Communication in networks with hierarchical branching

We present a simple model of communication in networks with hierarchical br anching. We analyze the behavior of the model from the viewpoint of critica l systems under different situations. For certain values of the parameters, a continuous phase transition between a sparse and a congested regime is o bserved and accurately described by an order parameter and the power spectr a. At the critical point the behavior of the model is totally independent o f the number of hierarchical levels. Also scaling properties are observed w hen the size of the system varies. The presence of noise in the communicati on is shown to break the transition. The analytical results are a useful gu ide to forecasting the main features of real networks.