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.

翻译：无线供能移动边缘计算（WP-MEC）将移动边缘计算（MEC）与无线能量传输（WPT）相结合，旨在同时延长无线设备（WD）的运行寿命并提升其计算能力。在WP-MEC系统中，无线能量传输与计算卸载需竞争有限的无线资源，这使得二者的联合调度尤为困难。本文研究了包含多个无线设备与多个接入点（AP）的WP-MEC网络中的能效在线调度问题。基于李雅普诺夫优化理论，我们构建了一个在线优化框架，将原始随机优化问题转化为确定性的时隙级优化问题。为降低计算复杂度，我们引入了边际能效的概念并推导了相关最优性条件，在此基础上提出一种“松弛-调整”方法以高效获得可行解。针对由此产生的非凸计算卸载子问题，我们分析了其最优解的结构特性，并将其转化为可高效求解的分配问题。我们进一步从理论层面证明了所提方法在时隙级与长期性能上的保障，建立了时延与能耗之间的基本权衡关系。为提升实际性能，我们引入了额外机制以平衡不同队列的规模，并在不增加能耗的前提下降低时延。大量仿真结果表明，所提算法在不同系统设置下均表现出优异的有效性与鲁棒性。