M. Naor and A. Wool. The load, capacity, and availability of quorum systems. SIAM Journal on Computing, 27(2):423--447. SIAM, April 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....5.3 Maximum Throughput A goal of a BQS axchitecture is to support a high throughput for a low system cost. Two factors affect system cost: 1) the number of different servers n and (2) the required power of these servers, dictated by the load factor and the desired throughput. The load factor [16] is defined as the minimal access probability of the busiest server, minimizing over the strategies , where the strategy is the algorithm used to pick a quorum. SBQ L has a load factor of n (n n 2.f 1 [ if only non confirmable writes axe supported and (n [n ] if confirmable writes ....

....which the writer does not need to identify a live quorum but instead sends a message to a quorum of servers without concerning himself with whether these servers axe responsive or not. According to this definition, all the protocols presented here use non blocking quorum systems. Several papers [4, 13, 16] study the load of Byzantine quorum systems, a measure of how increasing the number of servers influences the amount of work each individual server has to perform. A key conclusion of this previous work is 1 that the lower bound for the load factor of quorum systems is O( Our work instead ....

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

....that increasing concurrency has a measurable but modest effect on the latency of the reads. 7.4 Maximum Throughput A goal of a BQS architecture is to support a high throughput for a low system cost. The maximum throughput of a BQS architecture is proportional to the inverse of its load factor [15], which is the minimal access probability of the busiest server, minimizing over the strategies. SBQ L has a load factor of (n r ] if only non confirmable writes are supported and r ] T, n ) if confirmable writes are also supported, assuming that reads and writes occur with equal ....

....which the writer does not need to identify a live quorum but instead sends a message to a quorum of servers without concerning himself with whether these servers are responsive or not. According to this definition, all the protocols presented here use non blocking quorum systems. Several papers [4, 13, 15] study the load of Byzantine quorum systems, a measure of how increasing the number of servers influences the amount of work each individual server has to perform. A key conclusion of this previous work is that the lower bound for the load factor of quorum systems is O( Our work instead focuses ....

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

....that increasing concurrency has a measurable but modest e ect on the latency of the reads. 7.4 Maximum Throughput A goal of a BQS architecture is to support a high throughput for a low system cost. The maximum throughput of a BQS architecture is proportional to the inverse of its load factor [15], which is the minimal access probability of the busiest server, minimizing over the strategies. SBQ L has a load factor of 2n (n d e) if only non con rmable writes are supported and 2n (n d e) if con rmable writes are also supported, assuming that reads and writes occur with equal ....

....which the writer does not need to identify a live quorum but instead sends a message to a quorum of servers without concerning himself with whether these servers are responsive or not. According to this de nition, all the protocols presented here use non blocking quorum systems. Several papers [4, 13, 15] study the load of Byzantine quorum systems, a measure of how increasing the number of servers in uences the amount of work each individual server has to perform. A key conclusion of this previous work is that the lower bound for the load factor of quorum systems is O( 1 p ) Our work instead ....

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

....to index it and the ability to perform complex queries) Our intuition told us that we should be able to improve the system by using quorums but it was not clear which one would provide the best results. Although there are several studies of the availability and load distribution of quorum systems [13, 12, 4, 15, 2] we could not find in the literature any indication of what type of quorum could be most suitable for our purposes. Thus, we evaluated several protocols in order to better understand the problem. Unlike previous work, our analysis is based on realistic environments. For instance, comparisons among ....

M. Naor and A. Wool. The Load, Capacity, and Availability of Quorum Systems. SIAM Journal of Computing, 27(2):423--447, Apr. 1998.

....of failure in the peers set. If we further assume that k Theta n, we can approximate the load by neglecting all subsets of W 3T (m) containing any member of W active (m) or peers and obtain an access probability of roughly k( 1) n p. A related notion of load defined by Naor and Wool [15] considers for a given set system the access probability of the busiest server under the best possible access strategy. Their definition does not apply in our case since different messages have distinct collections of possible witness sets. 7 Conclusions Experience in constructing robust ....

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

....protocols for the latter service that tolerate faulty clients in addition to faulty servers in Section 6. We conclude in Section 7. 2 Related work Our work was influenced by the substantial body of literature on quorum systems for benign failures and applications that make use of them, e.g. [Gif79, Tho79, Mae85, GB85, Her86, ET89, CAA90, AE91, NW94, PW95]. In particular, our grid construction of Section 4 was influenced by grid like constructions for benign failures (e.g. CAA90] and we borrow our definitions of domination and load from [GB85] and [NW94] respectively. Quorum systems have been previously employed in the implementation of ....

.... that make use of them, e.g. Gif79, Tho79, Mae85, GB85, Her86, ET89, CAA90, AE91, NW94, PW95] In particular, our grid construction of Section 4 was influenced by grid like constructions for benign failures (e.g. CAA90] and we borrow our definitions of domination and load from [GB85] and [NW94], respectively. Quorum systems have been previously employed in the implementation of security mechanisms. Naor and Wool [NW96] described methods to construct an access control service using quorums. Their constructions use cryptographic techniques to ensure that out of date (but correct) servers ....

[Article contains additional citation context not shown here]

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

....by load we mean the expected maximum number of times any server is accessed per message. To compute load, we need to grow a set M of randomly selected messages to infinity, and examine the number of accesses at the busiest server divided by jM j. This definition is motivated by Naor and Wool [15], adapting their definition of load to our case where distinct messages have different witness ranges. We remark that this definition does not distinguish between the accesses requiring a server to sign messages and ones requiring it only to respond. We first look at the expected access ....

M. Naor and A. Wool. The load, capacity, and availability of quorum systems. SIAM Journal of Computing, 27(2):423--447, April 1998. 18

....protocols for replicated services that tolerate faulty clients in addition to faulty servers in Section 6. We conclude in Section 7. 2 Related work Our work was influenced by the substantial body of literature on quorum systems for benign failures and applications that make use of them, e.g. [Gif79, Tho79, Mae85, GB85, Her86, ET89, CAA90, AE91, NW94, PW95]. In particular, our grid construction of Section 5.1 was influenced by grid like constructions for benign failures (e.g. CAA90] and we borrow our definitions of domination and load from [GB85] and [NW94] respectively. Quorum systems have been previously employed in the implementation of ....

....that make use of them, e.g. Gif79, Tho79, Mae85, GB85, Her86, ET89, CAA90, AE91, NW94, PW95] In particular, our grid construction of Section 5. 1 was influenced by grid like constructions for benign failures (e.g. CAA90] and we borrow our definitions of domination and load from [GB85] and [NW94], respectively. Quorum systems have been previously employed in the implementation of security mechanisms. Naor and Wool [NW96] described methods to construct an access control service using quorums. Their constructions use cryptographic techniques to ensure that out of date (but correct) servers ....

[Article contains additional citation context not shown here]

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

....protocol for replicated services that tolerate faulty clients in addition to faulty servers in Section 6. We conclude in Section 7. 2 Related work Our work was influenced by the substantial body of literature on quorum systems for benign failures and applications that make use of them, e.g. [15, 42, 26, 14, 17, 13, 9, 4, 35]. In particular, our grid construction of Section 4 was influenced by grid like constructions for benign failures (e.g. 9] and we borrow our definition of load from [35] Quorum systems have been previously employed in the implementation of security mechanisms. Naor and Wool [36] described ....

.... literature on quorum systems for benign failures and applications that make use of them, e.g. 15, 42, 26, 14, 17, 13, 9, 4, 35] In particular, our grid construction of Section 4 was influenced by grid like constructions for benign failures (e.g. 9] and we borrow our definition of load from [35]. Quorum systems have been previously employed in the implementation of security mechanisms. Naor and Wool [36] described methods to construct an access control service using quorums. Their constructions use cryptographic techniques to ensure that out of date (but correct) servers cannot grant ....

[Article contains additional citation context not shown here]

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

....on behalf of the entire system. Compared with performing every operation at every server as in the State Machine Approach [Sch90] using quorums reduces the load on servers and increases service availability despite server crashes. Quorum systems have been extensively studied and measured (cf. [Gif79, Tho79, Mae85, GB85, Her86, BG87, ET89, CAA90, AE91, NW94, PW95a, PW95b]) Three measures of a quorum system will be of particular interest in this paper: load [NW94] fault tolerance [BG87] and failure probability (see [BG87, PW95b] The load of a quorum system is a measure of its efficiency. Intuitively, the load is the rate at which the busiest server will be ....

....servers and increases service availability despite server crashes. Quorum systems have been extensively studied and measured (cf. Gif79, Tho79, Mae85, GB85, Her86, BG87, ET89, CAA90, AE91, NW94, PW95a, PW95b] Three measures of a quorum system will be of particular interest in this paper: load [NW94], fault tolerance [BG87] and failure probability (see [BG87, PW95b] The load of a quorum system is a measure of its efficiency. Intuitively, the load is the rate at which the busiest server will be accessed. The fault tolerance, also called the availability, of a system is the number of servers ....

[Article contains additional citation context not shown here]

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

....protocol for replicated services that tolerate faulty clients in addition to faulty servers in Section 6. We conclude in Section 7. 2 Related work Our work was influenced by the substantial body of literature on quorum systems for benign failures and applications that make use of them, e.g. [15, 38, 26, 14, 17, 13, 9, 4, 30]. In particular, our grid construction of Section 4 was influenced by grid like constructions for benign failures (e.g. 9] and we borrow our definition of load from [30] Quorum systems have been previously employed in the implementation of security mechanisms. Naor and Wool [31] described ....

.... literature on quorum systems for benign failures and applications that make use of them, e.g. 15, 38, 26, 14, 17, 13, 9, 4, 30] In particular, our grid construction of Section 4 was influenced by grid like constructions for benign failures (e.g. 9] and we borrow our definition of load from [30]. Quorum systems have been previously employed in the implementation of security mechanisms. Naor and Wool [31] described methods to construct an access control service using quorums. Their constructions use cryptographic techniques to ensure that out of date (but correct) servers cannot grant ....

[Article contains additional citation context not shown here]

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

....buckets to be added one at a time sequentially. However our hash function allows the buckets to be added in an arbitrary order. Another scheme that we can improve on is given by Devine [2] In addition, we believe that consistent hashing will be useful in other applications (such as quorum systems [7] [8] or distributed name servers) where multiple machines with different views of the network must agree on a common storage location for an object without communication. 1.3 Presentation In Section 2 we describe our model of the Web and the hot spot problem. Our model is necessarily simplistic, ....

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

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

....regards the algorithmic complexity of finding a quorum in case of random failures. We show a tradeoff between the load of a quorum system and its probe complexity for non adaptive algorithms. We analyze the algorithmic probe complexity of the Paths quorum system suggested by Naor and Wool in [18], and present two optimal algorithms. The first is a non adaptive algorithm that matches our lower bound. The second is an adaptive algorithm with a probe complexity that is linear in the minimum between the size of the smallest quorum set and the load of the system. We supply a constant degree ....

....are included excluded from the system. 1.2 Measures of Quality The metrics that measure the quality of a dynamic quorum system relate both to its combinatorial structure and to its capability of being implemented in a distributed network. The following metrics were analyzed by Naor and Wool in [18] and are used to measure the quality of static systems as well. Load A strategy is a rule giving each quorum an access probability. A strategy induces a load on each element, which is the sum of the probabilities of quorums it belongs to. This represents the fraction of the time an element ....

[Article contains additional citation context not shown here]

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

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

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

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

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NAOR,M.AND WOOL, A. 1998. The load, capacity, and availability of quorum systems. SIAM J. Comput. 27, 2 (Apr.), 423--447.

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

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

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

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

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