The paper presents approaches to reliability and fault tolerance, including the use of residual class systems and dynamic load balancing methods, and demonstrates the promise in improving the stability and efficiency of fog systems. Simulations are carried out and the results confirm that the implementation of reliability improvement algorithms based on the residue number system can significantly reduce the probability of data loss. The use of redundant computational structures, adaptive control mechanisms and stable node communication protocols allows to create fault-tolerant solutions that can effectively cope with the risks and uncertainty characteristic of heterogeneous distributed computing environments.