## 5 Performance Evaluations  
### Cumulative Transfer Count  
Figure 9 shows the cumulative counts of DIS messages transmitted by the mobile node to select a parent node in the network topologies shown in Figure 8. As shown in Figure 8(a), in a grid network topology consisting of 36 router nodes, the proposed algorithm exhibits a cumulative DIS message transmission count that is 40.1% and 52.7% lower than that of the original trickle algorithm and the E-trickle algorithm, respectively. However, the proposed algorithm showed an 11.6% increase over ME-RPL. As shown in Figure 8(b),c, in random network topologies consisting of 36 and 72 router nodes, the proposed algorithm results in 23.3% and 37.9% fewer cumulative transmission counts than the original trickle algorithm on average, respectively; and 38.3% and 50.7% fewer cumulative transmission counts than the E-trickle algorithm. In random network topology consisting of 36 router nodes, the proposed algorithm showed a 9.1% increase as compared to ME-RPL, but it showed a decrease of 13.2% in the random network topology composed of 72 router nodes. As shown in Figure 8(d), in a linear network topology consisting of 6 router nodes, the proposed algorithm has 40.3% fewer transmission counts than the original trickle algorithm on average and 53.9% fewer transmission counts than the E-trickle algorithm. However, the proposed algorithm showed a 5.0% increase over ME-RPL.  
From the experimental results, it can be deduced that the proposed algorithm requires fewer DIS message transmissions for parent node selection than the original trickle algorithm or the E-trickle algorithm, but requires more than ME-RPL. In other words, the movement of a mobile node leads to a change in the network topology, and the proposed algorithm allows for the detection of this change with fewer messages than existing algorithms except ME-RPL. In the original trickle algorithm, a mobile node receives inconsistent information when the network topology is changed. From this information, the interval is set at the minimum value, and \(\tau\) is selected randomly from within the range of [\(I/2\), \(I\)]. While the E-trickle algorithm also sets the interval at the minimum value when the network topology is changed, the algorithm selects \(\tau\) randomly from within the range of [0, \(I\)],  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Definition** \\ \hline \(E\) & Total energy consumption when \(m\) bits packet delivered from source to destination \\ \(e_{elec}\) & Energy dissipation of the encoding and decoding \\ \(\varepsilon_{fs}\) & \(\varepsilon_{mp}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Definition of the parameters in the energy model.  
unlike the original trickle algorithm. Owing to this difference, the E-trickle algorithm transmits more messages than the original trickle algorithm in order to enforce consistency in the network. When the mobile node moves and receives information from neighboring router nodes, ME-RPL adjusts the time interval by multiplying or dividing the constant value. By contrast, the proposed algorithm selects the interval dynamically based on the time required for the mobile node to escape the transmission range of the parent node. Hence, the proposed algorithm was capable of achieving the consistency of the network with fewer messages than the original trickle and E-trickle algorithms. However, since ME-RPL has the property of performing the division operation when topology is changed, it maintains network consistency with fewer messages than the proposed algorithm.