A. Kumar. "Hierarchical Quorum Consensus: A new Algorithm for managing Replicated Data". IEEE Trans. Computers, pages 996--1004, September 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....PS host only needs to send beacons in O(1=n) of the all beacon intervals. Thus, when transmission takes more powers than reception, this protocol may be more energy efficient. The concept of quorums has been used widely in distributed system design (e.g. to guarantee mutual exclusion [23] 24] [25], 26] A quorum is a set of identities from which one has to obtain permission to perform some action [23] Typically, two quorum sets always have nonempty intersection so as to guarantee the atomicity of a transaction. Here we adopt the concept of quorum to design PS hosts wakeup patterns so ....

A. Kumar, "Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data," IEEE Transactions on Computers, vol. 40, pp. 996--1004, Sep 1991.

....PS host only needs to send beacons in O(1=n) of the all beacon intervals. Thus, when transmission takes more powers than reception, this protocol may be more energy efficient. The concept of quorums has been used widely in distributed system design (e.g. to guarantee mutual exclusion [24] 25] [26], 27] A quorum is a set of identities from which one has to obtain permission to perform some action [24] Typically, two quorum sets always have nonempty intersection so as to guarantee the atomicity of a transaction. Here we adopt the concept of quorum to design PS hosts wakeup patterns so ....

A. Kumar, "Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data," IEEE Transactions on Computers, vol. 40, pp. 996--1004, Sep 1991.

....data consistency. Recent developments in quorum consensus are mainly focused on 1) minimizing the total communication costs for processing a given set of transactions, and 2) minimizing the number of remote sites to be communicated while assembling a quorum. A number of quorum consensus protocols [5, 9, 11, 13, 14, 15, 16, 17, 20, 21] have been developed for these purposes. Note that in quorum consensus, since messages are sent (possibly by the multicast mechanism [18] to the multiple nodes in a quorum in order to ensure consistency of the operations the delays by passing messages through a long distance communication ....

A. Kumar, Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data, IEEE Transactions on Computers, 40(9), 996-1004, 1991.

....protocols based on communication will all or distant replicas should be avoided in internetworks. There are two approaches for managing replicated data: strong and weak consistency approaches. Strong consistency protocols enforce strict serializability by means of quorums [Gif79, CAA90, Kum91] and require synchronisation among a large number of replicas in order to ensure that replicas are mutually consistent. Synchronisation across internetworks is inappropriate for large scale systems. They suffer from relatively high latency and low throughput and a large number of replicas ....

A. Kumar. Hierarchical quorum consensus: a new algorithm for managing replicated data. IEEE transactions on Computers, 40(9):996--1004, September 1991.

....majority system presents the best possible availability when the individual failure probability of each element (that is considered equal to all elements) is 469 [15] but it requires quorums of size . To reduce the size of the quorums, the hierarchical quorum system (HQS) [8] is based on a n ary tree construction where elements are the leaves. A quorum is formed recursively from the root node, obtaining a quorum in a majority of sub trees. The quorum size in this system is . An alternative process that also uses a tree construction has been proposed in ....

.... failure probability for different quorum systems with approximately 15 and 28 elements respectively (the results for the Y quorum system have been obtained in [10] From the results presented it is possible to observe that the majority quorum system [5] and the hierarchical quorum system (HQS) [8] exhibit the lower failure probability. However, the size of the quorums used in these systems, and respectively, is larger than the others. From the systems that present quorum sizes hT grid, Paths (presented as the best construction proposed in [14] Y and ....

A. Kumar. Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data. IEEE Transactions on Computers, September 1991.

....and the concept of domination are introduced. Several basic properties of dominated and non dominated coteries are proved. Alternative protocols based on quorum systems (rather than on voting) appear in [28] using finite projective planes) 1] the Tree system) 5, 25] using a grid) and [23, 24, 38] (hierarchical systems) The triangular system is due to [26, 9] The Wheel system appears in [29] The CWlog system appears in [37, 36] The motivation for several of these alternative systems was to find constructions with high availability and low load (which is referred to in most of these ....

....Plugging the root of the tree we obtain y(S) h 2 : Therefore (y; h 2 ) is feasible for program DLP so the claim follows from the weak duality of linear programming. 6.4. The Hierarchical Quorum System. In this section we analyze the load and availability of the hierarchical system of [23]. In this system the elements are the leaves of a complete ternary tree. The internal nodes are 2 of 3 majority gates. We show that F p (HQS) exp( Gamma Omega Gamma n 3 and F p (HQS) n when 2 , and that L(HQS) n . The analysis is similar in nature to that of the AndOr system. ....

A. Kumar, Hierarchical quorum consensus: A new algorithm for managing replicated data, IEEE Trans. Comput., 40 (1991), pp. 996--1004.

....PS host only needs to send beacons in ###### of the all beacon intervals. Thus, when transmission takes more powers than reception, this protocol may be more energy efficient. The concept of quorums has been used widely in distributed system design (e.g. to guarantee mutual exclusion [24] 25] [26], 27] A quorum is a set of identities from which one has to obtain permission to perform some action [24] Typically, two quorum sets always have nonempty intersection so as to guarantee the atomicity of a transaction. Here we adopt the concept of quorum to design PS hosts wakeup patterns so ....

A. Kumar, "Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data," IEEE Transactions on Computers, vol. 40, pp. 996--1004, Sep 1991.

....protocols, such as those mentioned in [4, 5, 10, 13, 2] are needed to coordinate the operations on the replicas. This increases the cost of executing operations in replicated databases. One of the proposed protocols for the above problem is the hierarchical quorum consensus protocol [12]. In this paper, we generalize the hierarchical quorum consensus protocol and show that the generalized protocol can exhibit hybridized behaviour of different kinds of protocols. We present a special family of such protocols, which we call the hypercube quorum consensus. We show that the proposed ....

....is one that has max delay less than or equal to that of any other bicoterie over the same network. 2 4 4 Generalized HQC SUBGROUP 2 SUBGROUP 1 SUBGROUP 3 A B C D E F G H I 1 2 3 4 Figure 1: An example of nine copies organized into three subgroups The hierarchical quorum consensus (HQC) [12] is based on logically organizing a set of copies of an objects in a database into a multilevel tree of depth m and with the root at level 0. The following is a description of this protocol from [12] The physical copies of an object are stored only in the leaves of the tree (at level m) The ....

[Article contains additional citation context not shown here]

A. Kumar, Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data, IEEE Transactions on Computers, Vol. 40, No. 9, 1991, pages 996-1004.

....over the network. Recent developments in quorum consensus are mainly focused on 1) minimizing the total communication costs for processing a given set of transactions, and 2) minimizing the number of remote sites to be communicated while assembling a quorum. A number of quorum consensus protocols [5, 9, 11, 12, 13, 14, 16, 17, 20, 21] have been developed for these purposes. Note that in quorum consensus, since messages are sent (possibly by the multicast mechanism [19] to the multiple nodes in a quorum in order to ensure consistency of the operations the delays by passing messages through a long distance communication ....

A. Kumar, Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data, IEEE Transactions on Computers, 40(9), 996-1004, 1991.

....critical resource by competing sites. The main drawback of permission based mutual exclusion algorithms is that the communication cost to enter critical section is directly proportional to the size of quorums. Much research has been done to optimize communication and minimize the size of quorums [Mae85, GB85, AE91, Kum91, CAA92]. Maekawa [Mae85] has shown that under certain conditions (which are strongly desirable in a distributed system) the optimal quorum size is p N , where N is the total number of sites in the network. This optimal size is achievable when the sites in the network can be organized logically as a ....

A. Kumar. Hierarchical Quorum Consensus - A New Algorithm for Managing Replicated Data. IEEE Transactions on Computers, 39(9):996--1004, September 1991.

....defined on hybrid logical structures such as a grid [13] and a tree [3] Rangarajan and Tripathi [14] partition the sites into N classes and organize the classes to form a finite projective plane. Quorums are then defined using N classes and within each class a majority of sites is chosen. Kumar [12] uses the partitioning approach to recursively define hierarchical quorums based on the majority rule and quorums. Fujita et al. 6] also use a partitioning approach for (k 1) exclusion in which the sites are partitioned into k clusters and quorums are constructed so that mutual exclusion is ....

A. Kumar, "Hierarchical Quorum Consensus---A New Algorithm for Managing Replicated Data," IEEE Trans. Computers, vol. 39, no. 9, pp. 996--1,004, Sept. 1991.

....operation costs depend linearly on the number of replicas in the system. By assigning logical structures to the set of replicas, it is possible to reduce the communication cost. In the Multi Level Voting Protocol [6] which is based on an idea similar to the Hierarchical Quorum Consensus Strategy [9], it is proposed to assign a tree structure to the set of replicas. The replicas are located only in the leaves, whereas the non leaf nodes of the tree can be regarded as logical replicas , which are in a way summarizing the state of their descendants. Weighted Voting is used to manage both ....

A. Kumar. Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data. IEEE Transactions on Computers, 40(9):996-- 1004, 1991.

....new QC methods include coupling high data availability with a low communication cost for processing transactions. The achievements of a low communication cost may be either 1. through the minimization of the number of remote sites with which a transaction operation process has to communicate. [7,8,11,12], or 2. through the minimization of the total communication cost for processing a given set of transactions [9,10] In this paper, we restrict our interests to 1. Interested readers may refer to [9,10] for a detailed discussion about minimizing the total communication cost. A number of QC ....

....minimization of the total communication cost for processing a given set of transactions [9,10] In this paper, we restrict our interests to 1. Interested readers may refer to [9,10] for a detailed discussion about minimizing the total communication cost. A number of QC methods have been proposed [1,4,3,7,8,11,12] to reduce quorum group sizes; and thus, the number of remote sites with which a transaction operation process has to communicate is reduced. Among them, the QC methods in [1,3] have the smallest quorum group size Omega Gammaze n) where n is the number of sites storing the manipulating data ....

[Article contains additional citation context not shown here]

A. Kumar, Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data, IEEE Transactions on Computers, 40(9), 996-1004, 1991.

....through the intersection invariants, the situation that a write and a read cannot take place simultaneously on different copies of the same data, and neither can two writes. Thus, mutual consistency can be maintained. To resolve the limitations of a basic QC method, several other QC methods [1,10,3] have been proposed. Those approaches, including a basic QC approach, are associated with an assignment of a vote to each site. Moreover, to make each site bear equal responsibility for a read and a write, a number of distributed QC approaches [14,15] have been proposed. Those distributed QC ....

A. Kumar, Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data, IEEE Transactions on Computers, 40(9), 996-1004, 1991.

....results in [Wolfson and Milo 1991] also indicate that a comparable algorithm (distributed, An Adaptive Data Replication Algorithm Delta 35 efficient, and convergent optimal) is unlikely to exist for general networks. Works on Quorum Consensus (such as [Agrawal and Bernstein 1991; Gifford 1979; Kumar 1991; Thomas 1979; Triantafillou and Taylor 1991] Voting and Coterie (such as [Agrawal and El Abbadi 1990; Adam and Tewari 1993; Garcia Molina and Barbara 1985; Herlihy 1987; Jajodia and Mutchler 1990; Paris 1986; Spasojevic and Berman 1994] refer to performance in the presence of failures. They ....

Kumar, A. 1991. Hierarchical quorum consensus : A new algorithm for managing replicated data. IEEE Trans. Comput. 40, 9 (September), 996--1004.

....coterie and the concept of domination are introduced. Several basic properties of dominated and non dominated coteries are proved. Alternative protocols based on quorum systems (rather than on voting) appear in [27] using finite projective planes) 1] the Tree system) 6] using a grid) and [23, 24, 36] (hierarchical systems) The triangular system is due to [25, 10] The Wheel system appears in [28] The CWlog system appears in [34] The motivation for several of these alternative systems was to find constructions with high availability and low load (which is referred to in most of these papers ....

.... , 0; otherwise, 7) 27 for every i 2 U and S 2 Tree. Plugging the root of the tree we obtain y(S) 2 h 2 i 1 2 j 0 = 2 h 2 ; and the claim follows from Lemma 5.1. 7. 4 The Hierarchical Quorum System In this section we analyze the load and availability of the hierarchical system of [23]. In this system the elements are the leaves of a complete ternary tree. The internal nodes are 2 of 3 majority gates. We show that F p (HQS) exp( Gamma Omega Gamma n 0:63 ) when p 1 3 and F p (HQS) n Gammaff(p) when p 1 2 Gamma , and that L(HQS) n Gamma0:37 . The analysis ....

A. Kumar. Hierarchical quorum consensus: A new algorithm for managing replicated data. IEEE Trans. Comput., 40(9):996--1004, 1991.

....total number of replicas and therefore sites in the distributed system. Second, no two concurrent write accesses should be possible, thus, w n=2 [6] A large number of data replication protocols known from the literature use the above algorithm for ensuring serializability of replicated objects [5, 4, 9, 19]. Enforcing Serializability through Tokens, Version Vectors, and Synchronization Sets Within our framework, though, the vote of an object (or replica) a at site S i is represented by its token T i a . Granting a vote therefore corresponds to sending the token to the requester. Satisfying a ....

A. Kumar. Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data. IEEE Transactions on Computers, 40(9):996--1004, 1991.

....6. Communication delay The first metric on availability has been studied extensively but its significance has decreased as systems tend to be more and more reliable, a protocol needs only to have high availabilities under a reasonably reliable environment. Metrics (2) to (4) are listed in [10]. The quorum size is also a well studied issue because it can be related to the messaging cost. From [10] the p N algorithm in [13] is a fully distributed algorithm that achieves the smallest quorum size. The protocol in [16] has a bigger quorum size but remedies the availability and other ....

....has decreased as systems tend to be more and more reliable, a protocol needs only to have high availabilities under a reasonably reliable environment. Metrics (2) to (4) are listed in [10] The quorum size is also a well studied issue because it can be related to the messaging cost. From [10], the p N algorithm in [13] is a fully distributed algorithm that achieves the smallest quorum size. The protocol in [16] has a bigger quorum size but remedies the availability and other problems of [13] The third metric is whether all copies assume equal burden for synchronization, for ....

[Article contains additional citation context not shown here]

A. Kumar. Hierarchical quorum consensus: A new algorithm for managing replicated data. IEEE Transactions on Computers, 40(9):996--1004, 1991.

....well known method, called quorum consensus, uses weighted voting [14] In order to improve on the performance exhibited by quorum consensus, several researchers have proposed methods that impose a logical structure on the nodes. These methods include: Kumar s hierarchical quorum consensus protocol [17], Agrawal and El Abbadi s tree protocol and hybrid replica control protocols [1, 2] Rangarajan, Setia, and Tripathi s protocol [25] and Kumar and Cheung s hierarchical grid protocol [18] We have proposed a more general method, called composition [20] Composition generalizes all of the above ....

A. Kumar. Hierarchical quorum consensus: a new algorithm for managing replicated data. IEEE Transactions on Computers, 40(9):996--1004, 1991.

....d) With the grid protocol, there is always only one server in the intersection between any document quorum and any profile quorum. It is this server that performs the matching for a particular profile document pair. Another alternative is a hierarchical organization (related to protocols such as [AA90, RST92, Kum91]) To illustrate, consider 8 servers. Suppose we first split the servers into two logical units, each with four servers. Within each unit, we choose to arrange the servers into a 2 Theta 2 grid. Next we view the two units as two logical servers, and coordinate them using the majority consensus ....

A. Kumar. Hierarchical quorum consensus: a new algorithm for managing replicated data. IEEE Transactions on Computers, 40(9):996--1004, 1991.

....access an arbitrary replica requires the write operations to update all replicas. As discussed before, this protocol is costly and has a poor write availability. Instead, replication schemes should be used which provide better performance and availability [Agrawal and El Abbadi 1990, Koch 1993, Kumar 1991, Kumar and Cheung 1991] In the following, we use the Logarithmic Protocol (LP) Koch 1993] as an example for an efficient 1SRpreserving, strongly consistent replication control scheme. LP arranges the replicas as a logical tree structure and allows read and update operations to consult only a ....

A. Kumar. Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data. IEEE Transactions on Computers, 40(9):996--1004, 1991.

....structure, together with votes and quorums defined for each node is used to derive sets of nodes for cooperation purposes. The idea of using logical nodes in order to group physical nodes is also used by protocols for replication management like the Hierarchical Quorum Consensus schemes 1 and 2 [12, 13] and by Multi Level Voting [8] The means of structuring nodes for designing protocols guaranteeing one copy serializability which have desirable properties like high availability and or low costs is also commonly accepted. Examples are the Grid Protocol [6] the Tree Quorum Protocol [2] ....

A. Kumar. Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data. IEEE ToC, 40(9):996--1004, 1991.

....by replacing: ffl node a in Q 1 by nodes in a quorum of Q a ; ffl node b in Q 1 by nodes in a quorum of Q b ; and ffl node 1 is not changed. 65 7. 2 Hierarchical Quorum Consensus In order to improve on the performance exhibited by quorum consensus, Kumar proposed hierarchical quorum consensus [32, 33]. A complete tree of depth n is formed with the root at level 0. All non leaf nodes are logical nodes. A single vote is assigned to each node, except for the root. A pair of thresholds is assigned to each level, except for level 0. Let q i (q c i ) denote the quorum set (complementary quorum ....

A. Kumar. Hierarchical quorum consensus: a new algorithm for managing replicated data. IEEE Transactions on Computers, 40(9):996--1004, 1991.

....defined on hybrid logical structures such as a grid [13] and a tree [3] Rangarajan and Tripathi [14] partition the sites into N classes and organize the classes to form a finite projective plane. Quorums are then defined using N classes and within each class a majority of sites is chosen. Kumar [12] uses the partitioning approach to recursively define hierarchical quorums based on the majority rule and quorums. Fujita et al. 6] also use a partitioning approach for (k 1) exclusion in which the sites are partitioned into k clusters and quorums are constructed so that mutual exclusion is ....

A. Kumar, "Hierarchical Quorum Consensus---A New Algorithm for Managing Replicated Data," IEEE Trans. Computers, vol. 39, no. 9, pp. 996--1,004, Sept. 1991.

....and logical nodes. This structure, together with votes and quorums defined for each node is used to derive sets of nodes for cooperation purposes. The idea of using logical nodes in order to group physical nodes is also used by other protocols like the Hierarchical Quorum Consensus schemes 1 and 2 [14, 15] and by Multi Level Voting [9] Whereas in the first case, the logical nodes are only regarded as logical entities which are not able to perform operations, the latter case chooses physical nodes as representatives of logical nodes which perform operations originally directed to the logical one. ....

A. Kumar. Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data. IEEE Transactions on Computers, 40(9):996--1004, 1991.

....called optimistic. Pessimistic data replication schemes which take advantage of declared relationships between nodes owing replicas have become of particular interest for the data replication community during the last few years because of highly appreciated properties offered by these protocols [2, 5, 11, 7, 1]. The purpose of this work is to take advantage of a unifying framework for those protocols, called General Structured Voting [16, 15, 17] in order to achieve a three folded goal: First, the framework depends only on uniform relationships between the nodes involved in the operation execution. ....

A. Kumar. Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data. IEEE Transactions on Computers, 40(9):996--1004, 1991.

.... 12,13 1 1 R11,12, 13 1 2 R8,9,10 1 2 R 3 1 0 R5,6,7 1 2 R2,5, 6,7 1 1 R 2 1 0 R Gamma Gamma Gamma Psi 1 2 R 1 1 0 R 1; 13 1 1 R 2; 13 1 2 Figure 4: Node structure for Tree Quorum Protocol are MD(1,k) Voting [3] the Grid Protocol [4] Hierarchical Quorum Consensus [10], and Multi Level Voting [6] 5 Conclusions and Future Work We proposed a general framework for the management of replicated data objects. It can be classified as pessimistic syntactic and uses a logical hierarchy of physical and logical nodes together with votes and quorums to derive so ....

A. Kumar. Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data. IEEE Transactions on Computers, 40(9):996--1004, 1991.

....(if successful) This scheme allows good load sharing (because requests from different coordinators can be served by nodes from different quorums) and light network traffic. The performance of these systems depends on the size of read and write quorums, which motivated a search for small quorums [1, 4, 10]. Unfortunately, in information systems, it is often impractical to manage replication at such a small data granularity that all modifications of data items become total. Instead, operations in these systems update just a portion of the information in the data item. For example, in object oriented ....

A. Kumar. Hierarchical quorum consensus: a new algorithm for managing replicated data. IEEE Trans. on Computers, 40(9), pp. 996-1004.

....ones. Data replication schemes manage multiple replicas and offer a single copy image of the replicated data object in order not to put this burden on the application programmers. In recent years, several data replication schemes have been developed which use logical structures such as trees [1, 6], finite projective planes [9, 11] acyclic graphs [12] or grids [2, 8, 14] for managing the replicated data. Especially grid based protocols have been proven to be extremely efficient due to the high This work was partially supported by Digital Equipment Corporation s Campus based Engineering ....

....with desired properties has already proven to be a powerful design method [4, 7, 13] In particular, the hierarchical combination of replication schemes is suited for building scalable new schemes, e.g. replication schemes which manage a large number of replicas in an inexpensive manner. In [3, 6] this has been shown by the hierarchical layering of Quorum Consensus Protocols [5] 7] applies this approach to the original Grid Protocol. In this section, we show how hierarchical grid based protocols can be specified within the proposed framework in a homogeneous way. First, we model the ....

A. Kumar. Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data. IEEE Trans. on Computers, 40(9):996--1004, 1991.

....the processors. A Quorum System is a set system S that has the Intersection property: S R 6= for all S; R 2 S. The sets of the system are called quorums. Many quorum systems which are based on combinatorial constructions appear in the literature, such as [Mae85, GB85, AE91, CAA90, Kum91, KC91, NW94, PW97] However all the systems with optimal availability turn out to be defined by voting. Definition 2.2 Let v i be a positive vote assigned to element i, and let V = P i v i . The voting system defined by the votes v i is the collection of all the sets which have more than half ....

A. Kumar. Hierarchical quorum consensus: A new algorithm for managing replicated data. IEEE Trans. Comput., 40(9):996--1004, 1991.

.... The first paper to explicitly consider mutual exclusion protocols in the context of intersecting set systems is [GB85] Alternative protocols based on quorum systems (rather than on voting) appear in [Mae85] using finite projective planes) AE91] the Tree system) CAA90] using a grid) and [Kum91, KC91, RT91] hierarchical systems) The triangular system is due to [Lov73, EL75] The Wheel system appears in [MP92] The CWlog system appears in [PW94] The motivation for several of these alternative systems was to find constructions with high availability and low load (which is referred to ....

A. Kumar. Hierarchical quorum consensus: A new algorithm for managing replicated data. IEEE Trans. Comput., 40(9):996--1004, 1991.

....Ammar [2] suggest a logical two dimensional grid organization of the nodes. Each read quorum group contains at least one node from each column and a write quorum group consists of all nodes of one of the columns plus the nodes in a read quorum group. In the hierarchical quorum consensus protocol [8], the nodes are organized in a multilevel hierarchy with physical nodes at the lowest level of the hierarchy. Higher level logical nodes of the tree correspond to logical groups of the physical nodes. At any level except for the lowest one, a logical node needs permission from a majority of the ....

....a node is non faulty and is available to take part in the replica control procedure. We consider the following well know replica control protocols. ffl The majority voting protocol [11] ffl The tree protocol [1] ffl The grid protocol [2] ffl The hierarchical quorum consensus (HQC) protocol [8]. ffl The RST protocol [10] For each of the above protocols, we compute the average case message overhead and availability and consider the trade off between the two. We further compare these performance parameters across the different protocols. The average number of messages exchanged as part ....

[Article contains additional citation context not shown here]

A. Kumar, "Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data," IEEE Transactions on Computers, vol. 40, no. 9, pp. 996-1004, September 1991.

....of the data. The most commonly accepted correctness criterion is called one copy serializability [1] It assures that concurrent executions of operations are equivalent to serial executions on non replicated data objects. Several schemes in the literature use this notion of correctness [6, 8, 7]. Although a wide variety of replication strategies has already been proposed, the identification of the best suited scheme for a given application still remains a problem. Furthermore, due to the nature of distributed systems, modifications of the network This work was partially supported by ....

....correctness criterion. The definition of the operation costs takes into account that communication between processes on remote computers is more expensive than communication between processes on a local machine. This cost measure is therefore used by a variety of analyses of replication protocols [8, 7]. Definition 2.2 Let op be an operation of a replication strategy S. The availability P S;op of the operation op of S is defined as the probability that this operation can be executed successfully within the network at an arbitrary point in time. 2 Thus, we can describe the properties of the ....

A. Kumar. Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data. IEEE Transactions on Computers, 40(9):996-- 1004, 1991.

....and the concept of domination are introduced. Several basic properties of dominated and non dominated coteries are proved. Alternative protocols based on quorum systems (rather than on voting) appear in [28] using finite projective planes) 1] the Tree system) 5, 25] using a grid) and [23, 24, 38] (hierarchical systems) The triangular system is due to [26, 9] The Wheel system appears in [29] The CWlog system appears in [37, 36] The motivation for several of these alternative systems was to find constructions with high availability and low load (which is referred to in most of these ....

....obtain y(S) 2 h 2 Gamma 1 2 Delta 0 = 2 h 2 : Therefore (y; 2 h 2 ) is feasible for program DLP so the claim follows from the weak duality of linear programming. 6.4. The Hierarchical Quorum System. In this section we analyze the load and availability of the hierarchical system of [23]. In this system the elements are the leaves of a complete ternary tree. The internal nodes are 2 of 3 majority gates. We show that F p (HQS) exp( Gamma Omega Gamma n 0:63 ) when p 1 3 and F p (HQS) n Gammaff(p) when p 1 2 , and that L(HQS) n Gamma0:37 . The analysis is similar ....

A. Kumar, Hierarchical quorum consensus: A new algorithm for managing replicated data, IEEE Trans. Comput., 40 (1991), pp. 996--1004.

....a consistent state. Furthermore, the hospital computer system and the read operation must be highly available: as already pointed out, the paramedics do not have much time to decide where to transport the patients to. Voting strategies, like Majority Consensus [1] or Hierarchical Quorum Consensus [2], fulfill both requirements identified above: consistency and availability. However, there is still the possibility that read operations cannot be executed since computers or network links may fail. In such a critical situation, the rescue crew must wait until the system has recovered from ....

....In this case, reading an old version of the replicated object can still provide valuable information. Based on a general specification model for voting protocols described in [3] we are currently analyzing different classes of voting strategies. Examples are Hierarchical Quorum Consensus [2], the Logarithmic Protocol [12] the Tree Quorum Protocol [13] the Grid Protocol [10] and the Hierarchical Grid Protocol [14] Furthermore, we vary different parameters, like the number of replicas and the site availabilities. As a first result, we could identify voting strategies with a level ....

A. Kumar. Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data. IEEE Transactions on Computers, 40(9):996--1004, 1991.

....as noted earlier, no quorum assignment model needs to be maintained, and the quorum invariant does not have to be maintained across such a table. 2.1. 5 Hierarchical Quorum Consensus A novel approach to the replica control method is undertaken with the hierarchical quorum consensus protocol [7,8,9]. These papers observe that many early replica control 27 strategies required a majority of sites to be available in order for updates to be allowed (i.e. 2q w n) and notes that for large networks it becomes less likely that this goal can be reached. The protocol presented uses a hierarchical ....

A. Kumar. "Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data". IEEE Transactions on Computers, 40(9):996-1004, September 1991.

....and write operations. Therefore, operation requests which might lead to future inconsistencies will be eventually rejected, resulting in lower operation availabilities. Examples for pessimistic strategies are voting strategies, like Majority Consensus [Tho79] and Hierarchical Quorum Consensus [Kum91] These strategies preserve consistency at any time while offering high availability of access operations. However, it is still possible that read operations cannot determine the current value of the replicated object due to site and or link failures that prevent accessing sufficient replicas for ....

A. Kumar. Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data. IEEE ToC, 40(9):996--1004, 1991.

....We have seen in recent years the development of several replication control protocols specially tailored for the management of highly replicated data. These protocols include voting with tokens [14] the grid protocol [4] the tree quorum protocol [1] the hierarchical quorum consensus protocol [9, 10] and location based replication [17] The most attractive of these protocols is the grid protocol of Cheung et al. because it only requires O ( # ## n) messages per access while distributing the transaction processing load among all replicas. The grid protocol organizes the set of replicas of a ....

A. Kumar, "Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data," IEEE TC , Vol. TC-40, No. 9 (1990), pp. 996-1004.

....called optimistic. Pessimistic data replication schemes which take advantage of declared relationships between nodes owning replicas have become of particular interest for the data replication community during the last few years because of highly appreciated properties offered by these protocols [1, 4, 11, 6]. In particular, data replication schemes have recently been developed which use logical grid structures for managing the replicated data [4, 12, 19] Grid structure based protocols have been proven to be extremely efficient due to the high availability of read and write operations they offer and ....

....operation costs and availabilities. Finally, section 8 concludes the paper by summarizing the main achievements and describes our ongoing and future work on this subject. 2 Basic Idea In recent years, several data replication schemes have been developed which use logical structures such as trees [11, 1], finite projective planes [16, 14] or grids [4, 19, 13] for managing the replicated data. Especially the latter concept has been proven to be extremely efficient due to the high availability of read and write operations it offers and due to the very small number of copies which have to be ....

[Article contains additional citation context not shown here]

A. Kumar. Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data. IEEE Transactions on Computers, 40(9):996--1004, 1991.

....which is an of k threshold system (with k k=2) and recursively composing it over itself to depth h. In the sequel, we often omit the depth parameter h when it has no effect on the discussion. The RT systems generalize the recursive majority constructions of [MP92] the HQS system of [Kum91] is an RT(3; 2) system, and in fact the threshold system of [MR97] can be viewed as a trivial RT(4b 1; 3b 1) system with depth h = 1. As an example throughout this section we will use the RT(4; 3) system, depicted in Figure 2. Proposition 5.3 An RT(k; system of depth h is a fair quorum ....

A. Kumar. Hierarchical quorum consensus: A new algorithm for managing replicated data. IEEE Trans. Comput., 40(9):996--1004, 1991.

....Ammar [2] suggest a logical two dimensional grid organization of the nodes. Each read quorum group contains at least one node from each column and a write quorum group consists of all nodes of one of the columns plus the nodes in a read quorum group. In the hierarchical quorum consensus protocol [8], the nodes are organized in a multilevel hierarchy with physical nodes at the low est level of the hierarchy. Higher level logical nodes of the tree correspond to logical groups of the physical nodes. At any level except for the lowest one, a logical node has to collect votes from a majority ....

....in Section 5. 2 System Model We compute the average case message overhead of the following well known replica control algorithms. ffl The majority consensus voting algorithm [11] ffl The tree algorithm [1] ffl The grid algorithm [2] ffl The hierarchical quorum consensus (HQC) algorithm [8]. ffl The RST Algorithm [10] In the rest of the paper we assume that a functional node always gives permission (casts its vote) when it receives a request for permission. That is, we ignore the issue of resource contention and do not take into consideration the queuing delay which may be ....

[Article contains additional citation context not shown here]

A. Kumar, "Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data," IEEE Transactions on Computers, vol. 40, no. 9, pp. 996-1004, September 1991. 5 10 15 20 25 30 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 Availability of a Node Majority Tree Grid HQC RST

....are in V ) or remains the same after flipping the bits at both endpoints. This shows that the distribution of share values on a set Z that does not contain a quorum is independent of the secret. 6.2 The HQS and Tree Systems 6.2. 1 The Systems The hierarchical quorum system (HQS) is due to [Kum91]. In this system the elements are the leaves of a complete ternary tree, in which the internal nodes are 2 of 3 majority gates. In [NW95] the availability and load of the HQS are analyzed. It is shown that L(HQS) n Gamma0:37 . The HQS has the highest availability possible for such load, ....

A. Kumar. Hierarchical quorum consensus: A new algorithm for managing replicated data. IEEE Trans. Comput., 40(9):996--1004, 1991.

....copies [7] this solution, however, is not suitable to a system with a large number of copies because it would impose an undesirable centralized control. A better way to reduce quorum size is to organize the copies into some logical structure and then to derive the quorums from this structure [2, 10, 14, 15, 4]. Quorums formed in this way in general have sublinear size and do not have any equivalent vote assignment in the weighted voting protocol [12] Cheung, Ammar and Ahamad [10] for example, propose to organize the N copies of the replicated data into a rectangular grid; a read quorum is formed by ....

....the copies of a read quorum. When the number of rows equals the number of columns, read and write quorums size are p N and 2 p N Gamma 1, respectively. Agrawal and El Abbadi [4] use a tree structure to organize the copies and obtain quorums size varying from log N to N=2 1 copies. Kumar [14] proposes a generalization of the voting mechanism, called hierarchical quorum consensus (HQC) where a multilevel hierarchy of vertices organized as a tree is used. Copies of the replicated data correspond to the leaf vertices at the lowest level of the hierarchy, and vertices at higher levels ....

[Article contains additional citation context not shown here]

Akhil Kumar. Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data. IEEE Transactions on Computers, 40(9):996--1004, September 1991.

.... it to obtain smaller quorum sizes than is possible with conventional methods such as weighted voting [7] majority voting [11] dynamic voting [5] 8] and coteries [6] Examples of techniques based on logical structure are: tree protocol [1] grid protocol [4] and hierarchical quorum consensus [9]. The quorum sizes are O( p N) in Maekawa s p N algorithm [10] which arranges N copies of an object in projective planes, and the grid protocol [4] where N copies are organized into a rectangular grid of p N rows and p N columns. A read quorum is formed by obtaining one copy from each ....

Kumar, A., "Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data," IEEE Transactions on Computers, Vol 40, No 9, September 1991, pp 996-1004.

No context found.

A. Kumar. "Hierarchical Quorum Consensus: A new Algorithm for managing Replicated Data". IEEE Trans. Computers, pages 996--1004, September 1991.

No context found.

A. Kumar. Hierarchical Quorum Consensus: A New Algorithm for Managing Replicated Data, IEEE Transactions on Computers, 40 (9), September 1991, pp. 996-1004.

No context found.

KUMAR, A. 1991. Hierarchical quorum consensus: A new algorithm for managing replicated data. IEEE Trans. Comput. 40, 9 (Sept.), 996--1004.

No context found.

A. Kumar. Hierarchical quorum consensus: A new algorithm for managing replicated data. IEEE Transactions on Computers, 40(9):996--1004, September 1991.

No context found.

A. Kumar, "Hierarchical quorum consensus: A new algorithm for managing replicated data," IEEE Transactions on Computers, Vol. 40, No. 9, pp. 996--1004, Sep. 1991.

No context found.

A. Kumar. Hierarchical quorum consensus: A new algorithm for managing replicated data. IEEE Transactions on Computers 40(9):996--1004, 1991.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC