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Mobile-edge computing (MEC) has evolved as a promising technology to alleviate the computing pressure of mobile devices by offloading computation tasks to MEC server. Energy management is challenging since the unpredictability of the energy harvesting (EH) and the quality of service (QoS). In this paper, we investigate the problem of power consumption in a multiuser MEC system with EH devices. The system power consumption, which includes the local execution power and the offloading transmission power, is designated as the main system performance index. First, we formulate the power consumption minimization problem with the battery queue stability and QoS constraints as a stochastic optimization programming, which is difficult to solve due to the time-coupling constraints. Then, we adopt the Lyapunov optimization approach to tackle the problem by reformulating it into a problem with relaxed queue …