Quorum Size Research Articles

Scalable byzantine fault tolerance via partial decentralization

Byzantine consensus is a critical component in many permissioned Blockchains and distributed ledgers. We propose a new paradigm for designing BFT protocols called DQBFT that addresses three major performance and scalability challenges that plague past protocols: (i) high communication costs to reach geo-distributed agreement, (ii) uneven resource utilization hampering performance, and (iii) performance degradation under varying node and network conditions and high-contention workloads. Specifically, DQBFT divides consensus into two parts: 1) durable command replication without a global order, and 2) consistent global ordering of commands across all replicas. DQBFT achieves this by decentralizing the heavy task of replicating commands while centralizing the ordering process. Under the new paradigm, we develop a new protocol, Destiny that uses a combination of three techniques to achieve high performance and scalability: using a trusted subsystem to decrease consensus's quorum size, using threshold signatures to attain linear communication costs, reducing client communication. Our evaluations on 300-replica geo-distributed deployment reveal that DQBFT protocols achieve significant performance gains over prior art: ≈3x better throughput and ≈50% better latency.

Probabilistic Consistency Guarantee in Partial Quorum-Based Data Store

Many NoSQL databases support quorum-based protocols, which require a subset of replicas (called a quorum) to respond to each write/read operation. These systems configure the quorum size to tune the operation latency and adopt multiple consistency levels. Some recent works illustrate that using probability models to quantify the chance of reading the last update is important because it could avoid returning stale values under eventual consistency. There are two challenging issues: (1) from inconsistent replicas, how to determine the minimum quorum size (i.e., the lowest access latency) to read the newest data at a specified probability; (2) node failure frequently happens in large-scale systems, how to guarantee the probability-based consistent reads. This article presents Probabilistic Consistency Guarantee (PCG), which is the first dynamic quorum decision and failure-aware quantification model. PCG model respectively quantifies the server-side consistency after the latest write, which reflects the object's time-varying update progress, and the possibility of reading this update when responding to the end-users. Our theoretical analysis derives several formulas to determine the quorum size of a read quorum and the consensus result selected from this quorum is the data updated by the last write at the user-specified probability. When some replicas are unavailable, our model knows how to rescale the quorum and read values from surviving replicas could reduce the stale reads caused by node failures. The experimental results in Cassandra demonstrate that the PCG model can achieve up to 77.7 percent more accurate predictions and reduce up to 48.9 percent read latency than those of the previous model.

A Hybrid Quorum Protocol for Improved Availability, Capacity, Load and Reduced Overhead

Data replication is playing a vital role in the design of distributed information systems. This paper presents a novel and efficient distributed algorithm for managing replicated data and for better performance and availability. This paper presents an extension to existing wheel protocol for improved performance. Wheel protocol imposes a logical wheel structure on the set of copies of an object and gives smallest read quorum. In addition to small read quorum size for read intensive applications, it is necessary to have good write availability as well. This paper proposes two hybrid wheel protocols, which superimpose logarithmic and ring protocols on top of the wheel protocol. It shows that, both protocols help in improving write availability, read capacity, load and message overhead and also compare their performances with wheel and other protocols. Hybrid protocols expand usage of wheel protocol to different type of applications.

Model Checking Paxos in Spin

We present a formal model of a distributed consensus algorithm in the executable specification language Promela extended with a new type of guards, called counting guards, needed to implement transitions that depend on majority voting. Our formalization exploits abstractions that follow from reduction theorems applied to the specific case-study. We apply the model checker Spin to automatically validate finite instances of the model and to extract preconditions on the size of quorums used in the election phases of the protocol.

The Wheel Quorum Protocol: An Efficient Approach for Reading Replicated Data

Data is replicated in distributed systems to improve availability and performance. To keep logical data consistent, there must exist a control protocol responsible for synchronizing the access. In this paper, we present a novel and efficient distributed algorithm for managing replicated data. We impose a logical wheel structure on the set of copies of an object. The protocol ensures minimum read quorum size of one, by reading one copy of an object while guaranteeing fault-tolerance of write operations. Even in failure, read quorum remains one. Wheel structure has a wider application area as it can be imposed in a network with any number of nodes. It gives high read availability.

Exploiting Logical Structures to Reduce Quorum Sizes of Replicated Databases

Voting is a traditional mechanism used for maintaining the consistency of replicated data in distributed systems. A significant problem in protocols that use voting is the size of the quorum needed on each access to the replicated data. In this paper, we propose replica control protocols where the synchronization cost is reduced by exploiting the structural information of the underlying system. We also propose a novel logical structure for managing replicated data, by imposing a logical wheel structure on the set of copies of an object. The logical structure ensures minimum read quorum size of one, by reading one copy of an object while guaranteeing fault-tolerance of write operations.

A two-phase quorum queueing system with Bernoulli vacation schedule, setup, and N-policy for an unreliable server with delaying repair

We present in this paper a thorough classified review of queueing system with unreliable server. We then consider a queueing system where service is rendered to groups of customers of fixed quorum size. Service consists of two consecutive phases. The server needs a setup following an idle period, and may take a vacation following the second phase of service. The idle period ends only when at least N customers are in the queue. While providing service, the server may breakdown and a delay period precedes the repair period. This model generalises many of the models available in the literature. For this model, we obtain the steady state system size distributions and discuss the optimal management policy. Illustrative numerical examples are provided.

A quorum queueing system with unreliable server and restricted admission

We consider in this paper a bulk service, or quorum, queueing system. The server is unreliable and may break down while providing service. The admission to the system is controlled and some arrivals may be denied admission. The queueing process is studied and relevant performance measures, such as the mean number of customers in the system, the mean duration of the idle period, busy period, and busy cycle, are obtained. These measures are then used to design an optimal management policy for the system where the optimal quorum size is sought. The effect of relevant system parameters on the optimal quorum size and optimal expected total cost per unit of time are shown in a numerical example.

An Improved Quorum-Based Algorithm for Extended GME Problem in Distributed Systems

The extended GME (group mutual exclusion) problem is a natural extension of the GME problem. In extended GME problem, processes are allowed to request more than one resource at a time, in order that the processes that can proceed by having access to any one of the requested resource can be allowed to do so. Manabe-Park suggested a quorum based solution for the extended GME problem. However, the worst case message complexity of the Manabe-Park algorithm is 9q, where q is the quorum size. Further, the synchronization delay of Manabe-Park algorithm is 4T, where T is the maximum message propagation delay. In the present paper, we propose a quorum based solution for the extended GME problem. The worst case message complexity of our algorithm is 7q and synchronization delay is 3T. Moreover, in the best case, the synchronization delay and message complexity come down to 2T and 3q respectively.

Complex Dynamics Based on a Quorum: Decision‐Making Process by Cockroaches in a Patchy Environment

AbstractIn the absence of complex communication and a global knowledge of the environment, cockroaches are able to assess the availability of resources and to reach a consensual decision: the group aggregates in a single resting site. We show that the aggregation dynamics and the collective shelter selection of cockroaches are influenced by their social context as, unlike single individuals, groups of cockroaches are more likely to respond to environmental heterogeneities. The decision of individuals to stay under a shelter relies on the modulation of their resting time, according to the perception of two local cues: (1) the shelters luminosity and (2) the number of congeners. This study on the cockroach species Periplaneta americana highlights a shelter‐selection mechanism based on an amplification process resulting from the interactions between congeners. This mechanism leads to complex spatiotemporal aggregation dynamics characterized by transient bimodality, bifurcation patterns (shelter selection) and the existence of a quorum size in the settlement behaviour of the cockroaches. Finally, we discuss the generic aspect for other gregarious species of the collective decision‐making process demonstrated for cockroaches.

General Tree k-Coteries to Reduce the Degradation of Quorums

k-Coterie is a useful concept to solve the distributed k-mutual exclusion problem. The distributed k-mutual exclusion algorithms based on k-coteries have benefits of the high fault-tolerance and the low message cost. Harada and Yamashita proposed a basic tree structure to construct tree k-coteries. When the root fails, quorums are degraded and their sizes grow rapidly. In this paper, we propose the general tree structure to construct general tree 1-coteries to reduce the degradation of quorums. In the general tree 1-coterie, the responsibility of the root to construct small quorums could be adjusted. When the root fails, the degradation of quorums could be reduced. Then, we propose the coterie root-join operation to construct general tree k-coteries by root-joining k general tree 1-coteries at a common root. In the general tree k-coterie, the degradation of quorums and the quorum size could be reduced at same time. We show that general tree k-coteries could be complemental. Thus, general tree k-coteries are resilient when the network is 2-partitioned.

Expected quorum overlap sizes of quorum systems for asynchronous power-saving in mobile ad hoc networks

Quorum systems satisfying the rotation closure property can be used to realize asynchronous power-saving algorithms for mobile ad hoc networks . The FPP, grid, cyclic, torus and e -torus quorum systems can provide the algorithms with the lowest or near lowest active ratios since they have the optimal or near optimal quorum sizes. The algorithms guarantee that a node can sense the status of every neighbor by receiving one or more beacons from it within a round of beacon intervals. Traditionally, the smallest quorum overlap size (SQOS) and the maximum quorum overlap separation (MQOS) are used to measure the neighbor sensibility. However, it is difficult to differentiate the quorum systems by SQOS and MQOS since most of them have the same SQOS and MQOS values. In this paper, the expected quorum overlap size (EQOS) is proposed as an average-case neighbor sensibility measurement. We can easily judge the goodness of quorum systems by EQOS since they have different EQOS values. Larger than one EQOS values are desirable. Observing quorum systems are of EQOS values far larger than one, we are inspired to devise a new quorum system, called the fraction torus ( f -torus) quorum system, for the construction of flexible mobility-adaptive power-saving algorithms. The f -torus quorum system can further reduce the active ratio to save energy by shrinking the quorum size, while still keeping the EQOS larger than one. We derive EQOS values for all the above-mentioned quorum systems by analysis and simulation experiments. As we will show, the EQOS analysis and simulation results coincide very closely.

A Token-Based Distributed Group Mutual Exclusion Algorithm with Quorums

The group mutual exclusion problem is a generalization of mutual exclusion problem such that a set of processes in the same group can enter critical section simultaneously. In this paper, we propose a distributed algorithm for the group mutual exclusion problem in asynchronous message passing distributed systems. Our algorithm is based on tokens, and a process that obtains a token can enter critical section. For reducing message complexity, it uses coterie as a communication structure when a process sends a request messages. Informally, coterie is a set of quorums, each of which is a subset of the process set, and any two quorums share at least one process. The message complexity of our algorithm is O(|Q|) in the worst case, where |Q| is a quorum size that the algorithm adopts. Performance of the proposed algorithm is presented by analysis and discrete event simulation. Especially, the proposed algorithm achieves high concurrency, which is a performance measure for the number of processes that can be in critical section simultaneously.

Quorum size of Pseudomonas syringae is small and dictated by water availability on the leaf surface

The paradigm of bacterial quorum sensing (QS), which mediates cell-density-dependent gene expression, usually has been studied in high-cell-density planktonic liquid cultures or in biofilms in which signal concentrations accumulate to sufficiently high levels to induce QS. Presumably under conditions with restricted diffusion of the signal molecule, smaller population sizes could achieve such a state of QS induction. The plant-pathogenic bacterium Pseudomonas syringae, in which QS controls traits involved in epiphytic fitness and virulence, occurs on leaf surfaces in aggregates of various sizes. Because leaves often harbor limited surface water, we investigated the size of aggregates that would permit QS in a nonsaturated environment. QS induction was visualized via dual fluorescence of P. syringae cells harboring a transcriptional fusion of mRFP1 with ahlI, which exhibits N-acyl homoserine lactone-dependent transcriptional activity, and a constitutive GFP marker to account for all P. syringae cells on a leaf. Confocal microscopy revealed that, on wet leaves, no QS induction was evident within 2 days after inoculation, but it increased rapidly with increasing aggregate sizes >40 and 22 cells per aggregate by 3 and 4 days, respectively. In contrast, QS induction was common in aggregates >33 cells by 2 days after inoculation on dry leaves and increased rapidly with increasing aggregate sizes >35 and 13 cells after 3 and 4 days, respectively. These observations demonstrate that small groups of cells experience QS conditions on dry leaves where signal diffusion is restricted. Quorum size of bacteria in non-water-saturated environments such as on leaves is small, and QS induction may be commonly operative.

Transversal merge operation: a nondominated coterie construction method for distributed mutual exclusion

A coterie is a set of subsets (called quorums) of the processes in a distributed system such that any two quorums intersect with each other and is mainly used to solve the mutual exclusion problem in a quorum-based algorithm. The choice of a coterie sensitively affects the performance of the algorithm and it is known that nondominated (ND) coteries achieve good performance in terms of criteria such as availability and load. On the other hand, grid coteries have some other attractive features: 1) a quorum size is small, which implies a low message complexity, and 2) a quorum is constructible on the fly, which benefits a low space complexity. However, they are not ND coteries unfortunately. To construct ND coteries having the favorite features of grid coteries, we introduce the transversal merge operation that transforms a dominated coterie into an ND coterie and apply it to grid coteries. We call the constructed ND coteries ND grid coteries. These ND grid coteries have availability higher than the original ones, inheriting the above desirable features from them. To demonstrate this fact, we then investigate their quorum size, load, and availability, and propose a dynamic quorum construction algorithm for an ND grid coterie.

Quorum-Based Asynchronous Power-Saving Protocols for IEEE 802.11 Ad Hoc Networks

This paper investigates the power mode management problem for an IEEE 802.11-based mobile ad hoc network (MANET) that allows mobile hosts to tune to the power-saving (PS) mode. There are two major issues that need to be addressed in this problem: (a) wakeup prediction and (b) neighbor discovery. The former is to deliver buffered packets to a PS host at the right time when its radio is turned on. The latter is to monitor the environment change under a mobile environment. One costly, and not scalable, solution is to time-synchronize all hosts. Another possibility is to design asynchronous protocols as proposed by Tseng et al. in [25]. In this paper, we adopt the latter approach and correlate this problem to the quorum system concept. We identify a rotation closure property for quorum systems. It is shown that any quorum system that satisfies this property can be translated to an asynchronous power-saving protocol for MANETs. Thus, the result bridges the classical quorum system design problem in the area of distributed systems to the power mode management problem in the area of mobile ad hoc networks. We derive a lower bound for quorum sizes for any quorum system that satisfies the rotation closure property. We identify a group of quorum systems that are optimal or near optimal in terms of quorum sizes, which can be translated to efficient asynchronous power-saving protocols. We also propose a new e-torus quorum system, which can be translated to an adaptive protocol that allows designers to trade hosts' neighbor sensibility for power efficiency. Simulation experiments are conducted to evaluate and compare the proposed protocols.

A simple scheme to construct k‐arbiters with uniform quorum sizes

k‐Arbiter is a useful concept for solving the distributed h‐out of‐k mutual exclusion problem. The distributed h‐out of‐k mutual exclusion algorithms based on k‐arbiter have the benefits of high fault‐tolerance and low message cost. However, according to the definition of k‐arbiter, it is required to have a non‐empty intersection among any (k+1) quorums in a k‐arbiter. Consequently, constructing k‐arbiters is difficult. In this paper, we propose a simple scheme to construct k‐arbiters for any integer k. The constructed k‐arbiters, named binomial(q, k)‐arbiters, are uniform: each quorum in a k‐arbiter has the same size and each node contains the same number of quorums. Also, the constructed k‐arbiters perform better than other known k‐arbiters do on quorum size and availability.

A generalized grid quorum strategy for k-mutual exclusion in distributed systems

In the problem of k-mutual exclusion, concurrent access to shared resource or the critical section (CS) must be synchronized such that at any time at most k processes can access the CS. In this paper, we propose a generalized grid quorum strategy for k-mutual exclusion, which imposes a logical grid structure on the network. The quorum size is always equal to ⌈( M+1)/( k+1)⌉×⌈( N+1)/2⌉, where M is the number of rows and N is the number of columns in a grid. From our performance study, we show that the generalized grid quorum strategy can provide a good performance in terms of the quorum size and the availability.

Quorum Systems Constructed from Combinatorial Designs

A quorum system is a set system in which any two subsets have nonempty intersection. Quorum systems have been extensively studied as a method of maintaining consistency in distributed systems. Important attributes of a quorum system include the load, balancing ratio, rank (i.e., quorum size), and availability. Many constructions have been presented in the literature for quorum systems in which these attributes take on optimal or otherwise favorable values. In this paper, we point out an elementary connection between quorum systems and the classical covering systems studied in combinatorial design theory. We look more closely at the quorum systems that are obtained from balanced incomplete block designs (BIBDs). We study the properties of these quorum systems and observe that they have load, balancing ratio, and rank that are all within a constant factor of being optimal. We also provide several observations about computing the failure polynomials of a quorum system (failure polynomials are used to measure availability). Asymptotic properties of failure polynomials have previously been analyzed for certain infinite families of quorum systems. We give an explicit formula for the failure polynomials for an easily constructed infinite class of quorum systems. We also develop two algorithms that are useful for computing failure polynomials for quorum systems and prove that computing failure polynomials is #P-hard. Computational results are presented for several “small” quorum systems obtained from BIBDs.

Quorums from difference covers

Maekawa considered a simple but suboptimal grid-based quorum generation scheme in which N sites in the network are logically organized in the form of a N × N grid, and the quorum sets are row–column pairs. Even though the quorum size 2 N of the grid scheme is twice as large as finite projective plane with optimal sized quorums, it has the advantage of being simple and geometrically evident. Agrawal, Eğecioğlu, and El Abbadi proposed another grid based scheme producing quorums of size 2N . In this note, a very simple construction is given to produce a system of quorums of size 1.5N . These can be generated efficiently.