words, assuming that there is a constant energy demand while the energy arrival process has a stochastic nature, we can express the energy overflow probability with an exponential function as long as the constant energy demand is between the average and maximum values of the energy arrival process. Equivalently, given that there is a constant energy arrival process while the energy demand process is stochastic, we can express the energy overflow probability as an exponential function when the constant value of the energy arrival process is between the minimum and average values of the energy demand process.

Energy Outage {#sec:energy_outage}
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Recall that when there is not enough energy in the battery, i.e., when the energy in the battery is less than what the transmitter demands, an *energy outage* occurs; the transmitter consumes all the energy available in the battery, leaving the battery empty. We say that following an energy outage event, the battery enters state 0. Herein, we define a state space $\mathcal{W}=\{0,1,\cdots\}$ consisting of non-negative integers, where the state $w(i)$ at time $i$ denotes the consecutive number of times the harvested and stored energy successfully meet the energy demand since the last energy outage event. More specifically, assume 