## 4 Simulation Analysis  
The detailed performance comparison of the proposed EDOVE scheme in contrast to the conventional WDFAD-DBR scheme through simulations is presented in this section. During simulations, we considered the three-dimensional network area of 1 km length and width and 2 km of depth, (for example, \(X_{max}=Y_{max}=1\) km and \(Z_{max}=2\) km). A varying size network of 60, 90,..., up to 180 nodes has been considered in the simulations. All nodes are homogeneous in terms of transmission range, which ranges from 600 m to 1000 m. These parameters are sufficient enough to demonstrate the network's spares and denseness. During all simulations, the data generating node or source node is placed at the bottom of the ocean and the sink(s) are placed at the sea surface. In this scenario, the impact of depth as well as multi-hop forwarding on the depth-based proposed solutions can easily be investigated. Rest of the nodes are randomly deployed between source and sink node(s) in each simulation scenario. These nodes serve as the data forwarders or relaying nodes between data source and the sink(s). This typical scenario explicitly demonstrates, how the data relaying load among forwarders is distributed by the forwarding scheme. In first simulation trial for 60 nodes, except data source, all nodes are randomly deployed in the network area. In the next trial for 90 nodes, the first 60 nodes' position is un-altered and only the next 30 nodes are randomly placed in the network. There are five sinks deployed over the surface of the network area. It is assumed that the whole network is static throughout the simulation duration. Each node is assigned initial energy \(E_{0}\) that is equal to \(E_{min}+rand(E_{rand})\), Where \(E_{min}=60\) J and \(E_{rand}=20\) J. We use the simplified energy consumption model at each node. Energy consumed by a node to transmit \(m\) bits at distance \(k\) meters is presented as:  
\[E_{t_{x}}(m,k)=E_{ele}\times m+E_{amp}\times m\times k^{2}\]  
where \(E_{ele}\) is the energy required to send 1 bit and \(E_{amp}\) is the acoustic amplifier energy or acoustic wave attenuation coefficient. Energy consumption at the node, which receives \(m\) bits is represented as: \(E_{r_{x}}(m)=E_{ele}\times m\). The node's sending, receiving, and idle energies are 50 W, 158 mW and 58 mW, respectively. The data, control traffic, and acoustic network parameters used in the simulations are as follows: The header and payload size of data packet is 88 and 576 bits, respectively. Neighbor request and acknowledgment are 48 bits. The common header of 88 bits is used for all packet types in the simulation. Additionally, the acoustic propagation delay of 1500 m in the aquatic environment and the data rate of \(16\times 10^{3}\) bits per second have been considered in the simulations. In last, at MAC layer, the pure ALOHA is used because of its is not susceptible to delays and does not use any collision detection and avoidance mechanism. As stated earlier that the source node is deployed at the seabed and it generates data packets destined for the sink node(s). The average data packet generation rate is 0.2 packets per second or one packet per 5 s. Additionally, there are some constants that used by the WDFAD-DBR algorithm, e.g., weighting factor \(\alpha\) and global parameter \(\tau\). The value of \(\alpha=[0,1]\) prioritizes the depth differences (between _Sender_ and _receiver_ node and the receiver itself and its lowest depth neighbor) in the holding time computation of the WDFAD-DBR. To equality prioritize both the depth differences, we used \(\alpha=0.5\). Similarly, the global parameter \(\tau\) had been used to guarantee the holding time between two nodes should be large enough to guarantee packet suppression. About 100 simulations of a single network scenario (a network with the specific number of nodes and the transmission range) are performed. The final results are the average of simulation trials and presented with the 95% confidence interval in the graphs.