Delay analysis of BFT consensus : Case study of Narwhal and Bullshark protocols

IF 4.3 3区计算机科学 Q1 COMPUTER SCIENCE, INFORMATION SYSTEMS

Computer Communications Pub Date : 2025-07-25 DOI:10.1016/j.comcom.2025.108278

Khouloud Hwerbi , Ichrak Amdouni , Cédric Adjih , Leila Azouz Saidane , Anis Laouiti

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引用次数: 0

Abstract

Acknowledging the critical influence of consensus delays on blockchain performance, this paper presents an analytical and simulation-based exploration of delay characteristics in Byzantine Fault Tolerant (BFT) consensus mechanisms. Our focus is on SUI, a blockchain system that employs a Directed Acyclic Graph (DAG) structure to support parallel transaction execution. SUI relies on two integrated protocols: Narwhal, a mempool protocol responsible for efficient block dissemination and DAG construction; and Bullshark, which organizes DAG vertices to produce a consistent total order of transactions without incurring additional communication overhead.

While our previous work modeled Narwhal’s delay characteristics under various message propagation distributions, this study shifts attention to Bullshark—the protocol responsible for reaching consensus. We propose a probabilistic analytical model that estimates the number of rounds required to reach consensus. In this model, each validator’s decision is treated as a Bernoulli trial, and we apply the binomial distribution to determine the probability of reaching quorum. This framework enables us to analyze the expected delay of the protocol.

To validate our model, we implemented both Narwhal and Bullshark and conducted extensive simulations. The simulation results show strong agreement with our analytical predictions, confirming the accuracy of our model. For instance, under a Gaussian delay model with mean

μ = 1 ms

and standard deviation

σ = 0.25

ms—values representative of short-range wireless communication in real-world IoT or LAN settings [1]—we predict an average round duration of approximately 3.26 ms. Furthermore, based on our binomial-based model of block commitment, the expected number of rounds to reach consensus is approximately 1 when

f = 10

, indicating that blocks typically commit in a single round with high probability.

To the best of our knowledge, this is the first study to model Bullshark’s consensus process using Bernoulli trials and binomial distributions. Our contributions offer a novel framework for evaluating its efficiency and provide insights that can guide future optimization and scalability efforts for DAG-based BFT protocols.

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BFT一致性的延迟分析：以独角鲸协议和牛鲨协议为例

鉴于共识延迟对区块链性能的重要影响，本文对拜占庭容错（BFT）共识机制中的延迟特性进行了基于分析和仿真的探索。我们的重点是SUI，这是一个区块链系统，它采用有向无环图（DAG）结构来支持并行事务执行。SUI依赖于两个集成协议：narwhale，一个负责高效块分发和DAG构建的内存池协议；以及Bullshark，它组织DAG顶点以产生一致的事务总顺序，而不会产生额外的通信开销。虽然我们之前的工作模拟了各种消息传播分布下独角鲸的延迟特性，但本研究将注意力转移到牛鲨协议上——负责达成共识的协议。我们提出了一个概率分析模型来估计达成共识所需的轮数。在该模型中，每个验证者的决策被视为伯努利试验，我们应用二项分布来确定达到法定人数的概率。这个框架使我们能够分析协议的预期延迟。为了验证我们的模型，我们实现了独角鲸和牛鲨，并进行了广泛的模拟。模拟结果与我们的分析预测非常吻合，证实了模型的准确性。例如，在平均μ=1ms，标准差σ=0.25 ms的高斯延迟模型下-代表现实世界物联网或局域网设置中的短距离无线通信的值[1]-我们预测平均轮持续时间约为3.26 ms。此外，根据我们基于二项的区块承诺模型，当f=10时，达成共识的预期轮数约为1，这表明区块通常在单轮提交的概率很大。据我们所知，这是第一个使用伯努利试验和二项分布来模拟牛鲨共识过程的研究。我们的贡献提供了一个评估其效率的新框架，并提供了可以指导基于dag的BFT协议的未来优化和可伸缩性工作的见解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computer Communications 工程技术-电信学

CiteScore

14.10

自引率

5.00%

发文量

397

审稿时长

66 days

期刊介绍： Computer and Communications networks are key infrastructures of the information society with high socio-economic value as they contribute to the correct operations of many critical services (from healthcare to finance and transportation). Internet is the core of today''s computer-communication infrastructures. This has transformed the Internet, from a robust network for data transfer between computers, to a global, content-rich, communication and information system where contents are increasingly generated by the users, and distributed according to human social relations. Next-generation network technologies, architectures and protocols are therefore required to overcome the limitations of the legacy Internet and add new capabilities and services. The future Internet should be ubiquitous, secure, resilient, and closer to human communication paradigms. Computer Communications is a peer-reviewed international journal that publishes high-quality scientific articles (both theory and practice) and survey papers covering all aspects of future computer communication networks (on all layers, except the physical layer), with a special attention to the evolution of the Internet architecture, protocols, services, and applications.