## 6 Model Result
### Multi-Hop LoRaWAN Scenarios  
The following experiments estimate the capacity throughput and energy cost for temperature and pressure sensors; the sensors have different sample rates. Three multi-hop scenarios are used to evaluate the performance model. In these scenarios, the area length is set at 86 km, whereas it is set to 10 km in the multi-hop scenario described in Section 4.1. Also, we have 443 devices. The three scenarios have different hop ranges. The first scenario is hop-by-hop, where all sensors cooperate in communication. In the other scenario, the number of sensors involved in communication is reduced. Packets were sent to the third neighbor in the second scenario, and to the ninth neighbor in the third. Figure 7 shows the multi-hop scenarios. We considered different sensor types involving temperature and pressure sensors (temperature sensor generating eight packets/day and pressure sensor generating 24 packets/day). The payload size varied between 20, 30, and 51 bytes, and the other parameter values that were considered were SF = 7, BW = 125 kHz, TP = 2 dBm, and CR = 1. Table 4 shows the parameters of the scenarios. We used MATLAB to perform all evaluations. In the rest of this section, we will present the multi-hop LoRaWAN model results, showing the throughput and network capacity results and then the energy consumption results of both sensor types. We first estimated the throughput of both types of sensors for various payload sizes and used these results to assess the data traffic and network congestion, then discussed the LoRaWAN throughput limitation. Finally, we estimated the energy consumption of both sensor types at different multi-hop scenarios. In our experiments, we computed the highest limit the throughput could reach (traffic limitation) by considering the capability of the LoRaWAN. Two aspects affect the capability: the maximum bit rate and the maximum transmitted packets (based on duty cycle and ToA). Figure 6: Total energy consumption per day for the 50 devices—single-hop and multi-hop scenarios— (10 km) where the payload is 20 bytes. Results and Discussions  
The following throughput and energy consumption results were calculated using our analytical model for both sensor types and for each multi-hop scenario. Figure 8 presents the analysis of the generated packets per day for temperature sensors via the sensor network according to multi-hop scenarios. For example, device 400 generates 3200 packets in the first scenario, 1072 packets in the second, and 360 packets in the third. Scenario 1 obtained the highest throughput compared to the other scenarios. Figure 9a shows the maximum number of generated packets per day that the network can accommodate in the instance of a pressure sensor. \begin{table}
\begin{tabular}{c c} \hline \hline
**Study Area Length** & 88.6 km \\ \hline
**Distance (m)** & 200 m \\ \hline
**GWs** & 2 \\ \hline
**Devices** & 443 devices \\ \hline
**Payload** & 20 bytes \\ \hline
**BW** & 125 kHz \\ \hline
**SF** & 7 \\ \hline
**CR** & 1 \\ \hline
**TP** & 2 dBm \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experiment parameters for the multi-hop scenarios. Figure 7: Multi-hop communication scenarios [9]: (**a**) in the first scenario, the data are sent to the next neighbor (hop-by-hop); (**b**) in the second scenario, the data are sent to the third neighbor until the GW; (**c**) in the third scenario, the data are sent to the ninth neighbor until the GW. We computed the ToA to determine the maximum number of packets transmitted and the expected energy consumption. As we set the SF = 7 and BW = 125 kHz, the maximum bit rate that can be transmitted is 5470 bit/s, so the data traffic can be handled in all three scenarios and for both types of sensors. In order to determine the maximum number of packets that could be transmitted, we used Equation (12). When the payload is 51 bytes, ToA is equal to 118 ms, which results in a maximum packet rate equal to 305 packets/h.