Distributed Data Offloading in Ultra-Dense LEO Satellite Networks: A Stackelberg Mean-Field Game Approach

Abstract

The low earth orbit (LEO) satellite network is regarded as a promising technology for delivering seamless service to remote areas such as rural areas. In this paper, we consider a dynamic data offloading problem in ultra-dense LEO satellites networks with large-scale ground users, where each ground user makes the distributed offloading decision based on its state information, the influence from other ground users, and the fees paid to satellites. To investigate the interaction problem between ground users and satellites, we formulate the problem as a Stackelberg game. Specifically, the satellites serve as the leaders, who decide the data service price at each time slot. The ground users, on the contrary, are the followers who decide the power control based on their states, the influence from other ground users and the fees paid to satellites. Since the influence is difficult to estimate due to the large number of ground users, we employ the mean field game algorithm to transform the influence from others and satellites into the mean field term, and reformulate the optimization problem as a Stackelberg mean field game (SMFG). Each ground user makes the data offloading decision by learning the future impact of the whole network distributively. For ground users, we solve the power control optimization problem by utilizing the G-prox primal-dual hybrid gradient (PDHG) algorithm, where the Fokker-Planck-Kolmogorov (FPK) equation is converted into a linear form via the Taylor expansion. For satellites, we address the service pricing optimization problem by using the adjoint algorithm. Finally, the numerical results demonstrate the effectiveness of the proposed algorithm.