the packet, and listens for ACK from the AP(s). If No ACK is received in a bounded listening window, device retransmits the packet, and this procedure could be repeated up to $B_{i}-1$ times, where the bound may come from the fair use of the shared medium [@int2; @mag_all] or expiration of data. If data transmission is unsuccessful in $B_i$ attempts, we call it an outage event. The probability of outage for type $i$ in such setting could be derived as: $$\label{rel}\text{P}_{\text o}(i)=\big[1-\text{P}_{\text s}(i) \big]^{n_iB_i},$$ where $\text{P}_{\text s}(i)$ has been derived in theorem \[t3\].

Battery Lifetime Performance (Durability) {#bl}
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Packet generation at each device for most reporting IoT applications can be seen as a Poisson process [@3g]. Then, one can model energy consumption of a device as a semi-regenerative process where the regeneration point has been located at the end of each successful data transmission epoch [@nL]. For a given device of type-$i$, let us denote the stored energy in batteries as $E_{0}$, static energy consumption per reporting period for data acquisition from environment and processing as $E_{\text{st}}$, circuit power consumption in transmission mode as $P_{c}$, and inverse of power amplifier efficiency as $\eta$. Then, the expected battery lifetime is 