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.