approximation for the energy overflow probability, where we characterize the energy decay rate (i.e., the decay rate of the tail distribution of the stored energy) in the battery as a measure of energy utilization.

2.  Mapping the system evolution to a Markov chain, in which we have one state representing the energy outage, and other states representing the number of time frames since the last energy outage event, we provide an expression for the energy outage probability.

3.  Under energy overflow and outage constraints, we obtain the average data service rate in the wireless channel. Subsequently, we identify the effective capacity of the system, which characterizes the maximum data arrival rate at the transmitter buffer when there are QoS requirements in the form of constraints on the buffer overflow probability.

Apart from this paper, we invoke large deviation theory and queueing theory in [@akin2017energy; @akin2018energy], where we characterize the energy underflow probability. Specifically in this paper, we have a focus primarily on controlling energy waste and then energy outages under QoS constraints, whereas in [@akin2017energy; @akin2018energy], we principally control energy underflows, and hence outages, in communication settings under stricter QoS constraints, where transmission interruptions are not tolerated at any time.

