# HARE: Supporting Efficient Uplink Multi-Hop Communications in Self-Organizing LPWANs
## 7 Results
### Delay  
The time difference between the transmission of a data packet and the proper reception of the e2e ACK determines the end-to-end communication delay of an STA (\(D_{\text{e2e}}\)). This value can be computed by using the following equation:  
\[D_{\text{e2e}}=T_{r}+(r-1)\cdot T_{r}+(i-1)\cdot R\cdot T_{r}=(r+(i-1)\cdot R) \cdot T_{r}, \tag{4}\]  
where \(T_{r}\) is the duration of a ring slot, \(r\) is the ring to which the STA belongs, \(i\) is the index of the transmission window in which the STA receives the e2e ACK (with \(i\in[1,w]\)), and \(R\) is the total number of network rings.  
Figure 19 shows the computed average end-to-end communication delay (\(\overline{D_{\text{e2e}}}\)) of uplink transmissions from Section 7.2 for the two considered RDC sublayers and the two different network topologies. While the ring slot duration has a constant value of \(T_{r}=5\) s, the rest of variables (\(r\), \(i\), and \(R\)) varied depending on the network setting, and were obtained from _statistics packets_ gathered by the GW.  
Figure 18: Average total energy consumption per STA after a 1-hour test with \(T_{p}=3\) min.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Battery Lifetime (Days)**} \\ \cline{3-5}  & & \(T_{p}=3\) min & \(T_{p}=1\) h & \(T_{p}=4\) h \\ \hline \multirow{5}{*}{**NullRDC**} & \(E_{0/0}\) & 2.37 & 47.35 & 187.87 \\  & \(E_{10/5}\) & 2.21 & 44.19 & 175.41 \\  & \(E_{20/10}\) & 2.18 & 43.46 & 172.53 \\  & \(E_{30/15}\) & 2.14 & 42.70 & 169.53 \\ \cline{2-5}  & \multirow{2}{*}{**Multi-hop**} & \(E_{0/0}\) & 2.63 & 52.51 & 208.17 \\  & & \(E_{10/5}\) & 2.44 & 48.60 & 192.79 \\  & & \(E_{20/10}\) & 2.24 & 44.66 & 177.27 \\  & & \(E_{30/15}\) & 2.07 & 41.35 & 164.23 \\ \hline \multirow{5}{*}{**X-MAC**} & \multirow{5}{*}{**Single-hop**} & \(E_{0/0}\) & 4.46 & 88.75 & 349.64 \\  & & \(E_{10/5}\) & 4.27 & 85.00 & 335.07 \\ \cline{1-1}  & & \(E_{20/10}\) & 4.52 & 89.99 & 354.46 \\ \cline{1-1}  & & \(E_{30/15}\) & 4.56 & 90.79 & 357.55 \\ \cline{1-1} \cline{2-5}  & \multirow{2}{*}{**Multi-hop**} & \(E_{0/0}\) & 5.29 & 105.17 & 413.16 \\ \cline{1-1}  & & \(E_{10/5}\) & 5.08 & 101.04 & 397.21 \\ \cline{1-1}  & & \(E_{20/10}\) & 4.53 & 90.10 & 354.85 \\ \cline{1-1}  & & \(E_{30/15}\) & 4.39 & 87.38 & 344.31 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Average lifetime of an 800 mAh battery.  
As expected, multi-hop topologies suffer from higher delays (always at least 50% more than single-hop links in the considered cases) as messages must go through several hops until reaching their destination. With regard to RDC sublayers, X-MAC outperforms NullRDC in terms of delay, as STAs can send their messages _earlier_ (i.e., without needing so many transmission windows).  
Although end-to-end delay is a clear disadvantage of multi-hop topologies, the HARE protocol stack is intended to be used in non-delay sensitive applications. In any case, these values could be improved by adjusting the number of transmission windows (\(w\)), the duration of each ring slot (\(T_{r}\)), or simply by developing schemes where STAs sent critical and/or event-based traffic (i.e., alarms) directly to the GW by using a reserved time slot.