## 4 TB-RPL Mechanism
### Detailed Process of TB-RPL
Before the network size arrives at 36 nodes, the non-storing mode of RPL results in the worst end-to-end PDR. It is again caused by the long-path problem. The longer the path length, the greater the number of transmissions and retransmissions. Consequently, network congestion is more likely to occur. The performance of the storing mode drops quickly when the network size is greater than 36 nodes instead of 81 nodes. This is different from the previous two cases and requires more detailed discussion. The result suggests that some nodes start to run out of the memory space for route entries before the network size reaches 81 nodes. It means that the consuming of memory space is a gradual procedure, which does not just begin at the network size revealed by the path length and delay metrics. After the network size is over 36 nodes, the PDR of the storing mode of RPL decreases sharply. Instead of network congestion, the reason is again that the \(\alpha\) is too small (compared to the network size) for middle nodes near the LBR to save their children's route entries, which causes failures in some P2P communications. It is worth noting that the root cause of the sharp drops of performance is still the memory limitation. The unusually small number of \(\alpha\) makes such situation happen in even small-scale networks, which also means that the memory limitation problem is exposed more quickly. In the 100 nodes case, the PDR of the storing mode comes to 0, which expresses that no UDP packets arrive at destinations during simulation. As for the other three RPLs, the non-storing mode of RPL continually stays the worst performance of PDR. TB-RPL keeps the best performance, while H-RPL has a shift from the higher PDR to approach the same performance as that of the non-storing mode of RPL. The reason is that the more nodes of memory overloaded, the more similar the behavior of H-RPL to the non-storing mode of RPL. It is worth noting that compared to the storing mode of RPL, H-RPL exchanges time for connectivity; that is, it flushes the route tables and enters the non-storing mode to avoid the children-unreachable problem happening in the storing mode. However, the time consumption and resource waste are also kinds of hybrid-overhead. Figure 13 depicts the end-to-end packet loss of UDP packets. Packet loss is related to PDR but in different perspectives, which is an absolute number of the failed packets that usually represents the link quality of networks. In our evaluations, because the UDP packets are produced and sent regularly around 60 packets in every 10 min, and the success

Figure 12: End-to-end PDR of UDP messages on various network sizes. ratios of receiving and transmitting packets are also kept the same to every link in the P2P paths, the results analysis and discussion of end-to-end packet loss are logically consistent with that in the above PDR situations. #### 5.3.2 Impacts of Parameters

This section presents the results in the extra three groups of evaluation to verify TB-RPL and the impacts of different network parameters settings. Generally, these parameters represent different dimensions in describing a network. For all the extension groups of evaluation, the network sizes are fixed to 49 nodes. Figure 14 illustrates the group of different values of \(\alpha\), such as 4, 8, and 16. The transmission range is 70 m and the receive success ratio is 100%. From the results shown in Figure 14a, the worst end-to-end PDR is always maintained by the storing mode of RPL. This is because for all the three subgroups of evaluation, the memory for route entries of plenty of nodes has already been filled. In these cases, the children-unreachable problem in the storing mode occurs, so the PDR decreases heavily. Specifically, when the \(\alpha\) equals 4, it indicates that the memory space for the route table is much more limited, so the PDR is much lower than that of the non-storing mode.