  For a general energy harvesting (EH) communication network, i.e., a network
where the nodes generate their transmit power through EH, we derive the
asymptotically optimal online power allocation solution which optimizes a
general utility function when the number of transmit time slots, $N$, and the
battery capacities of the EH nodes, $B_{\rm max}$, satisfy $N\to\infty$ and
$B_{\rm max}\to\infty$. The considered family of utility functions is general
enough to include the most important performance measures in communication
theory such as the average data rate, outage probability, average bit error
probability, and average signal-to-noise ratio. The proposed power allocation
solution is very simple. Namely, the asymptotically optimal power allocation
for the EH network is identical to the optimal power allocation for an
equivalent non-EH network whose nodes have infinite energy available but their
average transmit power is constrained to be equal to the average harvested
power and/or the maximum average transmit power of the corresponding nodes in
the EH network. Moreover, the maximum average performance of a general EH
network converges to the maximum average performance of the corresponding
equivalent non-EH network, when $N\to\infty$ and $B_{\rm max}\to\infty$.
Although the proposed solution is asymptotic in nature, it is applicable to EH
systems transmitting in a large but finite number of time slots and having a
battery capacity much larger than the average harvested power and/or the
maximum average transmit power.
