A simple model of information flows represented by  package delivery  on  networks with hierarchical structures is considered.  The packages should be transfered from one network  node  to another and the delivery process is influenced by two types of noise. The first one is related to a diffusive part in a packet dynamics, i.e.  package paths do not follow from  completly  deterministic rules.   The second one is related to  partialy false knowledge of  network topology, i.e.  addresses tables in shipping algorithm  include a number of errors.   In both cases we observe a resonance-like phenomenon for communication efficiency, i.e.  the system performance measured as a fraction of packages that are delivered in a certain time period is maximal for an intermediate level of noise. The effect resembles the phenomenon of stochastic resonance existing in many complex systems. The resonance occurs also for a network formed by  former Enron Company employees.

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