performance levels in a general class of EH communication systems under energy overflow and outage probability constraints, and QoS requirements. Similarly to [@srivastava2013basic] and [@zhang2015joint], we take advantage of large deviation theory and Markov processes; however, different from these studies, we consider simultaneously the energy overflow and outage probabilities in an EH communication system, and perform the throughput analysis. Specifically, while [@srivastava2013basic] provides the energy underflow probability in the battery using large deviation theory , the authors in [@zhang2015joint] maximize the effective capacity under the energy underflow probability constraint. On the other hand, we formulate the energy overflow probability in the battery as an exponential function of the battery size by invoking large deviation theory, and the energy outage probability by employing the Markov process analysis. Particularly, we consider that the transmitter initially sets a transmission power policy taking into account the energy overflow and outage probability constraints, and the energy arrival statistics. It sets the transmission rate based on the power allocation policy. We assume that the transmitter knows the channel statistics, but is unaware of the instantaneous channel state. Specifically, we have the following contributions:

1.  Using large deviation theory and queueing theory, we formulate a simple exponential 