Distributed User Association in Energy Harvesting Small Cell Networks: An Exchange Economy With Uncertainty

We consider a user association problem in the downlink of a small cell network, where small cells are powered solely through ambient energy harvesting. Since energy harvesting is opportunistic in nature, the amount of harvested energy is a random variable, without a priori known statistical characteristics. Thus, at the time of user association, the amount of available energy is unknown. We model the network as a competitive market with uncertainty, where self-interested small cells, modeled as consumers, are willing to maximize their utility scores by selecting users, represented as commodities. The utility scores of small cells depend on the random amount of harvested energy, formulated as nature's state. For this model we prove the existence of Arrow-Debreu equilibrium. In addition, we analyze the equilibrium with respect to uniqueness, Pareto-efficiency, and social-optimality. Moreover, based on the Walras' tatonnoment process and the static knapsack problem, we develop an efficient distributed user association scheme which converges to the equilibrium. We demonstrate the effectiveness of our proposed model through intensive numerical analysis.