## 4 TB-RPL Mechanism
### Detailed Process of TB-RPL
There is a non-evident point that requires more detailed discussion. When the transmission range is 30 m, it is sharply unstable with respect to PDR in the storing mode and is extreme low (nearly 3% for the average statistics). Because the routes to most of a node's children are lost due to memory limitation from storing the greater number of children routing information, the remaining 3% PDR comes from the nodes that have the common parent and whose corresponding route has been also stored, which are very rare cases. The other 97% packets have been sent to the root due to there being no route in the middle nodes. Then, they are discarded by the root because the root, if lacking the support from middle nodes, also does not have the corresponding route information. However, the non-storing mode is not affected by the memory limitation of the middle nodes; all the route information is collected by root itself. TB-RPL and H-RPL operate successfully, and TB-RPL will still always obtain the highest PDR compared to others. In Figure 15b, the results of packet loss follow the same analysis and discussion as those in the above cases. Figure 15c,d verifies the situations with respect to path length and end-to-end delay metrics. For the storing mode, the path lengths rise slowly along with the transmission ranges expanding from 30 m to 70 m. The reason is that with more limited memory space for overall nodes, there is a higher probability that the route with shorter end-to-end path length would be stored completely. For the non-storing mode of RPL, the higher the transmission range, the lower the path length. The is because the higher the transmission range, the fewer levels in DODAG. In this case, the hops between parent to child are decreased, so the path length becomes lower. TB-RPL and H-RPL obey the same logic as the above subgroups, and TB-RPL still outperforms the others. The results of end-to-end delay follow a similar analysis and discussion. Figure 16 shows the group of different receive success ratios, namely, 60%, 80%, and 100%. The receives success ratio usually indicates the quality of the transmission environment. The situation in this group is comparatively apparent in logic. For the PDR and packet loss, all the different implementations of RPL suffer a similar decrease of PDR when the receive success ratios become lower. It is because the lower the receive success ratio, the greater the number of packet retransmissions, which leads to some degree of network congestion and results in a lower PDR. The result of the packet loss metric obeys the same logic. Figure 15: End-to-end evaluation on four metrics with different transmission range. As for the path length and end-to-end delay, the storing mode of RPL performs better than the non-storing mode in all subgroups. This is because the receive success ratio does not affect the required number of route entries. In this case, before the memory space for routes runs out, the P2P communication of the storing mode naturally has lower path length and end-to-end delay. However, it is worth discussing that the trend of end-to-end delay behaves differently from the trend of path length. The reason is that the delay metric not only reflects the path length but also represents the factor of transmission success ratio. Therefore, the end-to-end delay of all RPL implementations increases with the reduction of receive success ratios. However, in any case, TB-RPL maintain a comprehensively better performance throughout. ## 6 Conclusions

In this article, we propose a single and uniform hybrid-MOP-based TB-RPL to resolve the existing problems of downward routing MOPs in RFC 6550 and the present related works. Since RPL is the core routing solution in the LLN paradigm, analyzing the performance of a new hybrid-MOPs from both theoretical and practical perspectives is a meaningful development. To this end, TB-RPL achieves the expected objectives by dealing with the three identified critical problems.