# Low Power Multi-Hop Networking Analysis in Intelligent Environments
## 5 Discussion of the Results
### Multi-Hop Communications with Bluetooth Sniff Low Power Mode  
On the other hand, several figures are available to analyze the latency in Bluetooth multi-hop networks with nodes in sniff mode. Figure 6a summarizes the 95% percentile results of the latency tests vs. amount of hops for the master-to-slave communication when links in the network are always in the sniff mode. The results when the communication is from slave to master are compiled in Figure 6b. As in the park mode, in these two figures four cases of inactivity intervals were considered, namely 100, 500, 1000 and 2000 ms. Figure 6 shows that the latency in communication from master to slave when links are in the sniff mode is very close to the latency in the communication from slave to master. There is no major difference between these two latencies. The point is that the sniff mode can be exited by either the master or the slave sending a specific request command so that the requested device replies with the according acceptance command. If the master requests an exit from sniff mode it shall enter sniff transition mode and then send an _LMP_unsniff_req_ command. On the one hand, when the slave receives the _LMP_usniff_req_ it shall exit from sniff mode and reply with an _LMP_accepted_ command. On the other hand, when the master receives the _LMP_accepted_ command it shall exit from sniff transition mode and enter active mode. Figure 7a shows the dependence of the latency with the inactivity interval in the same case, i.e., master-to-slave communication when links are in sniff mode. The dependence of the latency with \begin{table}
\begin{tabular}{c c c} \hline
**Coefficient** & **Master-to-Slave** & **Slave-to-Master** \\ \hline \(t_{1 park}\) (ms) & 990 & 410 \\ \(\delta_{1}\) (ms) & 250 & 145 \\ \(\beta\) (\%) & 40 & 38 \\ \(\delta_{2}\) (ms) & 10 & 8 \\ R\({}^{2}\) & 0.9527 & 0.9396 \\ MSE & 0.0914 & 0.0895 \\ \hline \end{tabular}
\end{table} 
Table 1: Values of the coefficients in Equation (1) for master-to-slave and slave-to-master multi-hop communication with nodes in park mode. the inactivity interval for the slave-to-master communication when links are in the sniff mode can be seen in Figure 7b. As in the park mode, in these two figures five cases are depicted depending on the amount of hops considered, i.e., from two to six hops. Figure 7 confirms what Figure 6 points out, i.e., the latency from end-to-end in Bluetooth multi-hop wireless communications when links are always in the sniff mode exhibits linear dependence with the inactivity period of the nodes. The latency also depends on the amount of hops in the communication. This phenomenon happens not only in the master-to-slave communication but also in the slave-to-master communication. In addition, Figure 7 points out that the latency from end-to-end in Bluetooth multi-hop wireless communications when links are always in the sniff mode exhibits linear dependence with the amount of hops. It can be understood that there is no significant additional delay in the multi-hop communication due to errors or retransmissions. This phenomenon happens not only in the master-to-slave communication but also in the slave-to-master communication. These results are the basis to propose a model for the latency in asynchronous communications along Bluetooth multi-hop networks when master-slave gateway nodes are in sniff low power mode. Figure 6: Latency (vertical, seconds) vs. amount of hops (horizontal). Links always in _sniff_ mode. Inactivity intervals: 100, 500, 1000 and 2000 ms. (**a**) _master-to-slave_ communication; (**b**) _slave-to-master_ communication. Figure 7: Latency (vertical, seconds) vs. inactivity interval (horizontal, milliseconds). Links always in _sniff_ mode. From two to six hops. (**a**) _master-to-slave_ communication; (**b**) _slave-to-master_ communication. The model describes and anticipates the upper limit of the latency in Bluetooth networks with linear topology. It embraces the four inactivity periods considered in the tests, i.e., 100, 500, 1000 and 2000 ms.