# Multihop Latency Model for Industrial Wireless Sensor Networks Based on Interfering Nodes
## 5 Results and Model Validation  
The different results obtained from the simulations described above are shown below. The main results show the evolution of the DAO message reception time as a function of the number of interfering nodes. To represent this time as a function of the interfering nodes of several hops, multidimensional graphs have been plotted, so that the behaviour of this configuration can be seen by representing the most relevant slices. Figure 9 shows the results obtained for the simulations with a single hop. The curve represents the equation obtained from the analytical model, while the asterisks show the average value obtained from the simulations, and the typical deviation is represented by a plus sign. As can be seen in the figure, the results obtained from the simulations show a behaviour very close to the curve defined by the model. An interesting aspect that can be deduced from this figure is the behaviour of the standard deviation. Since the messages \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Duration of the TSCH timeslot & 10 ms \\ EB transmission period & 4 s \\ DIO transmission period & 16 s \\ Orchestra slotframe size for EBs & 397 \\ Orchestra slotframe size for RPL & 31 \\ Number of TSCH channels & 4 \\ Number of scan channels & 4 \\ \hline \end{tabular}
\end{table} 
Table 2: Configuration of protocol stack parameters. Figure 8: Evolution of the PDR value as a function of the number of interfering nodes, calculated empirically. are sent only in the slots dedicated to RPL, there is only one opportunity to send a message every 310 ms, which determines that the latency increases by multiples of this value each time interference occurs. Figure 10 shows the two-dimensional response for the two-hop configurations. To facilitate the representation and comparison of the results of these configurations, those slices of the surface corresponding to the first level interfering have been chosen, representing the curves in Figure 11.  
Figure 10: Multidimensional response of the DAO reception time for two hops. Figure 9: Simulation results for one hop. Each of the colours represents one of the sections marked in Figure 10. The curves represent the response of the proposed analytical model, while the asterisk and the plus sign represent the average and standard deviation obtained from the simulations. As with the single-hop simulations, the analytical model fits correctly, with the standard deviation increasing as the interference increases in each of the hops. For simulations with three hops, the representation would be characterized by a volume, since the three axes represent the interfering nodes in each of the hops. However, Figure 12 shows only the four surfaces of interest according to the simulated configurations. Figure 13 shows these 4 surfaces separately, indicating the sections of interest to be analysed, which correspond to the simulated configurations. Figure 11: Simulation results for two hops. Figure 12: Multidimensional response of 3-hop configurations. As in the previous cases, Figure 14 shows only the curves for each of the configurations of interest, in order to show in a simple way the comparison of the results with the analytical model. In these last configurations with three hops, the results obtained in the simulations also coincide with the expected behaviour of the proposed model. Analysis of the results presented in Figures 9, 11 and 14 shows that the behaviour of the proposed model, as a function of the number of hops to the root node and the number of interfering nodes, is similar to the real response of WSN based on TSCH and RPL.