  In this paper, we study the joint routing-scheduling problem in energy
harvesting communication networks. Our policies, which are based on stochastic
subgradient methods on the dual domain, act as an energy harvesting variant of
the stochastic family of backpresure algorithms. Specifically, we propose two
policies: (i) the Stochastic Backpressure with Energy Harvesting (SBP-EH), in
which a node's routing-scheduling decisions are determined by the difference
between the Lagrange multipliers associated to their queue stability
constraints and their neighbors'; and (ii) the Stochastic Soft Backpressure
with Energy Harvesting (SSBP-EH), an improved algorithm where the
routing-scheduling decision is of a probabilistic nature. For both policies, we
show that given sustainable data and energy arrival rates, the stability of the
data queues over all network nodes is guaranteed. Numerical results corroborate
the stability guarantees and illustrate the minimal gap in performance that our
policies offer with respect to classical ones which work with an unlimited
energy supply.
