## 4 Simulation Environment  
### Parameters and Network Topology for Simulation  
The proposed algorithm finds the time interval used by the mobile nodes to select the parent node in a dynamic manner. An experiment was conducted using MATLAB to compare and evaluate the proposed algorithm, the original trickle algorithm [2], the E-trickle (Enhanced trickle) algorithm [6] and the ME-RPL (Mobility Enhanced RPL) [10], which are used to adjust the network to a consistent state. The parameters used for the simulation are listed in Table 1. The packet size was set as 32 bytes including the RPL header, DODAGID and payload. A random waypoint model was used to simulate the motion of the mobile node [21]. In the random waypoint model, the average human walking speed  
Figure 7: Update state in the parent list table when the information of the previous parent node is not found at the new location. was set as the minimum and the average running speed as the maximum. The speed of the mobile node was selected randomly within a range defined by the minimum and maximum. The minimum interval for the mobile node was set as 212 ms, and the maximum interval was set as 202 ms, as defined by [PERSON] [22]. The interval used for selecting the parent node was determined based on each algorithm. During the experiment, the \(k\) value must be configured with a default value in order to exclude the duplicate information from neighboring router nodes. Therefore, in this paper, a \(k\) value of two was used for the original trickle algorithm and the E-trickle algorithm during the experiment. In order to compare the performance of our proposed algorithm with existing methods, three criteria were evaluated using different network topologies, as shown in Figure 8. Each experiment was conducted for 5000 s. The three criteria are the number of DIS message transmissions, the packet loss rate of the transmitted messages and the energy consumed during the transmission and reception of messages. To establish a grid network topology as shown in Figure 8a, 36 fixed router nodes were placed at a certain interval. Moreover, in order to perform an experiment in a random topology network that was similar to most actual environments, 36 and 72 fixed router nodes placed at random intervals were used, as shown in Figure 8b,c, respectively. The last network topology used for the experiment was a linear arrangement of 6 router nodes, as shown in Figure 8d. This limited the candidates for parent nodes to those among the neighboring router nodes. In the first experiment, we measured the number of DIS messages transmitted from the mobile node to select a parent node. The number of DIS message transmissions is related to the energy consumption in the mobile node. This is because even if a single DIS message is transmitted, the mobile node receives multiple DIO messages from each neighboring router node. Therefore, the number of DIS message transmissions with respect to time using each algorithm was obtained and compared. In the second experiment, the packet loss rate of the transmissions from the mobile node was obtained. The packet loss can happen as a mobile node moves to a location that is not covered by the current parent node of the mobile node. Then, the mobile node cannot transmit a DIS message to a new parent node because the predefined time interval on a previous parent node is not expired yet. When a mobile node makes a movement, the optimal parent node for the mobile node at the new location must be selected. However, owing to the interval time defined by each algorithm, there are cases where the parent node is not selected in a timely manner. Moreover, there are cases where the mobile node escapes the transmission range of the previous parent node. If the parent node information possessed by the mobile node is not renewed at this point, losses may occur in the packet transmitted from the mobile node. Therefore, for each algorithm, the loss rate of the packets transmitted from the mobile node with respect to time was obtained and compared.