  We consider online scheduling policies for single-user energy harvesting
communication systems, where the goal is to characterize online policies that
maximize the long term average utility, for some general concave and
monotonically increasing utility function. In our setting, the transmitter
relies on energy harvested from nature to send its messages to the receiver,
and is equipped with a finite-sized battery to store its energy. Energy packets
are independent and identically distributed (i.i.d.) over time slots, and are
revealed causally to the transmitter. Only the average arrival rate is known a
priori. We first characterize the optimal solution for the case of Bernoulli
arrivals. Then, for general i.i.d. arrivals, we first show that fixed fraction
policies [Shaviv-Ozgur] are within a constant multiplicative gap from the
optimal solution for all energy arrivals and battery sizes. We then derive a
set of sufficient conditions on the utility function to guarantee that fixed
fraction policies are within a constant additive gap as well from the optimal
solution.
