A. Wool. Quorum systems for distributed control protocols. Ph.D. Dissertation, Weizmann Institute of Science, Rehovot, Israel, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....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 failure probability and conversely, a high availability. In [43] it is shown 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 ....

A. Wool. Quorum systems for distributed control protocols. Ph.D. Dissertation, Weizmann Institute of Science, Rehovot, Israel, 1996.

....assignment is a valid quorum assignment if and only if the quorums contained in the assignment satisfy the quorum intersection property, such that any two quorums have at least one processor in their intersection set. Numerous algorithms for generating valid quorum assignments have been suggested [6,8,13,18,44,47,49,74,98,108,111,115,130,134,157, 158,159]. A coterie [74] is a quorum assignment with the property that no quorum is the proper subset of any other quorum. Unless otherwise stated, this work assumes that quorum assignments are simplex quorum assignments that are not necessarily coteries. The results of this work can be extended to ....

....resource is available, given that a non adaptive, or static, quorum assignment is used. These approaches typically assume that processors fail with a given probability. The probability that failures will violate progress or fairness as the system executes can be determined using theoretical models [6,97,121,131,134,158], empirical methods [4,79] or simulation [91,109,128] Quorum assignments are selected a priori to maximize the probability that 14 Introduction Chapter 1 progress and fairness will be satisfied. Such analyses do not assume that fault tolerance is to be provided deterministically. The second ....

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Wool, A., "Quorum Systems for Distributed Control Protocols," Ph.D. Thesis, Dept. of Applied Mathematics and Computer Science, The Weizmann Institute of Science, Rehovot, Israel, September, 1996, 144 pages.

....tolerance. This paper considers the operation of quorum systems in general, without reference to any particular safety property that can be enforced using quorums. The correctness of general quorum based control is proved in [7] and surveys of previous quorum systems research are available in [11,14,24,27]. A quorum assignment is the mapping from each processor in a system to the one or more quorums that can grant the processor permission to take a desired action. A dynamic quorum assignment can adapt when the state of a distributed system changes, to improve performance. For example, processors ....

....quorum mapping function that is best for a given application of quorums. This choice can be based on a number of quorum system metrics that predict the cost and performance of quorum assignments. Traditional metrics include the quorum size, quorum load, and quorum availability metrics discussed in [21,27]. Quorum size is the number of processors in each quorum; load is the number of quorums a processor is contained in; and availability is the probability that all members of a quorum are simultaneously not faulty. The quorum size, load, and availability metrics are not alone sufficient for ....

Wool, A., "Quorum Systems for Distributed Control Protocols, " Ph.D. Thesis, Dept. of Applied Mathematics and Computer Science, The Weizmann Institute of Science, Rehovot, Israel, September, 1996, 144 pages. N

....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 ....

A. Wool. Quorum systems for distributed control protocols. In PhD thesis, Dept. of Applied Mathematics and Computer Science, The Weizmann Institute of Science, Israel, 1996.

....are often based on one form or another of majority voting, preferring the version of the data supported by the majority of the available copies. Voting systems are used also to enforce data consistency by requiring changes to be performed on a quorum of the copies (cf. Gi79, GB85, SB94, PW95, W96] Informally, a quorum system is collection of sets every two of which have a nonempty intersection. Thus updating whole quorums ensures that each subsequent change will override earlier ones in at least one site. While a variety of quorum system types can be used for that purpose, voting ....

A. Wool. Quorum Systems for Distributed Control Protocols. Ph.D. Thesis, The Weizmann Institute, Rehovot, Israel, 1996.

....optimal load which can be achieved for b p n=2. A disadvantage of the M Grid system is its poor asymptotic crash probability. If crashes occur with some constant probability p then any configuration of crashes with at least one crash per row disables the system. Therefore, as shown by [KC91, Woo96] F p (M Grid) 1 Gamma (1 Gamma p) p n ) p n Gamma n 1 1: 9 3 of 4 3 of 4 3 of 4 3 of 4 3 of 4 Figure 2: An RT(4; 3) system of depth h = 2, with one quorum shaded. 5.2 Recursive threshold systems A recursive threshold system RT(k; of depth h is built by taking a ....

....seems poor, as the bound is higher than the crash probability of the Thresh components. However this is not an artifact of overestimates in our analysis. Rather, it is a result of the property that the crash probability of FPP is higher than p, and in fact F p (FPP) 1 as shown by [RST92, Woo96] In this light it is not surprising that boostFPP does not have an optimal crash probability. ffl The requirement p 1=4 is essential for this system; if p 1=4 then in fact F p (boostFPP) 1 as n 1. 7 The multi path system Here we introduce the construction we call the Multi Path system, ....

A. Wool. Quorum Systems for Distributed Control Protocols. PhD thesis, Department of Applied Mathematics and Computer Science, The Weizmann Institute of Science, Rehovot, Israel, 1996.

....optimal load which can be achieved for b p n=2. A disadvantage of the M Grid system is its poor asymptotic crash probability. If crashes occur with some constant probability p then any configuration of crashes with at least one crash per row disables the system. Therefore, as shown by [KC91, Woo96] Fp(M Grid) 1 Gamma (1 Gamma p) p n ) p n Gamma n 1 1: 5.2 Recursive threshold systems A recursive threshold system RT(k; of depth h is built by taking a simple building block, which is an of k threshold system (with k k=2) and recursively composing it over itself to ....

....seems poor, as the bound is higher than the crash probability of the Thresh components. However this is not an artifact of over estimates in our analysis. Rather, it is a result of the property that the crash probability of FPP is higher than p, and in fact Fp(FPP) 1 as shown by [RST92, Woo96] In this light it is not surprising that boostFPP does not have an optimal crash probability. ffl The requirement p 1=4 is essential for this system; if p 1=4 then in fact Fp(boostFPP) 1 as n 1. 7 The multi path system Here we introduce the construction we call the Multi Path system, ....

A. Wool. Quorum Systems for Distributed Control Protocols. PhD thesis, Department of Applied Mathematics and Computer Science, The Weizmann Institute of Science, Rehovot, Israel, 1996.

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