We consider the important problem of energy balanced data propagation in wireless sensor networks and we extend and generalize previous works by allowing adaptive energy assignment. We consider the data gathering problem where data are generated by the sensors and must be routed toward a unique sink. Sensors route data by either sending the data directly to the sink or in a multi-hop fashion by delivering the data to a neighbouring sensor. Direct and neighbouring transmissions require different levels of energy consumption. Basically, the protocols balance the energy consumption among the sensors by computing the adequate ratios of direct and neighbouring transmissions. An abstract model of energy dissipation as a random walk is proposed, along with rigorous performance analysis techniques. Two efficient distributed algorithms are presented and analyzed, by both rigorous means and simulation. The first one is easy to implement and fast to execute. The protocol assumes that sensors know a-priori the rate of data they generate. The sink collects and processes all these information in order to compute the relevant value of the protocol parameter. This value is transmitted to the sensors which individually compute their optimal ratios of direct and neighbouring transmissions. The second protocol avoids the necessary a-priori knowledge of the data rate generated by sensors by inferring the relevant information from the observation of the data paths. Furthermore, this algorithm is based on stochastic estimation methods and is adaptive to environmental change
