Backpressure based scheduling has revealed remarkable performance in wireless multihop networks as reported in a lot of previous work. However, its lack of consideration on energy use efficiency is still an obstacle for backpressure based algorithms to be deployed in resource-constrained wireless sensor networks (WSNs). In this paper, we focus on studying the design of energy efficient backpressure based algorithm. For this purpose, we propose a gradient-assisted energy-efficient backpressure scheduling algorithm (GRAPE) for WSNs. GRAPE introduces a new link-weight calculation method, based on which gradient information and nodal residual energy are taken into account when making decisions on backpressure based transmission scheduling. According to the decisions made by this new method, packets are encouraged to be forwarded to nodes with more residual energy. We theoretically prove the throughput-optimality of GRAPE. Simulation results demonstrate that GRAPE can achieve significant performance improvements in terms of energy use efficiency, network throughput, and packet delivery ratio as compared with existing work.
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