## 5 Performance Evaluation
On the other hand, the simulation for the Domingo routing protocol stops earlier than others because all MNs in the clusters near to the sink exhaust their energy beyond a threshold that we set up as a simulation ending point, much earlier. Figure 9: Standard deviation of energy consumption. To further elaborate on the impact of unequal energy consumption, we show the number of nodes whose residual energy \(E_{res}\) is greater than threshold \(E_{th}\) as function of time in Figure 10. It can be observed that the depletion of energy resources takes place at much lower rate in AUV-PN than for AUV-CH. This occurs because of the increased number of data-gathering neighborhoods in AUV-PN as compared with AUV-CH. As an example, it can be seen that 40 nodes deplete their energy resources beyond the threshold limit after the elapse of 4.4 \(\times 10^{4}\) s for AUV-CH, while the same number of nodes exhaust their energy resources after the elapse of 5 \(\times 10^{4}\) s for AUV-PN. The improved residual energy performance can also be attributed to the number of transmissions from the relay nodes. For AUV-PN, the number of transmissions from the relay-nodes is much less than for those for the AUV-CH. This results in much lower energy consumption at the relay node. Therefore, the change in relay node occurs at a much slower rate than in the AUV-CH case. The Domingo routing protocol has a larger depletion rate of residual energy as compared with the AUV-based approaches; this is a result of the increase in the rate of energy consumption for nodes near the sink. Thus, it can be concluded that the AUV-PN approach conserves energy resources more efficiently than the AUV-CH approach and the Domingo routing protocol. Figure 11 compares the data-gathering latency, which is defined as the time taken for the number of packets gathered at the sink. It can be noted that AUV-based approaches require more time than the Domingo routing protocol to gather data at sink. This can be explained by the fact that the AUV requires time to traverse the network to gather data and then deliver it to the sink. If we compare both AUV-based approaches, it is evident that the latency for AUV-PN becomes less than that for AUV-CH as the number of packets gathered at the sink increases. For AUV-PN, it is observed that the AUV stays for a longer time in the network during a data gathering round. This results in more data being received at the sink after the completion of a data-gathering round. This increase in the number of data packets gathered at the sink reduces the effect of a longer tour time for AUV-PN, which results in lower latency compared with AUV-CH. This effect becomes more visible with higher values of data packets gathered at the sink. Figure 7:0 Number of nodes with residual energy E\({}_{res}\)\(>\) E\({}_{th}\). To illustrate the effect of AUV stay time in the network, we show the average number of data packet gathered at the sink for 10 rounds in Figure 7:1 We know that a larger AUV tour distance in a round leads to a longer MN\(\rightarrow\)PN or CH data-gathering interval. Therefore, to obtain these types of results, we have set the threshold limit to \(E_{th}=500\) J in order to avoid frequent changes in relay nodes which may result in large changes in the AUV tour distance with respect to the previous round. As in every round, the AUV visits each relay node in an ordered sequence; therefore, the MN\(\rightarrow\)PN or CH data-gathering interval for subsequent relay nodes gradually increase which results in a higher AUV stay time at each subsequent relay node. This effect causes a steady increase in the number of data packets collected for both cases. It is observed that the effect of a gradual increase in data-gathering interval becomes smaller as the number of rounds increases. Thus, it can be concluded that the AUV stay-time in the network achieve a mean value after certain number of round.