Stochastic resonance for information flows on hierarchical networks

A simple model of information flows represented by package delivery on networks with hierarchical structures is considered. The packages should be transferred from one network node to another and the delivery process is influenced by two types of noise. The first type of noise is related to a partially false knowledge of network topology (topological noise), i.e. membership of nodes in communities in a shipping algorithm include a number of errors corresponding to a random rewiring of a fraction of network links. The second type of noise (dynamical noise) is related to a diffusive part in packet dynamics, i.e. package paths do not follow from completely deterministic rules. In the case of a pure topological noise and in the case of combination of both types of noises, we observe a resonance-like phenomenon for communication efficiency. The system performance measured as a fraction of packages that are delivered in a certain time period or as an inverse of time of a package delivery is maximal for intermediate levels of noise. This effect resembles the phenomenon of stochastic resonance that exists in many complex systems where a noise can enhance the information transfer.