## 4 Simulation Analysis
### Simulation Results in the Static Sink Scenario  
In this section, all the results are estimated for the network scenario with static sink. In this case, the Sink is placed at sea surface and the center of the network deployment region. Figures 5 and 6 show the total number of copies of the data message forwarded in the network versus varying network size and transmission range, respectively. It can be seen in Figure 5 that in a sparse network scenario, \(T_{r}=500\) and network size, the total copies of data packet forwarded in the network is smaller than the dense network scenario. The reason behind this phenomenon is that most of the copies of the data packet fail to reach the next hop forwarders. As the network size  
Figure 4: Mobile sink network scenario. increases, more copies of the data message are successfully propagated in the network. On the contrary, for large transmission range and small network size, more data packets are successfully forwarded in the network, but when the network size increases, most of the packets are dropped in the network due to a large collision probability. Increase in data packet copies due to large transmission range plus network size is due to two factors; (a) increase in the pipeline radius directly surges in the number of forwarding candidates in PFZ, (b) the propagation delay between potential forwarders in PFZ will be longer and could be more than the holding time difference between them. The next interesting trend that has been observed in the graphs is the difference between total copies of the data packet that are forwarded by AHH-VBF is larger than the proposed scheme. It shows that the holding time difference between the potential forwarders is less than the propagation  
Figure 5: Number of data message copies forwarded in the network for different network size. Figure 6: Number of data message copies forwarded in the network for different transmission range. delay between those nodes. Hence, multiple nodes from the PFZ send copy of the same data packet, which results in more energy consumption that is discussed later in this section. In contrast, the proposed scheme computes holding time and exponentially scales the holding time using normalized energy factor to increase the holding time difference between potential forwarders. Consequently, it minimizes the data packet duplication and saves energy in the proposed scheme. The same performance metric has been investigated for different transmission ranges and fixed network size and a similar trend has been observed in Figure 6. On average, the proposed scheme generates 27.55% less copies of the data packet for all \(T_{r}\) and network size of 450 nodes. Similarly, in \(T_{r}=900\) m and all network size scenarios, the proposed scheme disseminates about 21.93% fewer copies of the data packet in the network. A detailed performance gain achieved by the proposed scheme in this regard is shown in Figure 7. The maximum performance gain achieved by the ESEVBF in contrast to the AHH-VBF is 30.72% for the network size of 450 nodes and \(T_{r}=500\) m.  
Next, we investigate the end-to-end delay experienced by the successful data packets between the source \(S\) and sink node \(D\) for varying network size and transmission range as shown in Figures 8 and 9, respectively. The overall delay experienced by a data packet includes processing, propagation, and the holding time delay at each forwarding stage in the network. The impact of network sparseness and denseness can be seen in those graphs. It is evident from the graphs that the end-to-end delay experienced by the AHH-VBF is larger than the proposed scheme. The main reason behind this behavior is our proposed potential forwarder selection algorithm. As stated earlier in the proposed forwarder selection algorithm section, all the nodes share their location and residual energy information with their 1-hop neighbors. When a node receives data packet from any one of its neighbors, it computes its own holding time.