## 8 Conclusions  
In this paper we investigated by extensive simulation the influence of two important RPL parameters, the redundancy constant, \(k\), and the minimum interval, \(I_{min}\), on the network convergence process, on top of a variety of IEEE 802.15.4 multihop network densities and sizes. We also proposed and evaluated a mechanism called DIS-Trickle for accelerating the network convergence process by exploiting DIS messages.  
Results show that using low values for the redundancy constant yields high network convergence time in all network size and density scenarios considered, since a high number of DIO messages are suppressed by the Trickle algorithm. As the redundancy constant increases up to medium values, the network convergence time decreases. However, network convergence times do not vary significantly as the value of \(k\) increases beyond the values around the node degree. There exists a tradeoff between network convergence time and other performance parameters, such as the number of DIO messages transmitted and number of collisions that depends on \(k\). In order to achieve a low network convergence time, the redundancy constant should be set to a value equal or close to the average node degree, since greater values might cause an unnecessary increase in the number of DIO message transmissions and collisions in very dense network areas, which however would not yield a network convergence time decrease. As network density increases, the influence of the redundancy constant grows with the network size. In sparse networks, the relative influence of \(k\) is independent of the network size.  
With regard to the minimum interval, we found that there exists a tradeoff between network convergence time and DIO message overhead (and collisions) that depends on \(I_{min}\). Varying \(I_{min}\) in the range of values considered in this study has a greater quantitative effect on the number of DIO messages sent than on the network convergence time. Fine-tuning \(I_{min}\) has a greater impact on the number of DIO messages transmitted during network convergence as both the redundancy constant and network density grow, whereas the impact of \(I_{min}\) on network convergence time does not vary significantly with the redundancy constant, network size or network density.  
Finally, we proposed and evaluated DIS-Trickle, a mechanism that leverages DIS messages in order to reduce nodes' DODAG join time. Results show that using DIS-Trickle decreases network convergence time in 2-3 orders of magnitude, regardless of the network size or density. The improvement provided by this mechanism grows as network density decreases. Interestingly, in dense networks, DIS-Trickle does not increase or even reduces the total number of RPL messages sent during network convergence. However, in sparse networks, DIS-Trickle creates a trade-off between network convergence time and RPL message overhead. The influence of DIS-Trickle on network convergence performance decreases with the redundancy constant.  
The findings and contributions in this work offer a guideline for configuring and selecting adequately RPL parameters and mechanisms for achieving a good network convergence performance tradeoff, on the basis of network characteristics such as size and density.  
This work has been partly supported by the Spanish Government's Ministerio de Economia y Competitividad through project TEC2012-32531 and by FEDER.