Mobile Edge Computing (MEC) integrated with Wireless Power Transfer (WPT) is emerging as a promising solution to reduce task delays and extend the battery life of Mobile Devices (MDs). However, maximizing the long-term energy efficiency (EE) of a user-cooperative WPT-MEC system presents significant challenges due to uncertain load dynamics at the edge MD and the time-varying state of the wireless channel. In this paper, we propose an online control algorithm to maximize the long-term EE of a WPT-MEC system by making decisions on time allocations and transmission powers of mobile devices (MDs) for a three-node network. We formulate a stochastic programming problem considering the stability of network queues and time-coupled battery levels. By leveraging Dinkelbach’s method, we transform the fractional optimal problem into a more manageable form and then use the Lyapunov optimization technique to decouple the problem into a deterministic optimization problem for each time slot. For the sub-problem in each time slot, we use the variable substitution technique and convex optimization theory to convert the non-convex problem into a convex problem, which can be solved efficiently. Extensive simulation results demonstrate that our proposed algorithm outperforms baseline algorithms, achieving a 20% improvement in energy efficiency. Moreover, our algorithm achieves an $\left[O\right(1/V),O(V\left)\right]$ trade-off between EE and network queue stability.

Mobile Edge Computing (MEC) integrated with Wireless Power Transfer (WPT) is emerging as a promising solution to reduce task delays and extend the battery life of Mobile Devices (MDs). Cooperative user communication, or relay technology, enhances communication efficiency for users located far from the base station by mitigating the double near-far effect caused by distance. This is considered a key technology in Beyond 5G (B5G) and future communication systems. In this paper, we focus on maximizing the long-term energy efficiency (EE) of a user-cooperation WPT-MEC system, while taking into account the uncertain load dynamics at the edge MD and the time-varying state of the wireless channel. The joint optimization of wireless charging time fraction, MD offloading duration, helper node processing time, and transfer power decision presents significant challenges due to the coupling of data offloading among cooperative users and a volatile system environment. To address these challenges, we formulate the problem as a stochastic programming problem and propose an online control algorithm, DOUCA, to solve it. Our approach utilizes Dinkelbach’s method and Lyapunov optimization theory to decouple the sequential decision problem into a deterministic sub-problem for each time slot. For the sub-problem, we use variable substitution to convert the non-convex problem into a convex one, containing only a small number of variables, which can be efficiently solved. Furthermore, we provide a mathematical analysis of our algorithm’s performance. Extensive simulation results demonstrate the effectiveness of our proposed algorithm, as evidenced by an impressive energy efficiency improvement of over 20% compared to benchmark methods. Our algorithm also achieves a trade-off between EE and system stability.