Reliability of double-pole networks with additive structures: II. final probability of communication

摘要

A two-dimensional retransmitting communication network of additive structure is considered. The network is constructed by connecting in series additive (complemented) subnetworks to its current boundary. The number of nodes at the boundary determines the degree m of the network, while the number of connected subnetworks determines the rank n. Elements of the network are unreliable and their failures are mutually independent. An effective method is worked out for the estimation of the final probability of connection between fixed nodes (poles); it is found that the rank and degree of the network tend to infinity. For networks (lattices), studies are made of the asymptotics of the final probability for the case where not only the degree and the rank, but also the "distance" between poles increases infinitely. The threshold character of the asymptotics as a function of the reliability of communication channels is defined: the asymptotics is equal to zero below the threshold (networks are unreliable) and to a nonzero value above the threshold (networks are reliable). An error in the estimation of the asymptotics is defined, the boundary between reliable and unreliable networks is assessed, and results of the numerical modeling are given.