## 5 Performance Evaluations
### Energy Consumption of the Mobile Node  
Figure 12 shows the cumulative energy consumption expended by a mobile node for parent node selection in the network topologies shown in Figure 8. The measured energy consumption of the mobile node includes the energy used during the transmission and reception of DIS, DIO and DAO messages. In the 36-node grid network topology, the total energy consumption of the mobile node was 72.5 mJ, 78.9 mJ, 79.2 mJ and 77.5 mJ for the proposed algorithm, the original trickle algorithm, the E-trickle algorithm and the ME-RPL, respectively, as shown in Figure 12a. Therefore, the energy consumption of the proposed algorithm was 8.1% and 8.4% lower than that of the original trickle algorithm and the E-trickle algorithm and 6.5% less than that of the ME-RPL.  
In the 36- and 72-node random network topologies, the total energy consumption of the mobile node was 59.1 mJ and 95.1 mJ, respectively, for the proposed algorithm; 64.3 mJ and 102.4 mJ for the original trickle algorithm; 63.3 mJ and 99.9 mJ for the ME-RPL; and 64.5 mJ and 103.0 mJ for the E-trickle algorithm; as shown in Figure 12b,c. Therefore, the total energy consumption of the proposed  
Figure 11: Result of packet loss rate with varying mobile node speed in grid network topology. (a) Packet loss rate with 1.25 m/s velocity; (b) Packet loss rate with 2.5 m/s velocity.  
algorithm was 8.2% and 7.1% lower than that of the original trickle algorithm, 8.4% and 7.7% lower than that of the E-trickle algorithm on average, respectively, and 6.7% and 4.8% lower than that of the ME-RPL.  
As shown in Figure 12d, in the 6-node linear network topology, the total energy consumption of the mobile node was 53.6 mJ for the proposed algorithm, 55.8 mJ for the original trickle algorithm, 56.1 mJ for the E-trickle algorithm and 55.5 mJ for the ME-RPL. Therefore, the energy consumption of the proposed algorithm was 3.9% and 4.5% lower than that of the original trickle algorithm and the E-trickle algorithm on average and 3.4% less than that of the ME-RPL.  
From the experimental results, it can be deduced that the energy consumed by the mobile node for parent node selection is lower for the proposed algorithm than for the original trickle, the E-trickle algorithm or the ME-RPL. Fundamentally, energy consumption is proportional to the number of messages transmitted and received by the mobile node for the selection of a parent node. However, from the results shown in Figure 12a,b, it can be seen that the original trickle algorithm consumed energy similar to the E-trickle algorithm, despite the fact that the E-trickle algorithm transmitted more messages than the original trickle algorithm, as shown in Figure 9. Similarly, the ME-RPL, which has a smaller number of sending/receiving messages in Figure 9, also consumes relatively high energy.  
Figure 12: Result of energy consumption in a mobile node with different network topologies. (**a**) Grid topology with 36 router nodes; (**b**) Random topology with 36 router nodes; (**c**) Random topology with 72 router nodes; (**d**) Linear topology with 6 router nodes.  
Based on this observation, one can reach the conclusion that the original trickle algorithm and the ME-RPL exchanged more messages with the router nodes placed further than \(d_{0}\) than did the E-trickle algorithm. This is closely related to the time interval for finding the parent node, and the time interval is also related to the packet loss rate. As a result, it can be seen from the experiment result that it is necessary to find a new parent node when it is relatively far from the parent node or when communication with the existing parent node is not possible. By contrast, the proposed algorithm consumed less energy for parent node selection than the existing algorithms in all situations, as shown in Figure 12. This is possible only because the proposed algorithm had a significantly lower number of messages transmitted and received for parent node selection than the previous algorithms, owing to its characteristics.