## 4 Simulation Analysis
### Simulation Results in the Static Sink Scenario
As we recall from our previous discussion that the holding time computation only requires the location plus depth information of sender node \(S\), Sink node \(D\), node's own location, and the residual energy information. However, the same information of the neighboring nodes is also available in the neighborhood table of each node. Hence, the node can easily estimate the packet holding time of all common neighbors of \(S\) and node itself, which also fall in the \(PFZ\). Figure 7: Overall data packet suppression achieved by the proposed scheme for different \(T_{r}\) and network size. It is also a well-established fact that computation energy cost is very small compared to communication and other operations of the node. Once the node estimates the holding time of its own as well as its neighbors, it checks whether its own holding time is smaller than the neighbors or not. If the receiving node's holding time is smaller than its common neighbors, then instead of waiting for a long holding time duration, it forwards the packet after \(\frac{HT_{r}^{i}}{2}\). However, the AHH-VBF does not exploit the neighborhood information available at the node and each node has to wait for a holding time duration before further relaying the data packet. This is the reason that despite the energy scaling and expansion of the proposed holding time, its end-to-end delay is smaller than the AHH-VBF. Subsequently, the same behavior can be observed for any network scenario, refer Figures 8 and 9. In Figure 8, the trend of the end-to-end delay for a small transmission range (e.g., \(T_{r}=500\) m) is increasing with respect to the network size in contrast to the end-to-end delay behavior resulted by large transmission ranges. The main arguments behind this behavior are: (a) in case of a small \(T_{r}\), the packet fails to reach \(D\) if it is relayed over multiple hops, due to channel impairments,  
Figure 8: End-to-End delay between Source node that generated data message and Sink node versus the network size. Figure 9: End-to-End delay between the source node that generated data message and Sink node versus transmission range. path losses, high error rate of the acoustic channel, and so forth; (b) because of the network sparsity, end-to-end connectivity could not be established. Therefore, in a sparse network scenario, only the short hop-distant packets can reach \(D\) and experience a small end-to-end delay. On the contrary, in a dense network environment, the packet has to traverse a large number of hops, which causes a very long end-to-end delay. The similar trend is also observed in Figure 8. Furthermore, it is also noticed in Figure 8 that as \(T_{r}\) increases, the end-to-end delay descends, which is due to the collision that leads to a large data packet loss. This collision happens when different potential forwarders relay the same data packet because of the small holding time difference and the large propagation delay between these forwarders, refer the theory related to Figure 2. Data packets in the proposed ESEVBF scheme experience about 23.77%, 12.6%, and 3.65% less end-to-end delay compared to AHH-VBF in any network size scenario with \(T_{r}=500\) m, \(T_{r}=600\) m and \(T_{r}=700\) m, respectively. As the \(T_{r}\) increases, the end-to-end delay of both the schemes becomes identical because the Data packet is forwarded through less number of hops and directly reaches the sink node. The overall performance gain (percent improvement in end-to-end delay) achieved by the proposed ESEVBF is shown in Figure 5:0  
After the data packet broadcast and end-to-end delay analysis, we investigate the overall energy consumption in the network. Figures 11 and 12 show the total energy consumption in the network during the whole simulation duration for different network size and transmission range, respectively. In underwater acoustic networks, transmission of a packet is the most energy consuming operation in the network compared to the packet reception, idle listening, sensing, and the processing operations.