# Modeling the Energy Performance of LoRaWAN
## 5 Evaluation
### End-Device Lifetime  
Leveraging the average current consumption results obtained in the previous section, we next calculate the theoretical lifetime of a battery-operated end-device by using (12) and (29). We assume a battery capacity of 2400 mAh. Figure 13 illustrates the end-device lifetime for BER = 0 as a function of \(T_{Notif}\), and the DR, in unacknowledged transmission. Logically, the end-device lifetime behavior is the inverse of the current consumption one presented in Section 5.1. A greater end-device lifetime is obtained with higher \(T_{Notif}\) and DR. A maximum value of 5.96 years is obtained with DR6 and \(T_{Notif}\) = 1440 min. In addition, it can be shown that regardless of the DR employed, end-device lifetime tends asymptotically to 6.19 years, which can be achieved if the end-device is always sleeping (i.e., \(T_{Notif}\) = \(\infty\)). Note also that lower DRs lead to lower end-device lifetime, and this effect increases as \(T_{Notif}\) decreases. For example, for \(T_{Notif}\) = 5 min, end-device lifetime values fall below one year, ranging from 0.26 to 0.83 years (for DR0 and DR5, respectively). If \(T_{Notif}\) increases, a lifetime of several years is possible. For example, for \(T_{Notif}\) = 60 min and \(T_{Notif}\) = 360 min, multi-year lifetimes between 2.13 and 3.76 years, and between 4.55 and 5.52 years, can be achieved, respectively. We next compare end-device lifetime results of unacknowledged and acknowledged transmission (see Figure 14). As explained in Section 5.1.2, acknowledged transmission follows a tendency very similar to the unacknowledged one. The lower current consumption of acknowledged transmission yields higher end-device lifetime. Similarly to Section 5.1.2, the maximum end-device lifetime difference between unacknowledged and acknowledged transmission is \(\sim\)16%, for DR5 and a notification period of 0.5 min. For other DRs, such maximum difference tends to decrease, down to \(\sim\)3% for DR0. On the other hand, Figure 15 shows the impact of the frame payload size on end-device lifetime. In order to obtain the range of possible end-device lifetime values, 1-byte and also maximum-sized payload are considered for data messages in acknowledged transmission. The corresponding end-device lifetimes are depicted in Figure 15, as a function of \(T_{Notif}\), for different DR settings, and  
Figure 12: Impact of \(p_{coll}\) on the average current consumption of the end-device in acknowledged transmission, as a function of \(T_{Notif}\), for different DR settings and for BER = 0.  
for BER = 0. Only DR0 and DR5 are shown in the figure for the sake of illustration clarity. Impact of the payload size is noticeable only when \(T_{\textit{Notify}}\) is low. For DR0 and \(T_{\textit{Notify}}\) = 5 min, end-device lifetime ranges from 0.27 up to 0.41 years (i.e., a \(\sim\)52% relative difference), for the payload sizes considered. For DR5 and \(T_{\textit{Notify}}\) = 1 min, end-device lifetime ranges from 0.18 to 0.26 years (i.e., a relative difference of \(\sim\)49%). However, impact of frame payload size decreases when \(T_{\textit{Notify}}\) increases because sleep state, and thus its current consumption, becomes dominant. For example, for a \(T_{\textit{Notify}}\) = 60 min and DR0, end-device lifetime values range from 2.17 to 2.90 years (i.e., 33.4% difference), and from 3.90 to 4.44 years (i.e., a 13.78% difference) for DR5. Next we evaluate impact of BER on end-device lifetime (Figure 16). Similarly to the observations made in Section 5.1.2, end-device lifetime may decrease by up to one order of magnitude for DR5 and for the range of BER values considered. Impact of BER on end-device lifetime is lower for DR0, and it decreases with \(T_{\textit{Notify}}\), since end-device lifetime tends asymptotically to the lifetime of an always-sleeping end-device as \(T_{\textit{Notify}}\) increases. Finally, we also study the impact of \(p_{\textit{coll}}\) on end-device lifetime (Figure 17).