## 4 TB-RPL Mechanism
### Detailed Process of TB-RPL
Finally, the unit disk graph radio medium model is used to determine the radio propagation features during simulation, such as transmission range, interference range, and propagation loss scheme. Particularly, the threshold of the number of route entries, queue size, and maximum number of neighbors during experiments, and so on are summarized in Table 2. These constrained settings reveal the seriousness of the three defined problems more clearly. In all simulations, nodes are set to be static, and the position of each node is placed in grid deployment. Moreover, the position of root is always set to the top left corner. Z1 notes perform middle routers, while Sky note is chosen to be the LBR. In grid deployment, nodes are regularly and uniformly arranged in a rectangular experimental area. The nature of grid deployment is that it represents an application scheme in which all nodes' position can be decided by network designers. Figure 9 shows a grid deployment example used in our simulation. Generally, the vertical and horizontal distances between nodes are both \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline MAC protocol. & CSMA & Nodes deployment & Grid \\ \hline Adaption protocol & 6 LoWPAN & Distance between nodes & 20 m \\ \hline IP protocol & IPv6 & Network size & 9, 16, 25, 36, 49, 61, 81, 100 nodes \\ \hline Routing protocol & RPL modifications & Radio model & Unit disk graph medium \\ \hline Objective function & MRHOF & Loss model & Distance loss \\ \hline Transport protocol & UDP & Receive success ratio & 60\%, 80\%, 100\% \\ \hline Maximum neighbors & 16 & Transmission range & 30 m, 50 m, 70 m \\ \hline Route entries threshold \(\alpha\) & 4, 8, 16 & Interference range & 1.5 \(\times\) transmission range \\ \hline Queue size & 8 & Period per running & 10 virtual minutes in simulator \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulations environment configuration. 20 m. The number of nodes is defined as the term network size, and the largest network size is 100 nodes, so the maximum simulation area is 200 \(\times\) 200 m\({}^{2}\). Finally, P2P communication performs with the above environment settings and data models. A sender node sends an UDP packet to a receiver node in every 10 s with a small random variation. Each running lasts 10 min in simulator virtual time. For each turn, 10 times running are repeated to obtain a statistically average result. All the captured packets are analyzed by Wireshark. ### Discussion on Node Topology

Before staring the evaluations, there is a need for more detailed discussion about the validity and variability of the grid node topology used in the evaluations. Even though the positions of senders and receivers are fixed in grid topology of each network size, the DODAG and P2P path are generated randomly. Because the initial states of DAO timer and DIO timer of each node are randomly different in each running, the DODAG and P2P path formed by which are also randomly different in each running. In the above case, if the length of a P2P path is too short, it is difficult to expose the children-unreachable problem. This is because the shorter P2P path length, the nearer and easier to obtain the common parent, which reduces the opportunity of middle nodes to lose their children information, while, if the length of a P2P path is too long, it is difficult to examine the long-path problem due to the fact that the common parent of such a long P2P path is highly probable the LBR. In this case, there are no obvious discriminations between different versions of RPL; all the paths of which are nearly the same length. Therefore, a moderate length of a P2P path is preferred to verify the three issued problems in a logically valid and uncomplicated way.