Mean-Field Game Theory Based Altitude Control Strategy for Massive UAV Relay-assisted Mobile Edge Computing

Mobile Edge Computing (MEC) offers additional computational capabilities to low-resource Internet of Things (IoT) devices, where IoT devices need to offload tasks to base stations (BS) regularly to meet the Quality of Service (QoS) requirements. Due to limited transmission capacity and obstacles caused by buildings, a significant number of IoT devices are unable to offload tasks to BS in urban areas. To solve this problem, it is necessary to deploy a large number of UAVs relays. This article proposes a distributed UAV height control algorithm, where each UAV unloads IoT devices according to the demand for computational resources of the MEC and their own strategy, while minimizing the own flight energy consumption and relay consumption. Firstly, we describe the problem of dynamic offloading and altitude scheduling strategy as a stochastic differential game. Then, we use mean field game (MFG) to transform the problem into two partial differential equations, namely the Fokker-Planck-Kolmogorov (FPK) and Hamilton-Jacobi-Bellman (HJB) equations. Finally, we conduct numerical simulations to show that the algorithm can achieve Nash equilibrium and effectively reduce system consumption.