Joint D2D Collaboration and Task Offloading for Edge Computing: A Mean Field Graph Approach

Mobile edge computing (MEC) facilitates computation offloading to edge server, as well as task processing via device-to-device (D2D) collaboration. Existing works mainly focus on centralized network-assisted offloading solutions, which are unscalable to scenarios involving collaboration among massive users. In this paper, we propose a joint framework of decentralized D2D collaboration and efficient task offloading for a large-population MEC system. Specifically, we utilize the power of two choices for D2D collaboration, which enables users to beneficially assist each other in a decentralized manner. Due to short-range D2D communication and user movements, we formulate a mean field model on a finite-degree and dynamic graph to analyze the state evolution of D2D collaboration. We derive the existence, uniqueness and convergence of the state stationary point so as to provide a tractable collaboration performance. Complementing this D2D collaboration, we further build a Stackelberg game to model users' task offloading, where edge server is the leader to determine a service price, while users are followers to make offloading decisions. By embedding the Stackelberg game into Lyapunov optimization, we develop an online offloading and pricing scheme, which could optimize server's service utility and users' system cost simultaneously. Extensive evaluations show that our D2D collaboration can mitigate users' workloads by $73.8\%$ and task offloading can achieve high energy efficiency.