Single-User Channel With Data And Energy Arrivals: Online Policies

We consider a single-user channel in which the transmitter is equipped with finite-sized data and energy buffers. The transmitter receives energy and data packets randomly and intermittently over time and stores them in the finite-sized buffers. The arrival amounts are known only causally as they happen. We study the online power allocation problem, in which the transmitter relies only on the causal arrival (energy and data) information. We focus on the special case when the energy and data arrivals are fully-correlated. We first study the case when the arrivals are Bernoulli. For this case, we determine the optimal policy. Inspired by this policy and in order to study the case of general fully-correlated arrivals, we propose a structured policy and bound its performance by a multiplicative gap from the optimal. We then show that this policy is optimal when the energy arrivals dominate the data arrivals, and is within a constant additive gap from the optimal policy when the data arrivals dominate the energy arrivals.