Energy-Efficient Task Allocation for Green Aerial Edge Computing Based on Metaverse Users: A Mean Field Game Approach

We consider the energy-constrained task allocation problem in large-scale Aerial Edge Computing (AEC) systems, which encompasses a series of tightly coupled decision-making processes, includingwhichtasks need to be processed by unmanned aerial vehicles (UAVs),howto allocate these tasks and balance energy across UAVs for delay-sensitive requirements. However, little attention has been devoted to exploring the above coupled decision-making problem in AEC with various resource and energy constraints, which is further complicated by energy dynamics (UAV battery states), task-specific consumption, and allocation-feedback balance. In this paper, we formulate a multi-dimensional joint optimization problem, simultaneously optimizing task allocation and energy rewarding to maximize long-term system rewards while balancing service quality and energy efficiency. To this end, we propose a green aerial edge computing framework where partial UAVs are equipped with energy harvesting modules to collect ambient energy. To circumvent the intractable computational complexity arising from the coupled energy states of massive UAVs, we design a distributed solution method based on the mean field game, which decouples the dense multi-agent interactions into a game between an individual UAV and the aggregate population state, thereby transforming the complex global optimization problem into a set of equivalent scalable subproblems. We develop an optimal energy valuation scheme to guide UAV behavior. Numerical results show that our mechanism can effectively ensure sustainable system operation while maintaining high quality of service for metaverse users, outperforming existing methods in both system sustainability and service responsiveness.