Abstract
In a distributed heterogeneous fog environment, fog nodes may change their state at any time. Their reliability changes accordingly. A dynamic analysis of state changes can help one detect fault-tolerant fog nodes, which is conducive to promoting the reliability of fog services. This article proposes a fault-tolerant model based on a Markov chain for a fog system's performance optimization. The real-time reliability of fog nodes is analyzed by using dynamic distributed parameters. Thus, the state transition process of fog nodes is modeled with a continuous-time Markov chain. The steady-state probability of a fog system is analyzed. Then, a fault-tolerant strategy and its algorithms are designed to select nodes with the minimum cost based on their steady-state probabilities. The proposed method can predict the number of faulty ones of a fog system via the steady-state probability. An intelligent optimization method called simulated annealing (ISA) is designed and used to select the most appropriate fog nodes to substitute faulty ones. The experimental results show that the method is feasible and effective for selecting the right fault-tolerant nodes according to different performance requirements. ISA can well outperform such methods as random selection, discrete differential evolution, and simulated annealing in terms of cost and time.