Publisher Summary This chapter describes the problem investigated in Butrimenko's dissertation. The methods developed by M. L. Tsetlin are applied to construct a decentralized method of controlling communications networks. Communications network consists of nodes and the main lines connecting them. Load is produced by the nodes, and the main lines possess a limited number of channels. Both the main lines and the nodes may malfunction, and the network may include new main lines and nodes. The problem is to find routes which satisfy the requirements arising in nodes in such a way as to minimize the number of failures. The failures themselves may be due to overloads or a malfunctioning of individual links of the network.