In this paper, a novel approach for joint power control and user schedulingis proposed for optimizing energy efficiency (EE), in terms of bits per unitenergy, in ultra dense small cell networks (UDNs). Due to severe coupling ininterference, this problem is formulated as a dynamic stochastic game (DSG)between small cell base stations (SBSs). This game enables to capture thedynamics of both the queues and channel states of the system. To solve thisgame, assuming a large homogeneous UDN deployment, the problem is cast as amean-field game (MFG) in which the MFG equilibrium is analyzed with the aid oflow-complexity tractable partial differential equations. Exploiting thestochastic nature of the problem, user scheduling is formulated as a stochasticoptimization problem and solved using the drift plus penalty (DPP) approach inthe framework of Lyapunov optimization. Remarkably, it is shown that by weavingnotions from Lyapunov optimization and mean-field theory, the proposed solutionyields an equilibrium control policy per SBS which maximizes the networkutility while ensuring users' quality-of-service. Simulation results show thatthe proposed approach achieves up to 70.7% gains in EE and 99.5% reductions inthe network's outage probabilities compared to a baseline model which focuseson improving EE while attempting to satisfy the users' instantaneousquality-of-service requirements.
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