Abstract— Wireless sensor networks (WSNs) are energyconstrained in nature, in this paper, we formulate the problem of data transport in sensor networks as a network utility maximization (NUM) problem, but we argue that each source utility not only depends on its source rate, but also on the consumed energy, this leads to a coupled utility model, where the utilities are functions of source rates and consumed energy. Differentiating from the classical NUM framework which usually takes the consumed energy as constraints, Our utility model regards consumed energy as one of the components of measure of the utility values, which indicates the tradeoff of source rates and consumed energy, it is a more accurate utility model for ing the energy characteristics for data gathering and transmission in WSNs. Due to the coupled energy utility, our optimization problem is not separable. Despite the difficulty, we present a systematic approach to decouple our NUM problem with coupled utilities by i...