## 5 Performance Evaluation
To compare the proposed scheme with conventional data gathering protocols, the Domingo routing protocol [4, 5], which is a way of organizing the network into clusters and delivering the data by multihop transmission to reduce long-range transmission, is simulated along with the other AUV-employed schemes such as AUV-PN and AUV-CH. For the sake of fair comparative analysis for all protocols, the same network topology with an equal number of cluster has been kept, where _N = 100_ nodes are uniformly distributed over an area of 1000 \(\times\)1000 m\({}^{2}\). Using Equations (13) and (14), the total energy consumption is obtained by  
\[\mathbf{E}_{total}=\mathbf{E}_{p}+\mathbf{E}_{G} \tag{15}\]  
where \(E_{G}\) is the energy consumed by all sensor nodes during DG_Phase and is obtained by  
\[\mathbf{E}_{G}=\sum_{i=1}^{N}\mathbf{E}_{G\to i} \tag{16}\]  
where EG_i_ is the energy consumption related data gathering of node \(i\) and is obtained differently according to whether the node is an MN or a relay node. If node \(i\) is an MN,  
\[\mathbf{E}_{G\to i}=\mathbf{E}^{rx}+\mathbf{E}^{sdp}+\mathbf{E}^{lsrn} \tag{17}\]  
where \(\mathbf{E}^{rx}\), \(\mathbf{E}^{sdp}\) and \(\mathbf{E}^{lsrn}\) are energy consumptions for transmitting data to relay node, sleeping while PN works for PN\(\rightarrow\)AUV, and idle-listening after the PN\(\rightarrow\)AUV to hear, if any, announcement of new PN from CH, respectively. Here, we ignore the sleeping and idle-listening energies owing to very low power requirements during the sleeping process [10, 17], and the relatively small idle-listening duration as compared with the transmission time. If node \(i\) is a relay node that would be the CH in AUV-CH or a PN in AUV-PN,  
\[\mathbf{E}_{G\to i}=\mathbf{E}^{rx}+\mathbf{E}^{lsrd} \tag{18}\]  
where \(\mathbf{E}^{rx}\) and \(\mathbf{E}^{lsrd}\) are the energy consumptions for receiving data from the respective MNs and forwarding the data to AUV, respectively. Figure 8: Total energy consumption _versus_ the number of data packets gathered at the sink. Figure 8 shows the total energy consumption \(E_{total}\) for various numbers of data packets gathered at the sink. It is observed that the total energy consumption of AUV-PN is considerably less than those of AUV-CH and the Domingo routing protocol. This is primarily because AUV-PN has a larger number of relaying nodes than AUV-CH and uses single-hop transmission with a short distance, unlike the Domingo routing protocol, which uses multihop transmission with a longer distance. The larger number of relay nodes results in a shorter distance between MNs and the relay nodes, and therefore saves more energy. In addition to the amount of energy consumption, how evenly each node spends energy is necessarily considered, especially in order to augment the lifetime of the network. Thus, we examine system performance in terms of the standard deviation of energy consumption of each node, regardless of MNs and relay nodes in Figure 9. At the beginning, the standard deviation increases because the energy consumption is concentrated to several relay nodes such as PN and CH. However, as the relay nodes are replaced with new ones, the increase in standard deviation slows down and reaches a certain peak point where approximately half of the nodes have served as relay nodes. Then, the standard deviation starts to decrease as further changes in relay nodes take place. It is also observed that AUV-PN has the smallest standard deviation compared with AUV-CH and the Domingo routing protocol. This is because AUV-PN has a large number of relay nodes, each associated with a smaller data-gathering neighborhood as compared with AUV-CH, which results in a low number of data packets being received at the relay nodes and also being subsequently transmitted to the AUV. While in comparison with the Domingo routing protocol, AUV-PN does not require multihop transmission and thus avoids the transmission of unequal number of data packets between the relay nodes.