M. Naor and A. Wool. The load, capacity and availability of quorum systems. SIAM Journal of Computing, 27(2):423447, April 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....criteria Now consider some properties of quorum systems that are used to define some criteria against which the performance of quorum systems is measured. Availability: The property availability defines the ability of a quorum system to be operational in the presence of a failure. As defined in [32], if each element in the universe U fails with a probability p, the probability F p that the surviving elements does not contain a quorum is defined as the failure probability of the quorum system. The availability is defined as the probability (1 Gamma F p ) A good coterie will have a low ....

....that non dominated coteries have the highest availability among quroum systems. Load: The access frequency of elements in a quorum systems is called the load. In a good quorum system each element in universe U will share equal load. A more detailed and complete definition of load can be found in [32]. Probe complexity: When nodes in a distributed system have a probability to fail, before accessing a quorum the application has to determine that a quorum of nodes are functioning or have failed. The number of probes that need to be carried out in order to determine this is called the probe ....

M. Naor and A. Wool. The load, capacity and availability of quorum systems. SIAM Journal of Computing, 27(2):423--447, 1998.

....for response time and throughput. In view of the above, we introduce a metric here that measures the maximal number of read operations that can be handled simultaneously, which is effectively the maximal number of disjoint read quorums that can be formed. This metric is the read capacity. In [14, 15, 19], there is a metric called the load which roughly speaking measures the minimal load on the busiest site. It has a similar flavor to the metric of read capacity. However, 15] considers only a collection of quorums every two of which intersect. A protocol with a high read capacity can handle ....

M. Naor and A. Wool. The load, capacity and availability of quorum systems. In Proc. of the IEEE 35th Symposium on Foundations of Computer Science, pages 214--225, 1994.

....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 ....

M. Naor and A. Wool. The load, capacity and availability of quorum systems. SIAM Journal on Computing, 27(2):423--447, 1998.

....of S, and is usually denoted by k (cf. 12] p. 154) Furthermore, Proposition 5.12 of [12] shows that lim k =k = hence by the definition of the capacity and Lemma 3.5 we obtain: Corollary 3.9. Cap(S) 1 L(S) Therefore all the information regarding the capacity is captured by L(S) In [33] we gave a direct proof of Corollary 3.9 (without using the hypergraph machinery) which indicates how to schedule the quorum accesses so the capacity tends to 1=L(S) select the quorums independently at random using a strategy w which optimizes the load. 3.4. The Load with Failures. In this ....

M. Naor and A. Wool, The load, capacity and availability of quorum systems, in Proc. 35th IEEE Symp. Foundations of Comp. Sci. (FOCS), 1994, pp. 214--225.

....allowing any quorum to act on behalf of the entire system. Compared with performing every operation at every server, using quorums reduces the load on servers and increases service availability despite server crashes. Quorum systems are traditionally assessed by three measures of quality: load [34], fault tolerance [4] and failure probability (see [5, 35] The load of a quorum system is a measure of its eciency: it is the rate at which the busiest server is accessed. The fault tolerance of a system is the maximum number of server failures for which there is still guaranteed to be a quorum ....

....using probabilistic quorum constructions can be driven further toward zero when updates are suciently dispersed in time, making probabilistic quorum constructions useful in a wider variety of settings. 1.2. Related work Strict quorum systems have been extensively studied and measured (cf. [17, 40, 26, 16, 20, 5, 14, 10, 1, 34, 37, 35]) Byzantine quorum systems were introduced in [29] and further studied in [31, 8] Because of the possibility of inconsistency admitted by probabilistic quorum systems, they are most attractive for systems in which some level of inconsistency can be tolerated, and in particular, where the ....

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M. Naor and A. Wool. The load, capacity and availability of quorum systems. SIAM Journal of Computing, 27(2):423-447, April 1998.

....S, and is usually denoted by k (cf. 12] p. 154) Furthermore, Proposition 5.12 of [12] shows that lim k 1 k =k = hence by the definition of the capacity and Lemma 3.5 we obtain: Corollary 3.9. Cap(S) 1 L(S) Therefore all the information regarding the capacity is captured by L(S) In [33] we gave a direct proof of Corollary 3.9 (without using the hypergraph machinery) which indicates how to schedule the quorum accesses so the capacity tends to 1=L(S) select the quorums independently at random using a strategy optimizing the load. 3.4. The Load with Failures. In this section we ....

M. Naor and A. Wool, The load, capacity and availability of quorum systems, in Proc. 35th IEEE Symp. Foundations of Comp. Sci. (FOCS), 1994, pp. 214--225.

....systems. z e.g. ff = 0:5 and fi = 0:21 for RT(4; 3) Table 1: Constructions in this paper (n = number of servers) 2 Related work Our work borrows from prior work in benignly fault tolerant quorum systems, which is extensive (e.g. Gif79, Tho79, Mae85, GB85, Her86, BG87, ET89, AE91, CAA92, NW94, PW97b] The notion of availability we use here (crash probability) is well known in reliability theory [BP75] and has been applied extensively in the analysis of quorum systems (cf. BG87, PW95, PW97a] and the references therein) The load of a quorum system was first defined and analyzed in ....

.... PW97b] The notion of availability we use here (crash probability) is well known in reliability theory [BP75] and has been applied extensively in the analysis of quorum systems (cf. BG87, PW95, PW97a] and the references therein) The load of a quorum system was first defined and analyzed in [NW94] which proved a lower bound of Omega Gamma 1 p n ) on the load of any quorum system (and, a fortiori, any masking quorum system) over n servers. In proving load optimality of our constructions, we generalize this lower bound to Omega Gamma q b=n) for b masking quorum systems. Grids, ....

[Article contains additional citation context not shown here]

M. Naor and A. Wool. The load, capacity and availability of quorum systems. In Proc. 35th IEEE Symp. Foundations of Comp. Sci. (FOCS), pages 214--225, 1994. To appear in SIAM J. Computing.

.... used in the study of distributed control and management problems such as mutual exclusion (cf. GB85, Ray86] data replication protocols (cf. DGS85, Her84, JM90] name servers (cf. MV88] and selective dissemination of information (cf. YG94] We apply some recent constructions suggested in [NW94, PW95]. Secret sharing: Secret sharing was originally suggested for threshold access structures by Shamir and Blakely [Sha79, Bla79] It was extended to arbitrary access structures in [ISN87] The issue of efficiency (i.e. share sizes) of such schemes has been considered in several papers (cf. BD90, ....

....Q j 2 Q, i.e. P m j=1 w j = 1. For every element i 2 U , a strategy w of picking quorums induces a probability that the element i is accessed, which we call the load on i. The system load, L(Q) is the load on the busiest element induced by the best possible strategy. Formally, following [NW94]: Definition 2.4 Let a strategy w be given for a quorum system Q = Q 1 ; Qm ) over a universe U . For an element i 2 U , the load induced by w on i is w (i) P Q j 3i w j . The load induced by a strategy w on a quorum system Q is Lw (Q) max i2U w (i) The system load on a ....

[Article contains additional citation context not shown here]

M. Naor and A. Wool. The load, capacity and availability of quorum systems. In Proc. 35th IEEE Symp. Found. of Comp. Science, pages 214--225, 1994.

.... that a live quorum exists in the system) assuming a complete and fault free network, can be found in [8, 34, 12, 37, 7] Analyses of the expected size of a connected component containing a quorum, and the availability on ring networks are [32, 19] An analysis of the load can be found in [29, 18]. A queuing system analysis is [26] ffl Simulation: In this approach (cf. 21, 14, 24] a simulation model is constructed, and a simulation is run. This approach allows more complex models, which can not be analyzed completely. Usually, much stronger assumptions are made, such as failure ....

M. Naor and A. Wool. The load, capacity and availability of quorum systems. In Proc. 35th IEEE Symp. Foundations of Comp. Sci. (FOCS), pages 214--225, 1994. To appear in SIAM J. Computing.

.... systems have been used in the study of distributed control and management problems such as mutual exclusion (cf. 14, 40] data replication protocols (cf. 9, 21, 25] name servers (cf. 35] and selective dissemination of information (cf. 49] We apply some recent constructions suggested in [1, 28, 36, 39]. Secret sharing: Secret sharing (cf. 44] was originally suggested for threshold access structures by Shamir and Blakley [43, 5] It was extended to arbitrary access structures in [24] The issue of efficiency (i.e. share sizes) of such schemes has been considered in several papers (cf. 7, 6, ....

....the quorums Q j 2 Q, i.e. P m j=1 w j = 1. For every element i 2 U , a strategy w of picking quorums induces the frequency of accessing element i, which we call the load on i. The system load, L(Q) is the load on the busiest element induced by the best possible strategy. Formally, following [36]: Definition 2.8 Let a strategy w be given for a quorum system Q = Q 1 ; Qm ) over a universe U . For an element i 2 U , the load induced by w on i is w (i) P Q j 3i w j . The load induced by a strategy w on a quorum system Q is Lw (Q) max i2U w (i) The system load on a ....

[Article contains additional citation context not shown here]

M. Naor and A. Wool. The load, capacity and availability of quorum systems. SIAM J. Computing, 27(2):423--447, April 1998.

.... systems have been used in the study of distributed control and management problems such as mutual exclusion (cf. 13, 38] data replication protocols (cf. 8, 19, 23] name servers (cf. 32] and selective dissemination of information (cf. 44] We apply some recent constructions suggested in [33, 37]. Secret sharing: Secret sharing was originally suggested for threshold access structures by Shamir and Blakely [40, 4] It was extended to arbitrary access structures in [22] The issue of efficiency (i.e. share sizes) of such schemes has been considered in several papers (cf. 6, 5, 2] ....

....Q j 2 Q, i.e. P m j=1 w j = 1. For every element i 2 U , a strategy w of picking quorums induces a probability that the element i is accessed, which we call the load on i. The system load, L(Q) is the load on the busiest element induced by the best possible strategy. Formally, following [33]: Definition 2.4 Let a strategy w be given for a quorum system Q = Q1 ; Qm) over a universe U . For an element i 2 U , the load induced by w on i is w (i) P Q j 3i w j . The load induced by a strategy w on a quorum system Q is Lw (Q) max i2U w (i) The system load on a quorum ....

[Article contains additional citation context not shown here]

M. Naor and A. Wool. The load, capacity and availability of quorum systems. In Proc. 35th IEEE Symp. Found. of Comp. Science, pages 214--225, 1994.

....quorum systems and introduce quorum composition. In Sections 5 7 we describe our new constructions. We conclude in Section 8. 2 Related work Our work borrows from extensive prior work in benignly fault tolerant quorum systems (e.g. Gif79, Tho79, Mae85, GB85, Her86, BG87, ET89, AE91, CAA92, NW94, PW97b] The notion of availability we use here (crash probability) is well known in reliability theory [BP75] and has been applied extensively in the analysis of quorum systems (cf. BG87, PW95, PW97a] and the references therein) The load of a quorum system was first defined and analyzed in ....

.... PW97b] The notion of availability we use here (crash probability) is well known in reliability theory [BP75] and has been applied extensively in the analysis of quorum systems (cf. BG87, PW95, PW97a] and the references therein) The load of a quorum system was first defined and analyzed in [NW94] which proved a lower bound of Omega Gamma 1 p n ) on the load of any quorum system (and, a fortiori, any masking quorum system) over n servers. In proving load optimality of our constructions, we generalize this lower bound to Omega Gamma p b n ) for b masking quorum systems. Grids, ....

[Article contains additional citation context not shown here]

M. Naor and A. Wool. The load, capacity and availability of quorum systems. In Proc. 35th IEEE Symp. Foundations of Comp. Sci. (FOCS), pages 214--225, 1994. To appear in SIAM J. Computing.

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M. Naor and A. Wool. The load, capacity and availability of quorum systems. SIAM Journal of Computing, 27(2):423447, April 1998.

No context found.

M. Naor and A. Wool. The load, capacity and availability of quorum systems. SIAM Journal of Computing, 27(2):423--447, April 1998.

No context found.

M. Naor and A. Wool. The load, capacity and availability of quorum systems. SIAM Journal of Computing, 27(2):423--447, April 1998.

No context found.

M. Naor and A. Wool. The load, capacity and availability of quorum systems. SIAM Journal of Computing, 27(2):423447, April 1998.

No context found.

M. Naor and A. Wool. The load, capacity and availability of quorum systems. SIAM Journal on Computing, 27(2):423-447, 1998.

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