Online scheduling for energy harvesting broadcast channels with finite battery

We consider online transmission scheduling for an energy harvesting broadcast channel with a finite-sized battery. The energy harvests are independent and identically distributed (i.i.d.) in time, and the transmitter gets to know them only causally as they happen. We first consider the case of Bernoulli energy arrivals, and determine the optimum online strategy that allocates power over time and between users optimally. We then consider the case of general i.i.d. energy arrivals, and propose a sub-optimum strategy coined fractional power constant cut-off (FPCC) policy. We develop a lower bound for the performance of the proposed FPCC policy, and a universal upper bound for the capacity region of the energy harvesting broadcast channel. We show that the proposed FPCC policy is near-optimal in that it yields rates that are within a constant gap from the optimum online policy, for all system parameters.