Abstract—In this paper, we investigate the problem of controlling node sleep intervals so as to achieve the min-max energy fairness in asynchronous duty-cycling sensor networks. We propose a mathematical model to describe the energy efficiency of such networks and observe that traditional sleep interval setting strategy, i.e., operating sensor nodes with identical sleep intervals, or intuitive control heuristics, i.e., greedily increasing sleep intervals of sensor nodes with high energy consumption rates, hardly perform well in practice. There is an urgent need to develop an efficient sleep interval control strategy for achieving fair and high energy efficiency. To this end, we theoretically formulate the Sleep Interval Control (SIC) problem and find it a convex optimization problem. By utilizing the convex property, we decompose the original problem and propose a distributed algorithm, called GDSIC. In GDSIC, sensor nodes can tune sleep intervals through a local information exch...