# Bell-X, An Opportunistic Time Synchronization Mechanism for Scheduled Wireless Sensor Networks
## 5 Simulations and Testbeds
From this moment on, node 11 will be restarted to observe the time that it takes to get back the synchronization and connect to the RPL topology. The following figures show the beacon-advertising pattern for every single configuration analysed. Figures 9 and 10 show the proposed Bell-X mechanism with different bell configurations, the first one with an Interval Max parameter of 32 s and the second one with 65 s. From now on, these configurations will be called Bell-32 and Bell-65, respectively. Simulations trace the position in the stepped bell (this is, the value of beaconing period, from valley to peak) of node 11 neighbours so all cases are taken into \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Parameters** & **Values** \\ \hline \multicolumn{3}{c}{Global Parameters} \\ \hline \multirow{4}{*}{TSCH} & Scan Duration & 1 s \\  & Timeslot duration & 10 ms \\  & TSCH Slotframe Schedule: Modified Orchestra & EBs: 101 slots in length with only two enabled (TX and RX) \\  & Schedule [27] with multiple slotframes, each & RPL: 31 slots in length with only one enabled (Shared) \\  & \multicolumn{2}{c}{Number of Channels} & 4 channels \\  & Number of Scan Channels & 4 channels \\ \hline \multirow{4}{*}{RPL} & Trickle Timer Interval Min & 4 s \\  & Trickle Timer Interval Doublings & 8 \\ \cline{1-1}  & Trickle Timer Redundancy Constant & 10 \\ \cline{1-1}  & DIS Interval & 60 s \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Protocol stack configuration. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Physical Parameters**} \\ \hline Distance Between Neighbours & 40 m \\ Number of neighbours for central nodes (node 11) & 4 \\ Number of neighbours for nodes in the edges & 3 \\ Number of neighbours for nodes in the corners & 2 \\ Seeds per simulation & 15 \\ Minimum time before node 11 restart & 20 min \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation configuration. consideration. In this article, the X of the Bell-X mechanism represents the maximum value that the beacon transmission period can reach, but the rest of the parameters have the same relevance when controlling the Bell's behaviour. For this reason, it is possible to have different Bell-X configuration under the same name. Table 5 summarizes the configuration parameters for the Bell-X configurations that were proposed. These two configurations have been chosen to evaluate two different behaviours of the Bell-X mechanism. Bell-32 allows for a faster connection while Bell-65 saves energy by sending less advertising traffic. By configuring the values of the Valley Factor, Step Factor, and Peak Factor, it is possible to control the percentage of time that the transmission period is configured with the maximum value. This means, for energy savings, the selected configuration should include longer Peak periods and higher Interval Max, while faster network connectivity is achieved for longer valley periods and shorter Interval Max. Figures 11-13 show a configuration in which the beacon period is a fixed value of 4, 16, and 32 s, respectively. These three configurations with a fixed periodic advertising fit the solution that is  
Figure 10: Bell-65 Configuration. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Bell-32** & **Bell-65** \\ \hline Interval min & 2 s & 4 s \\ Doublings & 4 & 4 \\ Valley Period & 4 & 2 \\ Step Period & 4 & 1 \\ Peak Period & 12 & 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Configuration parameters for the Bell-32 and Bell-65 configurations. Figure 9: Bell-32 Configuration. proposed in the standard, which is the basis for the Contiki implementation. From now on, these three configurations will be called M4s, M16s, and M32s. Finally, Figure 14 shows a configuration in which the beacon transmission period is modified by the RPL Trickle Timer. As the Trickle Timer arrives at its maximum value of 50 s before the end of the first phase of the simulation, once phase two begins it is set directly to its maximum value.