otherwise. In order to ensure the delivery of the data, we assume that a simple automatic-repeat-request (ARQ) mechanism exists to acknowledge a successful reception, or to trigger the retransmission of erroneously decoded data. We assume that the transmitter does not have the channel state information, but knows the channel statistics. If the number of transmitted bits is smaller than the maximum rate that can be supported by the channel capacity in the $i^{\text{th}}$ time frame, transmission is assumed to be successful; otherwise, a decoding error occurs.

Energy Storage Characterization {#sec:Energy_Storage_Characterization}
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We explore the battery dynamics taking into consideration energy overflows and outages, and establish limits on the energy overflow and outage probabilities as the statistical battery (or energy management) constraints. Therefore, observing the structural similarity between a single server queuing system and the aforementioned storage model, we invoke queueing theory, large deviations theory [@chang_book] and network calculus [@jiang_book] to understand the energy overflows in the battery. Then, projecting subsequent energy demands that have been satisfied, and energy outages on a Markov process, we characterize the energy outage probability.

Energy Overflow {#sec:energy_overflow}
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We know that given a single service provider, the steady-state queue length tail distribution in a queueing 