## 5 Performance Evaluations
### Packet Loss Rate
#### 5.2.2 Packet Loss Rate with Varying Mobile Node Speed  
Figure 11 shows the relationship between the packet loss rate and the speed of motion of a mobile node in network topologies shown in Figure 8a. The experiment considered a situation where the mobile node moves in random directions at constant speeds, which were fixed at 1.25 m/s and 2.5 m/s, respectively.  
In the grid network topology, the average packet loss rates with a mobile node speed of 1.25 m/s were 0.3%, 19.4%, 0% and 11.3% for the proposed algorithm, the original trickle algorithm, the E-trickle algorithm and the ME-RPL, respectively, as shown in Figure 11a. Therefore, the average packet loss rates were 98.3% and 97.1% lower in the proposed algorithm than in the original trickle algorithm and the ME-RPL, and the average packet loss rate of the proposed algorithm was higher than that of the E-trickle algorithm. From the results in Figure 11a, standard deviations of 0.3%, 7.7% and 5.4% were observed for the proposed algorithm, the original trickle algorithm and the ME-RPL, respectively.  
When the mobile node speed was set at 2.5 m/s in the grid network topology, the average packet loss rates of the proposed algorithm, the original trickle algorithm, the E-trickle algorithm and the ME-RPL were 2.3%, 10.0%, 5.7% and 0.4%, respectively. Therefore, the average packet loss rates of the proposed algorithm were 77.2% and 60.4% lower than that of the original trickle algorithm and the ME-RPL, and the average average packet loss rate of the E-trickle algorithm was 84.4% lower than that of the proposed algorithm. In the results shown in Figure 11b, standard deviations of the proposed algorithm, the original trickle algorithm and the ME-RPL were 0.5%, 4.2%, 0.2% and 1.9%, respectively.  
From the experimental results, it can be inferred that the packet loss rate of the proposed algorithm with different mobile node speeds is lower than that of the original trickle algorithm and the ME-RPL,while it is higher than that of the E-trickle algorithm. With a lower mobile node speed, there are fewer changes in the parent node and the neighboring router nodes. Owing to fewer changes in the parent node, the network topology does not vary frequently either.  
However, the original trickle algorithm and the ME-RPL increase the time interval as the network stabilizes. At this time, when the node moves, a packet loss occurs because it cannot transmit a message to find the neighboring router nodes. The E-trickle algorithm also increases the time interval as the network becomes stable. However, the E-trickle algorithm lowers the packet loss rate because the mobile node initializes the time interval for finding the parent when it receives an inconsistent message from the neighboring node. Conversely, if the mobile node speed is high, the network topology changes frequently. At this time, the time interval for finding the parent is shorter than when the network topology is stabilized. Therefore, the packet loss rate is lower than when the mobile node is slow.  
As shown in Figure 11a,b, the proposed algorithm and the E-trickle algorithm showed better performance than the original trickle algorithm and the ME-RPL. The proposed algorithm has better performance than the original trickle algorithm and the ME-RPL, which update the time interval by calculating the constant value, although the performance is lower than the E-trickle algorithm, which continuously updates the time interval. In addition, the proposed algorithm increases the packet loss rate as the mobile node speed increases because the time interval for selecting the parent node does not exactly match due to the random movement characteristics of the mobile node, as mentioned in Section 5.2.1.