Joint Stochastic Geometry and Mean Field Game Optimization for Energy-Efficient Proactive Scheduling in Ultra Dense Networks

In this paper, we investigate the energy efficiency performance of optimal proactive scheduling strategies in the context of ultra-dense networks. The network consists of a superposition of homogeneous Poisson point process, whereas the users requests follow a space-time homogeneous point process. The objective is to define the optimal transmission powers at any time, that allows to completely serve every user request, while minimizing the total consumed energy. We also assume the system has predictive knowledge about the future transmission contexts. The problem is cast as a dynamic stochastic game which is hard to solve in ultra-dense networks, due to a complex coupling in the interference term, the large number of elements interacting, as well as uncertainties on the channel dynamics, interference, and future requests. Our contribution first lies in addressing the inherent complexity issue of the optimization, by transitioning into an equivalent and more tractable mean field game. Second, we propose to combine this mathematical framework with elements of stochastic geometry. The numerical simulations provide good insights on notable performance gains in terms of energy efficiency, compared to reference scheduling strategies. Additional simulations harnessing the impact of future knowledge uncertainty on the performance of the proposed strategies are also provided.