  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.
