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

Abstract

We consider a distributed user association problem in the downlink of a small cell network, where small cells obtain the required energy for providing wireless services to users through ambient energy harvesting. Since energy harvesting is opportunistic in nature, the amount of harvested energy is a random variable, without a priori known characteristics. 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 by commodities.The utility scores of small cells depend on the amount of harvested energy, formulated as natures' state. Under this model, the problem is to assign users to small cells, so that the aggregate network utility is maximized. The solution is the general equilibrium under uncertainty, also called Arrow-Debreu equilibrium. We show that in our setting, such equilibrium not only exists, but also is unique and is Pareto optimal in the sense of expected aggregate network utility. We use the Walras' tatonnement process with some modifications in order to implement the equilibrium efficiently.

Energy Efficient Resource Allocation in Machine-to-Machine Communications With Multiple Access and Energy Harvesting for IoT

“…(q q q, t t t) due to nonconvex objective function (27a) and constraints (27b)-(27c). Before solving problem (27), we have the following theorem. (27) is a convex problem w.r.t.…”

“…Proof: Please refer to Appendix E. According to the IPCTA-NOMA algorithm, the major complexity lies in solving the convex problem (27) with fixed τ τ τ . Considering that the dimension of the variables in problem…”

“…Obj , (E.1) where the inequality follows from that (q q q (v) , t t t (v) ) is a suboptimally optimal solution of problem (27) with fixed sets S (v) ij , while (q q q (v−1) , t t t (v−1) ) is the initial feasible solution of problem (34) with fixed sets S (v) ij . Furthermore, the total energy value (27a) is always non-negative.…”

“…In particular, direct and non-direct energy transfer based schemes for EH were investigated in [23], while in [24], the optimization of green-energy-powered cognitive radio networks was surveyed. Recently, the downlink resource allocation for EH in small cells was studied in [25]- [27]. By using EH, MTCDs are able to harvest wireless energy from radio frequency (RF) signals [28]- [31], and the system energy can be significantly improved.…”

Distributed Task Management in Cyber-Physical Systems: How to Cooperate Under Uncertainty?

“…As conventional, we assume the existence of a noiseless control channel, implying that the signals arrive error-free at CPSs and/or the auctioneer. Such an assumption is justified by the existence of coding schemes that reduce the transmission error probability to almost zero [41]; therefore, it is widely used in game theory and networks literature (see [23] and [42], among many others). While the analysis of the problem with noisy communication channel is beyond the scope of our work, there are some research works that study such setting.…”