We study data gathering problem in Rechargeable Sensor Networks (RSNs) with a mobile sink, where rechargeable sensors are deployed into a region of interest to monitor the environment and a mobile sink travels along a pre-defined path to collect data from sensors periodically. In such RSNs, the optimal data gathering is challenging because the required energy consumption for data transmission changes with the movement of the mobile sink and the available energy is time-varying. In this paper, we formulate data gathering problem as a network utility maximization problem, which aims at maximizing the total amount of data collected by the mobile sink while maintaining the fairness of network. Since the instantaneous optimal data gathering scheme changes with time, in order to obtain the globally optimal solution, we first transform the primal problem into an approximate network utility maximization problem by shifting the energy consumption conservation and analyzing necessary conditions for the optimal solution. As a result, each sensor does not need to estimate the amount of harvested energy and the problem dimension is reduced. Then, we propose a Distributed Data Gathering Approach (DDGA), which can be operated distributively by sensors, to obtain the optimal data gathering scheme. Extensive simulations are performed to demonstrate the efficiency of the proposed algorithm.

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