Finite-Horizon Prediction of Energy Depletions in Off-Grid Wireless Networks

In this paper, we present a simple analytic method that can be used to predict potential energy depletion in off-grid wireless backbone network nodes serving mobile users. The instantaneous energy depletion of the batteries of the network nodes is determined by random energy arrivals and departures and modeled as a G/G/1 queue. To evaluate the online energy depletion probability (EDP), an integral-free asymptotic approach is typically used by assuming that the prediction horizon approaches infinity. However, in many practical cases, the time required by user connections can be rather short. This indicates the need for proactive resource management decisions over finite horizons so that the transmission opportunities with limited energy and time horizons are not wasted. Using Hölder's inequality, we obtain a novel finite-horizon upper bound for the EDP, and the result is compared with the infinite-horizon method. The accuracy of the proposed bound, which is addressed both analytically and numerically, proves to be better for shorter prediction horizons. The finite- and infinite-horizon methods are then applied for an energy provisioning admission control (EP-AC) framework using off-grid backbone network nodes. The key observation of this paper is that the proposed finite-horizon prediction approach admits significantly more users to the network when the connection times are relatively short, while retaining an integral-free closed-form structure suitable for the online evaluation of the EDP.