## 4 TB-RPL Mechanism
### Detailed Process of TB-RPL
When the values of \(\alpha\) are 8 and 16, they behave by the same logic; however, the children-unreachable problems are comparatively in the milder degrees. For the other three RPL implementations, the PDRs of which are almost the same with different values of \(\alpha\) because the memory space limitations of middle nodes do not affect the PDR performance of the non-storing mode, as well as TB-RPL and H-RPL. As a conclusion, for all the subgroups of results, H-RPL performs with a little lower PDR than the non-storing mode of RPL due to the flushing of downward route tables of nodes and the reconstruction of source routing from the root. During that period, some related downward routes are interrupted shortly. On the other hand, TB-RPL performs the best, which fits the previous analysis. In Figure 14b, the end-to-end packet loss metric is evaluated. The situation and trend are almost the reverse of that of PDR metric, so their conclusions are logically consistent. TB-RPL outperforms the other three RPL modifications. However, there is a scenario in both Figure 14a,b worth further discussion, where the performances of the storing mode drop drastically when the values of \(\alpha\) decrease. The reason is that the values of \(\alpha\) (those are 4, 8, and 16) are too small to compare with the network size of 49 nodes. Consequently, some common parents of the P2P pair of nodes are full of the memory to store routing information. Especially for that common parent very near to the LBR, the probability to lose a child's downward routing information is drastically high. Figure 13: End-to-end packet loss of UDP messages on various network sizes. For the result depicted in Figure 14c, the three subgroups are almost in the same patterns. In all these cases, the non-storing mode of RPL has the longest path length. Because the path length metric only considers the packets that have already arrived successfully, even though the PDR of the storing mode is lower, the path length is still shorter than that of the non-storing mode. For those packets arriving at their destination through middle common parents, the path length should be shorter. In these cases, the storing modes of RPL, H-RPL, and TB-RPL would result in a similar path length. TB-RPL always obtains the lowest path length, besides that in storing mode, because the stored route entries are not removed; the related nodes could also utilize them to build the P2P path. The evaluation result verifies this situation. Finally, Figure 14d illustrates the comparison of end-to-end delay. It generally matches the situation of path length metric, i.e., that the longer the path length, the longer the end-to-end delay. In conclusion, TB-RPL outperforms the other PRL implementations in all cases, even in greatly memory-limited situations. Figure 15 shows the group of different transmission ranges, such as 30 m, 50 m, and 70 m. The \(\alpha\) is 8 and the receive success ratio is 100%. Because the distance between each node is fixed in a grid deployment, the shorter the transmission range, the smaller the number of neighbors which could be found. In the perspective of a single node, the neighbors of which become less dense; thus, it has a longer P2P route length. Figure 15a illustrates the comparison on PDR. It could be observed that the storing mode maintains the worst PDR performance; specifically, the shorter the transmission range, the lower the PDR that the storing mode has. This is because the network becomes sparse of neighbors in a single node's view, and every middle node must store a greater number of route entries of children; in other words, as the number of levels of the DODAG increases, each node has more children comparatively. However, the middle nodes do not have enough route entries to store the increased downward routing information, so the children-unreachable problem occurs. In this case, the P2P paths to those children are broken down. Figure 14: End-to-end evaluation on four metrics with different route entries threshold \(\alpha\).