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Wireless sensor network applications have a predominant traffic pattern: convergecast, in which sensor nodes send reports to the base station. Convergecast causes energy hole problem, i.e., nodes closer to the base station incur heavier workload and deplete their energy more quickly, which impairs network lifetime. Existing approaches that address energy hole problem do not consider the tradeoff with network performance degradation and ignore nodes' energy consumption due to idle listening. We provide a differential duty cycle approach that is designed based on energy consumed by both traffic and idle listening. It assigns different duty cycles for nodes at different distances from the base station to address the energy hole problem, improve network lifetime, and also maintain network performance. Through ns-2 simulation, we show that our differential approach, compared to the approach assigning uniform duty cycles to all nodes, can improve network lifetime without sacrificing end-to-end delay and throughput.