## 4 TB-RPL Mechanism
### Detailed Process of TB-RPL
In our evaluations in grid topology, five UDP senders and five corresponding receivers are selected on the edges of a grid network; the aim is to make the path lengths sufficiently long to collect representative data which can be evaluated via different metrics to verify whether the issued three problems in this research are improved. In addition, in order to simulate in as many network environments as possible, there are sets of network settings designed with the following: (1) the route entries threshold \(\alpha\) is set to different values to show the performance of TB-RPL in different degrees of memory limitation; (2) the transmission ranges are adjusted to different values to indicate the performance in different neighbor densities; (3) the different values of receive success ratio are used to represent various transmission qualities of network. Through the combinations of those different factors, more variabilities are introduced, even though the network topology is a grid. In summary, the variabilities of evaluation settings are from two sources:

Figure 9: The example of grid deployment in simulation. Node 1 is the root located at the top left corner of the upper border. (1) the random formation of DODAG and P2P paths in each running of experiment; (2) the various combinations of different network properties. ### Performance Evaluation and Analysis

This section presents the evaluation results of diverse RPL implementations based on different metrics. To ensure that the proposed work is suitable for memory-constrained nodes in LLN, we examine and compare TB-RPL with H-RPL [29] and two modes in standard RPL [13]. H-RPL is selected for comparison due to the fact that it also takes the number of route entries into consideration, which is the most relevant concern of our proposed TB-RPL, compared to other related works. However, it still adopts the logic of switching MOPs that introduces extra control overhead, while TB-RPL uses a fused MOPs mechanism. Through comparison with H-RPL, the improvement of TB-RPL by solving the hybrid-overhead problem can be illustrated directly. #### 5.3.1 Comparative Results Analysis

In this set of simulations, four RPL mechanisms are measured on different metrics within different network sizes to compare the performances between each other. The results indicate whether the three problems issued previously in this research are improved by TB-RPL. In each turn, the positions of UDP senders and receivers are kept the same for comparison. For all evaluations in this set, the transmission ranges are 70 m, the receive success ratios are 100%, and the thresholds of the number of route entries \(\alpha\) are 8 for all nodes except for the LBR. Finally, the network sizes in evaluation are set to 9 nodes, 16 nodes, 25 nodes, 36 nodes, 49 nodes, 64 nodes, 81 nodes, and 100 nodes. Figure 10 displays the result of path length metric on UDP packets. From the result, the end-to-end path lengths of all kinds of RPL increase along with the network size increasing. The reason is that the more nodes, the greater the distance from the UDP sender to receiver, which leads to a longer average path length. Before the network size arrives at 81 nodes, the non-storing mode of RPL results in the longest path length. It is caused by the long-path problem, i.e., that all downward routes must go through LBR. Besides the storing mode, the other three RPL implementations still work successfully after the network size is greater than 81 nodes due to the fact that LBR helps store the downward routes. There is no interruption of P2P communication occurs. It is noted that TB-RPL and H-RPL have the shorter path length than that in non-storing RPL. Because TB-RPL and H-RPL depend not only on LBR's source routing but also on the middle nodes storing its children's downward routes. Finally, the path length of H-RPL is approaching that of the non-storing mode of RPL, while TB-RPL still keeps the shortest path length.