标题： 实用拜占庭容错的性能和可靠性分析与可修复投票节点 显示英文标题

标题： Performance and Reliability Analysis for Practical Byzantine Fault Tolerance with Repairable Voting Nodes

摘要： 实用拜占庭容错（PBFT）共识协议是区块链技术发展中的基本共识协议之一。 同时，PBFT共识协议为其他一些重要的BFT共识协议奠定了基础，例如Tendermint、Streamlet、HotStuff和LibraBFT。 一般来说，投票节点可能会始终出现故障，从而在随机的时间间隔内离开基于PBFT的区块链系统，使得及时可用的投票节点数量不确定。 因此，这种不确定性使得对具有可修复投票节点的基于PBFT的区块链系统的分析更具挑战性。 在本文中，我们开发了一种具有可修复投票节点的新PBFT共识协议，并使用多维马尔可夫过程和首次通过时间方法来研究这种新的区块链系统。 基于此，我们提供了性能和可靠性分析，包括吞吐量、可用性和可靠性，针对具有可修复投票节点的新PBFT-based区块链系统。 此外，我们提供了一种近似算法来计算新PBFT-based区块链系统的吞吐量。 我们采用数值示例来证明我们理论结果的有效性，并说明关键系统参数如何影响具有可修复投票节点的基于PBFT的区块链系统的性能指标。 我们希望本文中开发的方法论和结果将激发未来的研究努力，并在此领域开辟新的研究方向。 显示英文摘要

摘要： The practical Byzantine fault tolerant (PBFT) consensus protocol is one of the basic consensus protocols in the development of blockchain technology. At the same time, the PBFT consensus protocol forms a basis for some other important BFT consensus protocols, such as Tendermint, Streamlet, HotStuff, and LibraBFT. In general, the voting nodes may always fail so that they can leave the PBFT-based blockchain system in a random time interval, making the number of timely available voting nodes uncertain. Thus, this uncertainty leads to the analysis of the PBFT-based blockchain systems with repairable voting nodes being more challenging. In this paper, we develop a novel PBFT consensus protocol with repairable voting nodes and study such a new blockchain system using a multi-dimensional Markov process and the first passage time method. Based on this, we provide performance and reliability analysis, including throughput, availability, and reliability, for the new PBFT-based blockchain system with repairable voting nodes. Furthermore, we provide an approximate algorithm for computing the throughput of the new PBFT-based blockchain system. We employ numerical examples to demonstrate the validity of our theoretical results and illustrate how the key system parameters influence performance measures of the PBFT-based blockchain system with repairable voting nodes. We hope the methodology and results developed in this paper will stimulate future research endeavors and open up new research trajectories in this field.