  We consider the delay minimization problem in an energy harvesting
communication network with energy cooperation. In this network, nodes harvest
energy from nature for use in data transmission, and may transfer a portion of
their harvested energies to neighboring nodes through energy cooperation. For
fixed data and energy routing topologies, we determine the optimum data rates,
transmit powers and energy transfers, subject to flow and energy conservation
constraints, in order to minimize the network delay. We start with a simplified
problem with fixed data flows and optimize energy management at each node for
the case of a single energy harvest per node. This is tantamount to
distributing each node's available energy over its outgoing data links and
energy transfers to neighboring nodes. For this case, with no energy
cooperation, we show that each node should allocate more power to links with
more noise and/or more data flow. In addition, when there is energy
cooperation, our numerical results indicate that, energy is routed from nodes
with lower data loads to nodes with higher data loads. We extend this setting
to the case of multiple energy harvests per node over time. In this case, we
optimize each node's energy management over its outgoing data links and its
energy transfers to neighboring nodes, over multiple time slots. For this case,
with no energy cooperation, we show that, for any given node, the sum of powers
on the outgoing links is equal to the single-link optimal power over time.
Finally, we consider the problem of joint flow control and energy management
for the entire network. We determine the necessary conditions for joint
optimality of a power control, energy transfer and routing policy. We provide
an iterative algorithm that updates the data and energy flows, and power
distribution over outgoing data links. We show convergence to a Pareto-optimal
operating point.
