## 6 DIS-Trickle: A Mechanism for Accelerating Network Convergence
### DIS-Trickle Evaluation
Note that this density corresponds to a sparse network and, as shown in Figure 4, the average network convergence time is high in the absence of the DIS-based mechanism, therefore we can observe the maximum influence of DIS-Trickle on network convergence performance within the range of considered network densities. The results obtained for these different configurations are plotted in Figure 21, which shows average results for the following performance parameters: network convergence time, number of DIO and DIS messages transmitted, and number of collisions (considering both DIO and DIS messages) during network convergence. Note that Configuration 1 (dashed line curve results in Figure 21) is the default set of DIS-Trickle parameter values used in our previous simulations. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Parameter**} & \multicolumn{5}{c}{**Configuration**} \\ \cline{2-6}  & **1** & **2** & **3** & **4** & **5** \\ \hline DIS initial delay & 200 ms & 100 ms & 300 ms & 200 ms & 200 ms \\ Interval length, \(I_{DIS}\) & 30 ms & 30 ms & 30 ms & 15 ms & 45 ms \\ \hline \end{tabular}
\end{table} 
Table 4: DIS-Trickle parameter configurations evaluated. Figure 20: Influence of using DIS-Trickle on the number of collisions in the small, medium and large networks for different average node degrees, NDeg, as a function of the redundancy constant, \(k\), when the \(I_{min}\) value is set to 8 ms compared with not using DIS messages: (**a**) Small network size, (**b**) medium network size, and (**c**) large network size. As shown in Figures 21a and 21b, when the initial delay is set to 100 ms (Configuration 2), the network convergence time and the total number of RPL messages transmitted are greater than those obtained for an initial delay of 200 ms. The main reason is that 100 ms is lower than the time needed by DIO messages to propagate through the network. Thus, nodes that are not close to the root may start to prematurely (and unnecessarily) transmit DIS messages while their neighbors are receiving or sending DIO messages, increasing the number of collisions during the network convergence process (Figure 21e). On the other hand, when the initial delay is set to 300 ms (Configuration 3), network convergence time increases compared with using Configuration 2, due to the slower rate of DIS message generation (Figure 21d), while the rest of performance parameters do not vary significantly. As previously mentioned, a suitable value for the initial delay has to be set taking into account network characteristics such as density and size. From the results obtained, an initial delay of 200 ms offers good performance in the scenario considered, since it offers reasonably low network convergence time, low number of DIO and DIS message transmissions and low number of collisions. Figure 21: Comparing performance of different DIS-Trickle parameters settings (shown in Table 4) in medium network scenario when the average nodes degree is 5. Regarding the length of the DIS-Trickle interval, \(I_{DIS}\), we have tested values within the range of the DIS response time values presented in subsection 6.1. Figure 21 illustrates that, although a small value for \(I_{DIS}\) such as 15 ms (Configuration 4), reduces slightly the network convergence time compared with the default \(I_{DIS}\) value of 30 ms (Configuration 1), it causes the rest of performance parameters analyzed to significantly degrade. When \(I_{DIS}\) is set to a low value such as 15 ms, many premature DIS message transmissions take place, leading also to a high number of collisions. On the other hand, using a greater value for \(I_{DIS}\), such as 45 ms (Configuration 5), has the opposite effect on performance. Results show that there is a tradeoff between the network convergence time and the rest of performance parameters that depends on \(I_{DIS}\). A medium \(I_{DIS}\) value within the DIS response time range yields a good performance tradeoff.