## 6 DIS-Trickle: A Mechanism for Accelerating Network Convergence
### DIS-Trickle Evaluation
However, a large network size exacerbates the number of DIS message transmissions in sparse networks, due to the multiplicative effect of a greater number of end-to-end hops from the root to the most distant nodes. Therefore, in sparse networks, the high number of DIS message transmissions dominates the total number of RPL messages transmitted during network convergence, shown in Figure 16.  
Figure 17: Influence of using DIS-Trickle on the number of DIO messages transmitted in the small, medium and large network scenarios, for different average node degrees, NDeg, as a function of the redundancy constant, \(k\), when the \(I_{min}\) value is set to 8 ms: (**a**) Small network size, (**b**) medium network size, and (**c**) large network size. Figure 18: Influence of using DIS-Trickle on the number of DIS messages transmitted in the small, medium and large networks, for different average node degrees as a function of the redundancy constant, \(k\). when the \(I_{min}\) value is set to 8 ms. (**a**) Small network size, (**b**) medium network size, and (**c**) large network size. Figure 19 illustrates the influence of network density, network size, and the redundancy constant setting on the relative performance of DIS-Trickle (_i.e._, compared with not using DIS messages) in terms of both network convergence time and number of RPL message transmissions. In sparse networks (e.g., when the average node degree is 5), using DIS-Trickle improves network convergence time, but degrades the total number of RPL messages transmitted, since a high number of DIS message transmissions are required, as aforementioned. As the network density increases, the network convergence time improvement due to using DIS-Trickle becomes lower, and does not vary significantly with the network size. This occurs because the probability that a node receives DIO messages without the need to send DIS messages increases with the network density. However, in dense networks, the total number of RPL message transmissions does not grow or even slightly decreases when DIS-Trickle is used. The reason for this result is that, in dense networks, a low number of DIS messages are required, and the DIS messages transmitted help reduce to a similar or even greater extent the number of DIO messages sent. Therefore, in dense networks, DIS-Trickle improves both network convergence time and number of RPL message transmissions, or at least does not degrade this last performance parameter (note that the result obtained in small networks, for a node degree of 10 and \(k=1\) is an exception to this conclusion, whereby the number of RPL message transmissions is slightly degraded when DIS-Trickle is used). Lastly, it can also be observed in Figure 19 that the influence of DIS-Trickle decreases as the redundancy constant grows, since a greater amount of DIO messages are naturally transmitted and a lower amount of DIS message transmissions are required. With regard to the number of collisions, for both DIO and DIS messages, it does not vary significantly by using DIS-Trickle (see Figure 20). This occurs because DIS messages are likely to be sent from nodes that have a low number of neighbors, and in addition, DIS-Trickle randomizes DIS  
Figure 19: Convergence time (**a**) and number of DIO messages sent (**b**) improvement by using DIS-Trickle in three network size scenarios, for different average node degrees as a function of the redundancy constant, \(k\). message transmission time and suppresses redundant DIS message transmissions. Therefore, when DIS-Trickle is used, the number of message collisions does not significantly increase compared with the one observed in absence of DIS messages. Finally, in order to understand the influence of \(I_{DIS}\) and the DIS initial delay on performance of DIS-Trickle, we carried out simulations with different configurations of these DIS-Trickle parameters. The considered configurations of the aforementioned parameters are shown in Table 4. The evaluation is done in the medium network size scenario, for a node degree of 5.