D.Malkhi,M.K.Reiter,A.Wool,andR.N.Wright. Probabilistic quorum systems. Inform. and Comput., 170(2):184--206, 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....jobs from a heavily loaded processor to a less loaded neighbor. The e# ciency of the algorithm depends only on the expansion of the network. If the network is an expander then the algorithm balances the load in O(log n) rounds. Probabilistic quorums were suggested by Malkhi et al. in [17]. A quorum set is chosen by randomly sampling # n processors. A random walk on an expander could serve as a procedure for sampling # n processors in a dynamic setting. 6. EMULATING GENERAL GRAPHS In this section we show how our technique can be used to dynamically construct a graph which embeds ....

D. Malkhi, M. K. Reiter, and R. N. Wright. Probabilistic quorum systems. In Symposium on Principles of Distributed Computing (PODC), pages 267--273, 1997.

....Unfortunately, original quorum systems, also termed strict quorum systems, do not apply well to highly dynamic environments [3] This is because the very construction of these quorums is not a trivial task, as their outcome is strongly subject to membership changes. Probabilistic quorum systems [14], thanks to their less strict design rules, seem to be more appropriate for highly dynamic environments. By introducing probabilities for the intersection of individual quorums, the construction rules for these quorums are relaxed, and more freedom is left for trading protocol overhead for ....

....Our gossip based protocol, as demonstrated before, behaves in a predictable way, while requiring no separate membership tracking. As a consequence of gossip based access protocol, the design of quorum systems becomes more straightforward. According to the theory of probabilistic quorum systems [14], the # is designed to meet the requirement of a certain intersection property # in a replication system with n servers. However, as any unreliable access protocol is concerned, the di#erence between # and # does exist. Also, it is # that is essential to the estimation of reliability. Our ....

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D. Malkhi, M.K. Reiter, and A. Wool, "Probabilistic quorum systems," Information and Computation, vol. 170, no. 2, pp. 184--206, 2001.

....jobs from a heavily loaded processor to a less loaded neighbor. The e ciency of the algorithm depends only on the expansion of the network. If the network is an expander then the algorithm balances the load in O(log n) rounds. Probabilistic quorums were suggested by Malkhi et al. in [17]. A quorum set is chosen by randomly sampling n processors. A random walk on an expander could serve as a procedure for sampling n processors in a dynamic setting. 6. EMULATING GENERAL GRAPHS In this section we show how our technique can be used to dynamically construct a graph which embeds ....

D. Malkhi, M. K. Reiter, and R. N. Wright. Probabilistic quorum systems. In Symposium on Principles of Distributed Computing (PODC), pages 267-273, 1997.

....is lessened, since any values returned will satisfy the deterministic specification. Examples of this situation include [20, 19, 10] discussed below. Randomized implementations have been proposed for several shared data structures in various architectures, as we now discuss. Malkhi et al. [18, 17] have proposed a probabilistic quorum algorithm to implement a readwrite variable on top of a message passing system. Each read is translated into messages to a subset ( quorum ) of the processes to obtain the latest value, and each write is translated into messages to a quorum of the processes to ....

....obtain the latest value written. The smaller the quorums, the more message efficient the algorithm is, but the larger the probability that a read will observe an out of date value. Probabilistic quorums seem like a useful distributed building block, thanks to their good performance (analyzed in [18]) However, to make them usable by programmers, a more complete semantics of the register which they implement must be given, together with techniques for programming effectively with them. Shavit and Zemach have implemented novel synchronization mechanisms called combining funnels [20] and ....

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D. Malkhi, M. Reiter, and R. Wright. Probabilistic Quorum Systems. In Proceedings of the 16th Annual ACM Symposium on Principles of Distributed Computing, pages 267--273, Aug. 1997.

....commit the updates in increasing order of the CSN. The problem with this approach is that using a single primary to decide the order may not scale well when there is a large number of replicas. A third approach, used by Deno [39] is based on an optimistic version of the quorum consensus protocol [19, 30, 34, 49]. Deno assigns each replica a weight in such a way that the weight of the replicas adds up to 1. Each update is associated with a vote that increases by an amount that is equal to a replica s weight, when the update is received by the replica. When multiple updates circulate simultaneously, the ....

D. Malkhi, M. Reiter, and R. Wright. Probabilistic Quorum Systems. In Proc. of the 16th ACM Symposium on Principles of Distributed Computing, August 1997.

....Station, TX 77843 3112, U.S.A. fhlee, welchg cs.tamu.edu Abstract This paper presents a specification of a randomized shared queue that can loose some elements or return them out of order (not in FIFO) shows that the specification can be implemented over the probabilistic quorum algorithm of [8], and analyzes the behavior of this implementation. Distributed algorithms that can tolerate some lost and out of order messages are candidates for replacing the message queues with random queues. The modified algorithms will inherit positive attributes concerning load and availability from the ....

....algorithms when it is implemented using random queues is analyzed. 1 Introduction Quorum systems have been receiving significant attention because they provide consistency and availability of replicated data and reduce the communication bottleneck of some distributed algorithms (cf. [8] for references) The probabilistic quorum model [8] relaxes the intersection property of the strict quorum system, such that pairs of quorums only need to intersect with high probability. In [6] random registers are defined as memory cells in which certain types of random errors can occur. It is ....

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D. Malkhi, M. Reiter, and R. Wright. Probabilistic Quorum Systems. In Proc. of the 16th Annual ACM Symp. on Principles of Distributed Computing, pp. 267--273, Aug. 1997.

....intersection. An update can be performed with only a quorum available, unlike other replication techniques where all of the members must be available. 2 The intersection property of quorums guarantees consistency. Quorum systems have been extensively studied and used in applications, e.g. [1, 7, 8, 18, 23, 24, 34, 38]. The use of quorums has been proven effective also against Byzantine failures [32, 33] Pre defined quorum sets can yield efficient implementations in settings which are relatively static, i.e. failures are transient. However they work less well in settings where processes routinely join and ....

D. Malkhi, M.K. Reiter, and R. Wright. Probabilistic quorum systems. In Proceedings of the 16 th ACM Symposium on Principle of Distributed Computing (PODC), pages 267--273, 1997.

....simple and fast. In comparison to quorum systems, we use the very simple concept of quorum as a strict majority over each virtual store layout group. This approach is similar to work on use of quorum for replication control [18, 11] We have not yet investigated if more generalized quorum systems [19] are applicable (or necessary) for our target of data storage systems in the face of site failure and arbitrary partitions. 8 Conclusions We have designed a replication management system that automatically and correctly recovers from the large scale failures we expect in distributed data storage ....

D. Malkhi, M. Reiter, and R. Wright. Probabilistic quorum systems. In Proc. of the 16th ACM Symp. on Principles of Distributed Computing, August 1997.

....point of view, the RDG can also be considered as a special case of the tactical configuration [9] or t designs[10] 11] which is an extension of the Balanced Incomplete Block Design. The RDG construction can also be considered as a special case of the probabilistic quorum systems presented in [12], where each k group is corresponding to one of the probabilistic quorums. It is probabilistic in the sense that every two groups intersect at a certain number of databases only with some probability. In Section II, we describe in more detail the Randomized Database Group mobility management ....

D. Malkhi, M. Reiter, and R. Wirght, "Probabilistic Quorum Systems," Proc. ACM PODC, pp. 267-273, Santa Barbara, 1997.

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D.Malkhi,M.K.Reiter,A.Wool,andR.N.Wright. Probabilistic quorum systems. Inform. and Comput., 170(2):184--206, 2001.

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D. Malkhi, M. K. Reiter, A. Wool, and R. N. Wright. Probabilistic quorum systems. Inf. Com., 170(2):184--206, 2001.

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Malkhi D, Reiter M, Wright R: Probabilistic quorum systems. In: Proceedings of the 16th ACM Symposium on Principles of Distrib Comput, pp 267--273, August 1997

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D. Malkhi, M. Reiter, A. Wool and R. Wright. Probabilistic quorum systems. The Information and Computation Journal 170(2):184--206, November 2001.

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D. Malkhi, M. Reiter, and R. Wright. Probabilistic quorum systems. In Proceedings of the 16th ACM Symposium on Principles Distributed Computing, pages 267--273, August 1997.

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D. Malkhi, M. Reiter, A. Wool and R. Wright. Probabilistic quorum systems. The Information and Computation Journal 170(2):184--206, November 2001.

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D. Malkhi, M. Reiter, A. Wool and R. Wright. Probabilistic quorum systems. The Information and Computation Journal 170(2):184206, November 2001.

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D. Malkhi, M. Reiter, A. Wool and R. Wright. Probabilistic Quorum Systems. The Information and Computation Journal 170(2), November 2001.

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D. Malkhi, M. K. Reiter, A. Wool, and R. N. Wright. Probabilistic quorum systems. Information and Computation 170(2), November 2001.

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D. Malkhi, M. Reiter, and R. Wright. Probabilistic quorum systems. In Proceedings of the 16th ACM Symposium on Principles Distributed Computing, pages 267-273, August 1997.

....consists of persistent servers and (potentially transient) clients. Servers hold replicas of object state and provide support for implementing method invocations on each Fleet object. Clients share information indirectly through servers by invoking methods on Fleet objects. Previous papers [MR98a, MR98b, MR00, MRW00, MRWW01, CMR01] described the various quorum based replication protocols supporting object replication in Fleet. These technologies provide Fleet objects with their fault tolerance and scalability features: Fault tolerance: Fleet protocols are designed to allow for the arbitrary (Byzantine [LSP82] failure of ....

....under Byzantine client failures, Fleet focuses on supporting the benign client case for general objects. Scalability: Fleet protocols are designed to scale well in both the number of clients and the number of servers. This is achieved via object replication using Byzantine quorum systems [MR98a, MRW00, MRWW01], which enable each operation on a Fleet object to be performed at a small subset of servers at which the object is replicated. This results in better load balancing across servers and lower access costs per operation as compared to prior approaches for implementing Byzantine fault tolerant ....

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D. Malkhi, M. K. Reiter, A. Wool, and R. N. Wright. Probabilistic quorum systems. Information and Computation, 2001. To appear.

....is taken, at the limit, over the set of all potential messages broadcasted via the protocol. ffl The overhead of forming agreement on messages contents in active t in faultless circumstances is determined by two constants that depend on ffl only (and not on the system size or t) Malkhi et. al [12] consider relaxed consistency requirements in the context of general quorum systems. Their probabilistic dissemination quorum systems resemble the witness sets we use in the active t protocol, but cannot be employed by corrupt clients as is the case we have in our protocols (where senders may be ....

D. Malkhi, M. Reiter and R. Wright. Probabilistic Quorum Systems. In Proceeding of the 16th Annual ACM Symposium on the Principles of Distributed Computing (PODC 97), Santa Barbara, CA, August 1997. To appear.

....path of data operations. In this way, the system can still efficiently guarantee strict consistency in case a full quorum is accessed, but can additionally provide relaxed consistency guarantees when only local information is used. Another variation on quorum systems, probabilistic quorum systems [MRW97, MRWW98], stands to benefit from properly designed message diffusion in different ways than above. Probabilistic quorum systems are a means for gaining dramatically in performance and resilience over traditional (strict) quorum systems by allowing a marginal, controllable probability of inconsistency for ....

D. Malkhi, M. Reiter, and R. Wright. Probabilistic quorum systems. In Proceedings of the 16th ACM Symposium on Principles Distributed Computing, pages 267--273, August 1997.

....can be surprisingly small e.g. comprised of only O( p n) out of a total of n servers and thus client access protocols can efficiently scale to hundreds and possibly even thousands of servers. Quorum systems can be constructed to tolerate failures ranging from benign to fully arbitrary [26, 32, 30], and for either type of failure can provide either strict consistency guarantees or only probabilistic ones [31] Phalanx allows clients to dynamically tune the quorums they use for their application needs. The goal of this paper is to give an overview of this architecture with an eye toward how ....

....we expect that in the applications we envision, consensus objects will seldom be contended for by more than a handful of clients at any time. Scalability with growth in the number of servers is primarily dictated by the quorum system used, as quorum systems exist with a wide array of properties [26, 30, 32, 31]. For example, there are Byzantine constructions that have quorum sizes as small as p n (so, e.g. for n = 1000, quorum size is roughly 32) Moreover, probabilistic constructions exist with such quorum sizes that simultaneously have outstanding availability. These latter constructions admit a ....

D. Malkhi, M. Reiter and R. Wright. Probabilistic quorum systems. In Proceeding of the 16th ACM Symposium on the Principles of Distributed Computing, pages 267--273, August 1997.

....protocols can efficiently scale to hundreds and possibly even thousands of servers. Quorum systems can be constructed to tolerate failures ranging from benign to fully arbitrary [26, 32, 30] and for either type of failure can provide either strict consistency guarantees or only probabilistic ones [31]. Phalanx allows clients to dynamically tune the quorums they use for their application needs. The goal of this paper is to give an overview of this architecture with an eye toward how it can be used to support client coordination. We describe various shared data elements emulated by servers that ....

....we expect that in the applications we envision, consensus objects will seldom be contended for by more than a handful of clients at any time. Scalability with growth in the number of servers is primarily dictated by the quorum system used, as quorum systems exist with a wide array of properties [26, 30, 32, 31]. For example, there are Byzantine constructions that have quorum sizes as small as p n (so, e.g. for n = 1000, quorum size is roughly 32) Moreover, probabilistic constructions exist with such quorum sizes that simultaneously have outstanding availability. These latter constructions admit a ....

D. Malkhi, M. Reiter, A. Wool and R. Wright. Probabilistic quorum systems. Submitted for publication. (Brief announcement appears in Proceeding of the 17th ACM Symposium on the Principles of Distributed Computing, page 321, June 1998).

....tradeoff between low load and good resilience, so that it is in fact impossible to simultaneously achieve both optimally. In particular, quorum systems over n servers that achieve the optimal load of 1 p n can tolerate at most p n faults. To break these limitations, Malkhi et al. propose in [6] to relax the intersection property of a quorum system so that quorums chosen according to a specified strategy intersect only with very high probability. They accordingly name these probabilistic quorum systems. These systems admit the possibility, albeit small, that two operations will be ....

....than certain consistency. This might be the case if the cost of inconsistent operations is high but not irrecoverable, or if obtaining the most up to date information is desirable but not critical, while having no information may have heavier penalties. The family of constructions suggested in [6] is as follows: W(n; Let U be a universe of size n. W (n; 1, is the system hQ; wi where Q is the set system Q = fQ U : jQj = p ng; w is an access strategy w defined by 8Q 2 Q; w(Q) 1 jQj . The probability of choosing according to w two quorums that do not intersect is less ....

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D. Malkhi, M. Reiter, and R. Wright. Probabilistic quorum systems. In Proceedings of the 16th ACM Symposium on Principles of Distributed Computing (PODC), pages 267--273, August 1997.

....subsequent paper [31] is devoted to constructions of masking quorum systems for the special case of a threshold of faulty servers. Bazzi [6] explored a variation of our quorum systems for synchronous systems. Probabilistic constructions for dissemination and masking quorum systems are explored in [32] and [33] respectively. A practical effort for building a large scale survivable data repository using Byzantine quorums is described in [29] and the construction of a survivable consensus object in this context is described in [30] 3 Preliminaries 3.1 System model We assume a universe U of ....

D. Malkhi, M. Reiter, and R. Wright. Probabilistic quorum systems. In Proceedings of the 16th ACM Symposium on Principles of Distributed Computing (PODC), pages 267--273, August 1997.

....in measures of both availability and efficiency. 1 Overview Quorums are tools for increasing the availability and efficiency of replicated services. A quorum system is a set of subsets (quorums) of servers such that every pair of quorums intersect. Recently, probabilistic quorum systems [MRW97b], in which any two chosen quorums intersect with high probability rather than with certainty, have been introduced to break availability and efficiency tradeoffs inherent in nonprobabilistic (strict) quorum systems. However, this prior work addressed only crash server failures and limited forms ....

....2 [PW95] When p 1 2 then F p (Q) p 1 2 for strict quorum systems, and typically F p (Q) 1 when p 1 2 . 3 Probabilistic masking quorum systems To formulate a probabilistic version of masking quorum systems, a natural place to start is the definition of a probabilistic quorum system [MRW97b]. A probabilistic quorum system is a set system and an accompanying access strategy such that any two quorums selected via the access strategy intersect with high probability. It is important to note that this definition admits set systems with pairs of sets that do not intersect, provided that ....

[Article contains additional citation context not shown here]

D. Malkhi, M. Reiter, and R. Wright. Probabilistic quorum systems. In Proc. 16th ACM Symp. Princip. Distributed Computing (PODC), pages 267--273, August 1997.

....protocols can efficiently scale to hundreds and possibly even thousands of servers. Quorum systems can be constructed to tolerate failures ranging from benign to fully arbitrary [20, 23] and for either type of failure can provide either strict consistency guarantees or only probabilistic ones [24]. Phalanx allows clients to dynamically tune the quorums they use for their application needs. Quorums are fundamental to Phalanx, and all objects are implemented using quorum based protocols. The basic operation performed by a Phalanx client is a quorum remote procedure call (Q RPC; see Figure ....

....we expect that in the applications we envision, mutex objects will seldom be contended for by more than a handful of clients at any time. Scalability with growth in the number of servers is primarily dictated by the quorum system used, as quorum systems exist with a wide array of properties [20, 23, 24]. For example, there are dissemination constructions whose resilience is b = p n Gamma1 2 and that have quorum sizes as small as O(n 3=4 ) so, e.g. for n = 1000, quorum size is 200) Moreover, probabilistic constructions exist with quorums of size O( p n) that simultaneously have ....

D. Malkhi, M. Reiter, A. Wool and R. Wright. Probabilistic quorum systems. Submitted for publication. Preliminary version appears in Proceedings of the 16th ACM Symposium on Principles of Distributed Computing, pages 267--273, August 1997.

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D. Malkhi, M. Reiter, and R. Wright. Probabilistic Quorum Systems. In Proceedings of ACM PODC'97, pages 267-- 273, Santa Barbara, CA, August 1997.

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D. Malkhi, M. Reiter, and R. Wright. Probabilistic Quorum Systems. In Proceedings of PODC '97, pages 267--273, Santa Barbara, CA, August 1997.

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D. Malkhi, M. Reiter and R. Wright, Probabilistic quorum systems. PODC 97.

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D. Malkhi, M.K. Reiter, and A. Wool, "Probabilistic Quorum Systems," Information and Computation, vol. 170, no. 2, pp. 184-206, 2001.

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D. Malkhi, M. Reiter, and R. Wright, "Probabilistic quorum systems," in Proceedings of the 16th Annual ACM Symposium on the Principles of Distributed Computing (PODC 97), Santa Barbara, CA, August 1997, pp. 267--273.

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D. Malkhi, M.K. Reiter, and A. Wool, "Probabilistic quorum systems," Information and Computation, vol. 170, no. 2, pp. 184--206, 2001.

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D. Malkhi, M. Reiter, A. Wool and R. Wright. Probabilistic quorum systems. The Information and Computation Journal 170(2):184206, November 2001.

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D. Malkhi, M. Reiter, and R. Wright. Probabilistic quorum systems. In Proceedings of the 16th Annual ACM symposium on Principles of Distributed Computing, 1997.

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D. Malkhi, M. Reiter, A. Wool, and R. N. Wright. Probabilistic quorum systems. Information and Computation, (2):184--206, November 2001.

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D. Malkhi, M.K. Reiter, and R. Wright. Probabilistic quorum systems. In Proceedings of the 16 ACM Symposium on Principle of Distributed Computing (PODC), pages 267-273, 1997.

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D. Malkhi, M. K. Reiter, A. Wool, and R. N. Wright. Probabilistic quorum systems. Information and Computation, 2001.

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