Abstract— MaxWeight algorithm, a.k.a., back-pressure algorithm, has received much attention as a viable solution for dynamic link scheduling in multi-hop wireless networks. The basic principle of the MaxWeight algorithm is to select a set of interference-free links with the maximum overall link weights in the network, where the link weight is determined by the queue difference between the transmitter and the receiver. While the throughput-optimality of the MaxWeight algorithm is well understood in the literature, the energy consumption induced by the MaxWeight algorithm is less studied, which is of great interest in energy-constrained wireless networks such as wireless sensor networks. In this paper, we propose an energy-conserving scheduling scheme, a.k.a., minimum energy scheduling (MES) algorithm for multi-hop wireless networks with stochastic traffic arrivals and time-varying channel conditions. We show that our algorithm is energy optimal in the sense that the proposed MES algo...