## 6 Model Result
### Results and Discussions  
The following results were calculated using our analytical model for both single-hop and multi-hop scenarios. Table 3 shows the capacity and throughput and also the maximum number of packets that can be transmitted according to the LoRaWAN duty cycle. The results in Table 3 show that the multi-hop scenario achieves more throughput compared to the single-hop, for example when the distance from the sensor to the GW is 6 km and the payload is 51 bytes, in a single-hop scenario the throughput is 21,504 bytes/h and the maximum packet rate transmitted is 97 packets/h, whereas in the multi-hop scenario, the throughput is 391,680 bytes/h and the packet rate is 7320 packets/h. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Study Area Length** & \multicolumn{2}{c}{10 km} \\ \hline
**Communication Topology** & Single-hop & Multi-hop \\ \hline
**Distance (m)** & 200 & 200 \\ \hline
**Devices** & 50 & 50 \\ \hline
**Max No. Hops** & 1 & 49 \\ \hline
**No. Packets (packets/day)** & \multicolumn{2}{c}{24} \\ \hline
**Experiment Duration** & \multicolumn{2}{c}{1-day} \\ \hline
**LoRaWAN Parameters** & CR = 1, BW = 125 KHz, TP = 2 dBm, Payload = 20, 30, 51 bytes \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Single-hop and multi-hop experiment parameters. Figure 3 shows the generated packets per day in a single hop at different payloads (20, 30, 51 bytes). It is limited by GW coverage, as we discussed previously. The network has high generated data traffic when payload = 51 bytes. Figure 4 shows a throughput comparison between single- and multi-hop scenarios (when the payload length is equal to 20 bytes). The multi-hop LoRaWAN monitoring network achieved more throughput than the single-hop network. Considering the previous results, the multi-hop solution has more throughput than the single-hop by 38%; however, it increases the data traffic (leading to network congestion). Furthermore, in a single-hop network, the sensors are deployed non-uniformly (the zone close to GW has a larger number of sensors, and it decreases when we go far away). That affects scalability. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Single-Hop**} & \multicolumn{3}{c}{**Multi-Hop**} \\ \cline{3-10}
**Distance to** & **Devices** & **Payload** & **Total** & **Max. Packets** & **Devices** & **Payload** & **Total** & **Max. Packets** \\
**GW (km)** & **Devices** & **(bytes)** & **Throughput per Node** & **(bytes/h)** * & **(bytes/s)** & **Throughput per Node** & **per Node** \\ \hline \multirow{2}{*}{**4 km**} & \multirow{2}{*}{\(18\)} & 20 & 15,120 & 268 & \multirow{2}{*}{20} & 20 & 680,400 & 24,000 \\ \cline{3-10}  & & 30 & 18,576 & 233 & & 30 & 835,920 & 19,776 \\ \cline{3-10}  & & 51 & 27,648 & 175 & \multirow{2}{*}{10} & 51 & 1,244,160 & 14,640 \\ \cline{3-10}  & & 20 & 11,760 & 145 & & 20 & 214,200 & 12,000 \\ \cline{3-10}
**6 km** & 14 & 30 & 14,448 & 125 & \multirow{2}{*}{14} & 20 & 30 & 263,160 & 9888 \\ \cline{3-10}  & & 51 & 21,504 & & 97 & \multirow{2}{*}{10} & 51 & 391,680 & 7320 \\ \cline{3-10}  & & 20 & 8400 & 79 & & 20 & 130,200 & 12,000 \\ \cline{3-10}
**8 km** & 10 & 30 & 10,320 & 67 & & 30 & 159,960 & 9888 \\ \cline{3-10}  & & 51 & 15,360 & 51 & & 51 & 238,080 & 7320 \\ \hline \multirow{2}{*}{**10 km**} & \multirow{2}{*}{\(8\)} & 20 & 5040 & 43 & \multirow{2}{*}{10} & 20 & 46,200 & 12,000 \\ \cline{3-10}  & & 30 & 6192 & 36 & & 30 & 56,760 & 9888 \\ \cline{3-10}  & & 51 & 9216 & 27 & & 51 & 84,480 & 7320 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Capacity and throughput calculations for single-hop and multi-hop scenarios. Figure 3: Generated bytes per day for 50 devices (10 km)—single hop scenario using different payloads (20, 30, 51 bytes). For energy-cost estimation, we computed the energy consumption per node in the single-hop and multi-hop for 1 day with a payload of 20 bytes. The LoRaWAN configurations for single-hop considered SF values equal to 7, 8, 9, 10, and 11, whereas for multi-hop scenarios, SF was considered to be equal to 7.