability i VT, A VT,R is as give i Eq. (5), where is the total umber of odes that has the votes or sometime it is called replica A VT,R = p i (1 - p) -i, k 1 (5) k i ad the correspodig formulatio for write availability i VT, A VT,W is as i Eq. (6), where k is the umber of votes for read or write quorum A VT,W = i = + 1 k i p i (1 - p) -i (6) This protocol is popular ad easy to implemet but writig a object is fairly expesive (Mat Deris, 2001), where write quorum (w) of copies must be larger tha the majority votes (v), w > v/ Tree Quorum (TQ) Protocol TQ protocol proposed by (Agrawal, 1992; Agrawal, 1990) is a logical tree structured over a etwork. Figure 4 illustrates the tree quorum structured. Oe advatage of this protocol is that a read operatio may access oly oe copy ad the umber of copies to access write operatio is always less tha a majority of quorum. The size of quorum may icrease to maximum of /2 + 1 site whe failures occur where is the umber of copies. Write operatios i the TQ must access a write quorum, which is formed from the root, a majority of its childre ad a majority of their childre ad so forth util the leaves of the tree are reached. The size of a write quorum is fixed but the members ca be differet. The root or majority of the childre of the root ca form the read operatios. Let A TQ,h,R ad A TQ,h,W be the availability of the read ad the write operatios with the height, h of tree, respectively. D deotes the degree of sites i the tree ad M is the majority of D. Uder this protocol, as give by Chug (1990), the availability formulatio of a read operatio for a tree of height h ca be represeted as i Eq. (7) D A TQ,h,R = D p + ( p) A ( A TQ ) TQ i, 1 D i 1 (7), h 1, R h 1, R M i ad the availability formulatio of a write operatio for a tree of height h is as give i Eq. (8) D D A i A TQ h 1, W TQ, h 1, W M i A TQ,h,W = D i ( ) p, 1 (8) 98

5 where p is the probability that a copy is available. If the height of a tree is oe, the read operatio, R 0 ad write operatio, W 0 is equal to p. Tree quorum (TQ) uses quorum that is obtaied from a logical tree structure imposed o data copies. However, if more tha a majority of the copies i ay level of the tree become uavailable write operatio caot be performed (Agrawal, 1992; Maekawa, 1992). 3.4 Grid Cofiguratio (GC) Protocol GC protocol proposed by (Maekawa, 1992) has copies of data objects that are logically orgaized i the form of x grid as show i Figure 5. I Figure 5, the umber of odes is 25 i 5 x 5 grid etwork where is five. The figure shows three grey circles, which represet odes that are dow or ot active. The odes which are dowed ca be placed logically aywhere i the grid structure. Read operatios o the data item are executed by acquirig a read quorum that cosists of data copy from each colum i the grid, while write operatios are executed by acquirig a write quorum that cosists of all copies i oe colum ad a copy from each remaiig colum. From (Agrawal, 1996), the formulatio of read availability i the GC protocol, A GC,R is as give i Eq. (9) 1 i i = 1 A GC,R = i p ( p) i where p is the probability that a copy is accessible ad p is from 0.1 to 0.9. While, the formulatio of write availability i the GC, A GC,W is as give i Eq. (10). A GC,W = ( 1 p) [ ] [ ( 1 ( 1 p) ) p ] (9) 1 (10) This protocol requires a bigger umber of read ad write quorum for the read operatios to be executed. Read quorum must be at every colum ad for write operatios to be executed, write quorum must exist at oe of the etire colum ad exist at least oce at other colums. Thus, this decreases the data availability. It is also vulerable to the failure of etire colum or row i the grid (Agrawal, 1996). 3.5 Three Dimesio Grid Structure (TDGS) Protocol TDGS protocol replicated its data i logical box shape structure with four plaes (Mat Deris, 2001; Mat Deris, 2007). Figure 6 illustrates eight copies of data object. The read operatios i TDGS are executed by acquirig a read quorum that cosists of ay hypoteuse copies. For the example show i Figure 6, hypoteuse copies are {A, H}, {B, G}, {C, F}, ad {D, E}. Read operatios are executable by these pairs of hypoteuse copies. Write operatios are executable from ay plaes that cosist of hypoteuse copy. Plaes i Figure 6 are {H, A, B, C, D}, {C, F, E, G, H), ad etc. Example, to execute read operatio, copies from {A, H} must be accessible ad to execute write operatio, copies from {H, A, B, C, D} must also be accessible. I TDGS protocol, read quorum ca be costructed from four hypoteuse copies. From (Mat Deris, 2001), the formulatio of read availability, A TDGS,R is as give i Eq. (11), where p is the probability that a copy is accessible ad p is from 0.1 to 0.9. A TDGS,R = 1(1-p 2 ) 4 (11) whereas, formulatio of write availability, A TDGS,W is as give i Eq. (12), A TDGS,W = 1-(1-β) 4 (12) where β = p φ + p φ - p 2 (φ * φ) (Mat Deris, 2001), φ = p 4 (1+p-p 2 ) ad φ = p 4 (2-p 2 ) Read operatios are executed by acquirig a read quorum, which must come i pairs at the vertices of the box shape structure. If oe of the copies of each pairs is uavailable, thus that hypoteuse copies are ot accessible. Therefore, write operatios are ot executable at the write quorum. Read ad write quorum must itersect otherwise the hypoteuse of read quorum is ot accessible ad the write quorum is also ot accessible to update the latest data. This affects the cosistecy of the data. 3.6 Diagoal Replicatio o Grid (DRG) Protocol Diagoal Replicatio o Grid (DRG) proposed by (Mat Deris, 2004), is a protocol which is logically orgaized i a two dimesioal grid structure. For example, if a DRG cosists of twety-five sites, the etwork is logically formed ito 5 x 99

6 Vol. 1, No. 2 Computer ad Iformatio Sciece 5 grids as show i Figure 5. Each site has a master data file. A site is either operatioal or failed ad the state (operatioal or failed) of each site is statistically idepedet to the others. Whe a site is operatioal, the copy at the site is available; otherwise it is uavailable. Sites ca be dow or ot active. I Figure 5, sites 23, 24, ad 25 are ot active or fail. Sets of diagoal sites i the grid are selected such as set {1, 7, 13, 19, 25}. After the diagoal sites are idetified, the primary copy of the data is placed o the replica which is distributed diagoally (Mat Deris, 2004). For example, diagoal set D 2 (s) is {s(2), s(8), s(14), s(20), s(21)} ad D 3 (s) is {s(3), s(9), s(15), s(16), s(22)}. Each site has the same copies of replica. Figure 7 illustrates the diagoal sets of D 2 (s) which is grey i color ad D 3 (s) which is i doted circles. The total umber of the diagoal odes is preseted as d ad L v is the total umber of votes o grid. Let S(B) be the set of sites at which the replicated copies are stored correspodig to B. Whereas i ad j are the umber of colums ad rows respectively. S(B) = {S(i, j) B(S(i, j)) = 1, 1 i, 1 j } 100 L v = s( i, j) D( s) B ( S( i, j)) = d I estimatig the availability for DRG, all copies are assumed to have the same availability p. Let Av(t) be the read/write availability of protocol t. If the probability that a arrivig operatio of read ad write for data file x are f ad (1-f), respectively, the the read/write availability ca be defied as, Av(t) = fav(t read ) + (1-f)Av(t write ) For ay assigmet B ad quorum q for the data file x, Eq. (13) defies ϕ (B x, q) to be the probability that at least q sites i Ω (B x ) are available, the ϕ (B x, q) = Pr {at least q sites i Ω (B x ) are available} = Pj (1 Pj ) (13) G Q ( Bx, q) j G j S ( Bx ) G I Eq. (14) the availability of read ad write operatios for the data file x, are ϕ (B x, r) ad ϕ (B x, w), respectively. Av(DRG) = f ϕ (B x, r) + (1-f) ϕ (B x, w) (14) 4. Results ad Discussio I this sectio, DR2M protocol is compared to the results of read ad write availability of the previous protocols, amely: ROWA, VT, TQ, GC, TDGS, ad DRG. Figure 8 shows the results of read availability i a 81 odes size of etwork. ROWA protocol has the highest read availability about average of % for probability of data accessig 0.1 to 0.9 eve whe the umber of odes icreases. This is because oly oe replica is accessed by a read operatio for ay odes of etwork size but ROWA has the lowest write availability. Figure 8 illustrates the write availability for 81 umbers of odes, where the probability is from 0.1 to 0.9. The result show i Figure 9 proves that the DR2M protocol has average of % higher for write availability for all probabilities of data accessig. This is due to the fact that replicas are selected from the middle locatio of the diagoal site i each quorum. 5. Coclusios I this paper, a ew protocol, called Diagoal Replicatio i 2D Mesh (DR2M) protocol has bee proposed to maage the data replicatio i a large etwork size such as i distributed system ad especially i grid eviromet. DR2M protocol, selects oe replica i a diagoal site of a quorum i a 2D mesh logical structure. The umber of odes i each quorum is odd so it is easy to select oly oe ode from the diagoal site i each quorum. The aalysis of the DR2M protocol was preseted i terms of read ad write availability. The results demostrate that the DR2M protocol provides a coveiet approach for write operatios. This is due to the miimum umber of quorum size required. DR2M has overcome the read ad write availability issues of TDGS which is the latest replica cotrol protocol. Refereces Krauter, K., et al. (2002). A taxaomy ad survey of grid resource maagemet systems for distributed computig. Iteratioal Joural of Software Practice ad Experiece, 32(2), Foster, I., et al. (2002). Grid services for distributed system itegratio. Computer, 35(6), Ragaatha, K., & Foster, I. (2001). Idetifyig dyamic replicatio strategies for a high performace data grid.

7 Proceedigs of Iteratioal Workshop o Grid Computig, Dever. Lamehamedi, H., Szymaski, B., Shetu, Z., & Deelma, E. (2002). Data replicatio strategies i grid eviromet. Proceedigs of ICAP 03, Beijig, Chia, IEEE Computer Sciece Press, Los Alamitos, CA, Lamehamedi, H., Shetu, Z., & Szymaski, B. (2003). Simulatio of dyamic data replicatio strategies i data grids. Proceedigs of the 17th Iteratioal Symposium o Parallel ad Distributed Processig, Lamehamedi, H. (2005). Decetralized data maagemet framework for data grids. New York: Resselaer Polytechic Istitute Troy, (Ph.D. thesis). Europea Datagrid Project. Advaced replica maagemet with reptor. [Olie] Available: Guy, L., et al. (1997). Replica maagemet i data grids. Preseted at Global Grid Forum 5. Kuzst, P., et al. (2003). Advaced replica maagemet with reptor. 5th Iteratioal Coferece o Parallel Processig ad Applied Mathematics, Czestochowa, Polad. Mat Deris, M., et al. (2003). Biary vote assigmet o grid for efficiet access of replicated data. Iteratioal Joural of Computer Mathematics, Taylor ad Fracis, Mat Deris, M., Abawajy, J. H., & Suzuri, H. M. (2004). A efficiet replicated data access approach for large scale distributed systems. IEEE/ACM Cof. O Cluster Computig ad Grid (CCGRID2004), Chicago, USA. Yu, T. W., & Her, K. C. (1997). A ew quorum based replica cotrol protocol. Proceedigs of the 1997 Pacific Rim Iteratioal Symposium o Fault-Tolerat Systems, Mat Deris, M. (2001). Efficiet access of replicatio data i distributed database systems. Uiversiti Putra Malaysia. (Ph.D. thesis). Mat Deris, M., et al. (2004). High system availability usig eighbor replicatio o grid. 2 d Workshop o Hardware/Software Support for High Performace Scietific & Egieerig Computig, Special Issue i IEICE Tras. O Iformatio ad System Society, E87-D (7), Ozsu, MT., & Valduriez, P. (1996). Distributed ad parallel database systems. ACM Computig Surveys, 28(1). Jai, R. (1991). The art of computer systems performace aalysis. Wiley. Ozsu, M.T. (1999). Priciples of distributed database systems. New Jersey Pretice Hall Secod Editio. Agrawal, D., & El Abbadi, A. (1992). The geeralized tree quorum protocol: a efficiet approach for maagig replicated data. ACM Trasactios Database System, 17(4), Agrawal, D., & El Abbadi, A. (1990). The tree quorum protocol: a efficiet approach for maagig replicated data. Proceedig 16th Iteratioal Coferece o Very Large Databases, Chug, SM. (1990). Ehaced tree quorum algorithm for replicated distributed databases. Iteratioal Coferece o Database, Tokyo, Maekawa, M. (1992). A algorithm for mutual exclusio i decetralized systems. ACM Trasactios Computer System, 3(2), Agrawal, D., & El Abbadi, A. (1996). Usig recofiguratio for efficiet maagemet of replicated data. IEEE Trasactios o Kowledge ad Data Egieerig, 8(5), Mat Deris, M., H. Abawajy, J., & Mamat, A. (2007). A efficiet replicated data access approach for large-scale distributed systems. Future Geeratio Computer Systems, 24, 1-9. Mat Deris, M., et al. (2004). Diagoal replicatio o grid for efficiet access of data i distributed database systems. ICCS 2004, LNCS 3038,

8 Vol. 1, No. 2 Computer ad Iformatio Sciece API User Service Processig Security Replica Maagemet Service Core MetaData Catalog ReplicaLocatio Service Collectio Optimizatio Trasport Sessios Cosistecy ReplicaSelectio Subscriptio AccessHistory ReplicaIitiatio Figure 1. The mai compoet i Replica Maagemet System q1 q2 s(1,1) s(1,1) q1 a s(2,2) b c d e a b s(2,2) c d e q2 f g h i j f g h i j s(3,3) s(3,3) k l m o k l m o s(4,4) s (4,4) p q r s t p q r s t s(1,1) u v w x a b c d s(5,5) y e u s(1,1) a v b w c x d s(5,5) y e s(2,2) s(2,2) q3 f g h s(3,3) i j f g h s(3,3) i j q4 k l m o k l m o s(4,4) s(4,4) p q r s t p q r s t s(5,5) s(5,5) u v w x y u v w x y q3 q4 Figure 2. A grid orgaizatio with 81 odes, each of the odes has a data file a, b,, ad y respectively. 102

9 Mai Iput umber of row or colum, N = ext odd umber after N If is a odd iteger the Fid the umber of quorum, Q q = Q= q 2 10 Fid the umber of odes X i each quorum, X = q Get the ext odd iteger after X Select the middle replica, R Copy the data file at R Else add oe virtual colum ad row, Col ew + Row New N = Col ew * Row New the Retur N to Mai. Figure 3. Algorithm of the data replicatio i DR2M protocol Figure 4. A tree orgaizatio of 9 copies of data object Figure copies of sites i DRG 103

10 Vol. 1, No. 2 Computer ad Iformatio Sciece Figure 6. Eight copies of data object Figure 7. Diagoal sets of D 2 (s) ad D 3 (s) Read Availability Vs Probability 1.2 Read Availability ROWA VT TQ CG TDGS DRG DR2M Probability Figure 8. Results for read availability 104

11 Write Availability Vs Probability 1.2 Write Availability ROWA VT TQ CG TDGS DRG DR2M Probability Figure 9. Results for write availability 105