A quorum system is a collection of sets (quorums) every two of which intersect. Quorum systems have been used for many applications in the area of distributed systems, including mutual exclusion, data replication and dissemination of information Given a strategy to pick quorums, the load L(S) is the minimal access probability of the busiest element, minimizing over the strategies. The capacity Cap(S) is the highest quorum accesses rate that S can handle, so Cap(S) = 1=L(S).

Abstract — A distributed mobility-management scheme using a class of uniform quorum systems (UQS) is proposed for ad hoc networks. In the proposed scheme, location databases are stored in the network nodes themselves, which form a selforganizing virtual backbone within the flat network structure. The databases are dynamically organized into quorums, every two of which intersect at a constant number of databases. Upon location update or call arrival, a mobile’s location information is written to or read from all the databases of a quorum, chosen in a nondeterministic manner. Compared with a conventional scheme [such as the use of home location register (HLR)] with fixed associations, this scheme is more suitable for ad hoc networks, where the connectivity of the nodes with the rest of the network can be intermittent and sporadic and the databases are relatively unstable. We introduce UQS, where the size of the

Quorum systems serve as a basic tool providing a uniform and reliable way to achieve coordination in a distributed system. They are useful for distributed and replicated databases, name servers, mutual exclusion, and distributed access control and signatures. Traditionally, two basic methods have been used to evaluate quorum systems: the analytical approach, and simulation. This paper proposes a third, empirical approach. We collected 6 months' worth of connectivity and operability data of a system consisting of 14 real computers using a wide area group communication protocol. The system spanned two geographic sites and three different Internet segments. We developed a mechanism that merges the local views into a unified history of the events that took place, ordered according to an imaginary global clock. We then developed a tool called the Generic Quorum-system Evaluator (GQE), which evaluates the behavior of any given quorum system over the unified, real-life history. We compared fo...

Abstract. Replicated services accessed via quorums enable each access tobe performed at only a subset (quorum) of the servers and achieve consistency across accesses by requiring any two quorums to intersect. Recently, b-masking quorum systems, whose intersections contain at least 2b+1 servers, have been proposed to construct replicated services tolerant of b-arbitrary (Byzantine) server failures. In this paper we consider a hybrid fault model allowing benign failures in addition to the Byzantine ones. We present four novel constructions for b-masking quorum systems in this model, each of which has optimal load (the probability of access of the busiest server) or optimal availability (probability of some quorum surviving failures). To show optimality we also prove lower bounds on the load and availability of any b-masking quorum system in this model.

Abstract—We suggest a method of controlling the access to a secure database via quorum systems. A quorum system is a collection of sets (quorums) every two of which have a nonempty intersection. Quorum systems have been used for a number of applications in the area of distributed systems. We propose a separation between access servers, which are protected and trustworthy, but may be outdated, and the data servers, which may all be compromised. The main paradigm is that only the servers in a complete quorum can collectively grant (or revoke) access permission. The method we suggest ensures that, after authorization is revoked, a cheating user Alice will not be able to access the data even if many access servers still consider her authorized and even if the complete raw database is available to her. The method has a low overhead in terms of communication and computation. It can also be converted into a distributed system for issuing secure signatures. An important building block in our method is the use of secret sharing schemes that realize the access structures of quorum systems. We provide several efficient constructions of such schemes which may be of interest in their own right. Index Terms—Quorum systems, replication, secret sharing, security, cryptography.

... this article, we analyze several quorum types in order to better understand their behavior in practice. The results obtained challenge many of the assumptions behind quorum based replication. Our evaluation indicates that the conventional read-one/write-all-available approach is the best choice for a large range of applications requiring data replication. We believe this is an important result for anybody developing code for computing clusters as the read-one/write-all-available strategy is much simpler to implement and more flexible than quorum-based approaches. In this article, we show that, in addition, it is also the best choice using a number of other selection criteria

Quorum systems serve as a basic tool providing a uniform and reliable way to achieve coordination in a distributed system. They are useful for distributed and replicated databases, name servers, mutual exclusion, and distributed access control and signatures. The un-availability of a quorum system is the probability of the event that no live quorum exists in the system. When such an event occurs the service is completely halted. The un-availability is widely accepted as the measure by which quorum systems are evaluated. In this paper we characterize the optimal availability quorum system in the general case, when the failure probabilities may take any value in the range 0 ! p i ! 1. Then we deal with the practical scenario in which the failure probabilities are unknown, but can be estimated. We give a robust and efficient algorithm that calculates a near optimal quorum system based on the estimated failure probabilities. Keywords: Quorum systems, distributed computing, fault tolerance...

A quorum system is a collection of subsets of servers, every two of which intersect. Quorum systems have been suggested as a tool for concurrency control in replicated databases almost twenty years ago. They promised to guarantee strict consistency and to provide high availability and fault-tolerance in the face of server crashes and network partitions. Despite these promises, current commercial replicated databases typically do not use quorum systems. Instead they use mechanisms which guarantee much weaker consistency, if any. Moreover, the interest in quorum systems seems to be waning even in the database research community. This paper

A distributed counter allows each processor in an asynchronous message passing network to access the counter value and increment it. We study the problem of implementing a distributed counter such that no processor is a communication bottleneck. We prove a lower bound of\Omega\Gamma/20 n= log log n) on the number of messages that some processor must exchange in a sequence of n counting operations spread over n processors. We propose a counter that achieves this bound when each processor increments the counter exactly once. Hence, the lower bound is tight. Because most algorithms and data structures count in some way, the lower bound holds for many distributed computations. We feel that the proposed concept of a communication bottleneck is a relevant measure of efficiency for a distributed algorithm and data structure, because it indicates the achievable degree of distribution. 1 Introduction Counting is an essential ingredient in virtually any computation. It is therefore highly de...

Abstract. A quorum system is a collection of sets (quorums) every two of which intersect. Quorum systems have been used for many applications in the area of distributed systems, including mutual exclusion, data replication, and dissemination of information. When the elements may fail, a user of a distributed protocol needs to quickly find a quorum all of whose elements are alive or evidence that no such quorum exists. This is done by probing the system elements, one at a time, to determine if they are alive or dead. This paper studies the probe complexity PC(S) of a quorum system S, defined as the worst case number of probes required to find a live quorum or to show its nonexistence in S, using the best probing strategy. We show that for large classes of quorum systems, all n elements must be probed in the worst case. Suchsystems are called evasive. However, not all quorum systems are evasive; we demonstrate a system where O(log n) probes always suffice. Then we prove two lower bounds on the probe complexity in terms of the minimal quorum cardinality c(S) and the number of minimal quorums m(S). Finally, we show a universal probe strategy which never makes more than c(S) 2 − c(S) +1 probes; thus any system with c(S) ≤ √ n is nonevasive.