In this paper we present two protocols for asynchronous Byzantine Quorum Systems (BQS) built on top of reliable channels---one for self-verifying data and the other for any data. Our protocols tolerate Byzantine failures with fewer servers than existing solutions by eliminating nonessential work in the write protocol and by using read and write quorums of different sizes. Since engineering a reliable network layer on an unreliable network is difficult, two other possibilities must be explored. The first is to strengthen the model by allowing synchronous networks that use time-outs to identify failed links or machines. We consider running synchronous and asynchronous Byzantine Quorum protocols over synchronous networks and conclude that, surprisingly, "self-timing" asynchronous Byzantine protocols may offer significant advantages for many synchronous networks when network time-outs are long. We show how to extend an existing Byzantine Quorum protocol to eliminate its dependency on reliable networking and to handle message loss and retransmission explicitly.

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).

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.

... 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

Providing reliable group communication is an ever recurring topic in distributed settings. In mobile ad hoc networks, this problem is even more significant since all nodes act as peers, while it becomes more challenging due to highly dynamic and unpredictable topology changes. In order to overcome these difficulties, we deviate from the conventional point of view, i.e., we "fight fire with fire," by exploiting the nondeterministic nature of ad hoc networks. Inspired by the principles of gossip mechanisms and probabilistic quorum systems, we present in this paper PILOT (ProbabilistIc Lightweight grOup communication sysTem) for ad hoc networks, a two-layer system consisting of a set of protocols for reliable multicasting and data sharing in mobile ad hoc networks. The performance of PILOT is predictable and controllable in terms of both reliability (fault tolerance) and efficiency (overhead). We present an analysis of PILOT's performance, which is used to fine-tune protocol parameters to obtain the desired trade off between reliability and efficiency. We confirm the predictability and tunability of PILOT through simulations with ns-2.

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

In the weighted voting protocol which is used to maintain the consistency of replicated data, the availability of the data to read and write operations not only depends on the availability of the nodes storing the data but also on the vote and quorum assignments used. We consider the problem of determining the vote and quorum assignments that yield the best permormance in a distributed system where node availabilities can be different and the mix of the read and write operations is arbitrary. The optimal vote and quorum assignments depend not only on the system parameters such as node availability and operation mix, but also on the performance measure. We present an enumeration algorithm that can be used to find the vote and quorum assignments that need to be considered for achieving optimal performance. When the performance measure is data availability, an analytical method is derived to evaluate it for any vote and quorum assignment. This method and the enumeration algorithm is used ...

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.