Byzantine fault-tolerant (BFT) systems are able to maintain the availability and integrity of IoT systems, in presence of failure of individual components, random data corruption or malicious attacks. Fault-tolerant systems in general are essential in assuring continuity of service for mission critical applications. However, their implementation may be challenging and expensive. In this study, IoT Systems with Byzantine Fault-Tolerance are considered. Analytical models and solutions are presented as well as a detailed analysis for the evaluation of the availability. Byzantine Fault Tolerance is particularly important for blockchain mechanisms, and in turn for IoT, since it can provide a secure, reliable and decentralized infrastructure for IoT devices to communicate and transact with each other. The proposed model is based on continuous-time Markov chains, and it analyses the availability of Byzantine Fault-Tolerant systems. While the availability model is based on a continuous-time Markov chain where the breakdown and repair times follow exponential distributions, the number of the Byzantine nodes in the network studied follows various distributions. The numerical results presented report availability as a function of the number of participants and the relative number of honest actors in the system. It can be concluded from the model that there is a non-linear relationship between the number of servers and network availability; i.e. the availability is inversely proportional to the number of nodes in the system. This relationship is further strengthened as the ratio of break-down rate over repair rate increases.

翻译：拜占庭容错（BFT）系统能够在个别组件故障、随机数据损坏或恶意攻击的情况下，维持物联网系统的可用性和完整性。容错系统通常对于确保关键任务应用的服务连续性至关重要，但其实现可能具有挑战性且成本高昂。本研究考虑具有拜占庭容错的物联网系统，提出了分析模型与求解方法，并进行了详细的可用性评估分析。拜占庭容错对于区块链机制尤为重要，进而对物联网至关重要，因为它能为物联网设备提供安全、可靠且去中心化的基础设施，使其能够相互通信和交易。所提出的模型基于连续时间马尔可夫链，分析了拜占庭容错系统的可用性。虽然可用性模型基于连续时间马尔可夫链（其中故障和修复时间服从指数分布），但网络中研究的拜占庭节点数量服从多种分布。数值结果报告了可用性作为系统中参与者数量及诚实行为者相对数量的函数。从该模型可以得出结论：服务器数量与网络可用性之间存在非线性关系，即可用性与系统中的节点数量成反比。随着故障率与修复率之比的增加，这种关系进一步增强。