Wireless Powered Mobile Edge Computing (WP-MEC) integrates mobile edge computing (MEC) with wireless power transfer (WPT) to simultaneously extend the operational lifetime and enhance the computational capability of wireless devices (WDs). In WPMEC systems, WPT and computation offloading compete for limited wireless resources, which makes their joint scheduling particularly challenging. In this paper, we investigate the energy-efficient online scheduling problem for WPMEC networks with multiple WDs and multiple access points (APs). Based on Lyapunov optimization, we develop an online optimization framework that transforms the original stochastic problem into deterministic per-slot optimization problems. To reduce computational complexity, we introduce the concept of marginal energy efficiency and derive an associated optimality condition, based on which a relax-then-adjust approach is proposed to efficiently obtain feasible solutions. For the resulting non-convex computation offloading subproblem, we analyze the structural properties of its optimal solution and transform it into an assignment problem that can be solved efficiently. We further provide theoretical performance guarantees for both the per-slot and long-term solution, establishing a fundamental trade-off between latency and energy consumption. To improve practical performance, additional mechanisms are introduced to balance the magnitudes of different queues and reduce latency without increasing energy consumption. Extensive simulation results demonstrate the effectiveness and robustness of the proposed algorithm under various system settings.

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