## 4 System Model
### Gedpar
### Network Parameters Setting

The network is deployed over the area of 1500 m \(\times\) 1500 m \(\times\) 1500 m. The number of nodes and sinks are 100 and 45, respectively. Initially, nodes are deployed randomly. The initial transmission range of each node is 245 m and nodes can transmit up to 270 m using some extra energy. This happens only when current forwarder cannot find the next node in its transmission area. The initial energy of each node is 100 J. The velocity of acoustic waves and bandwidth for the network is considered 1500 m/s and 3000 kHz, respectively. Transmission energy, reception energy and idle time energy are considered as 2 W, 0.1 W and 10 \(\times\) 10\({}^{-3}\) W, receptively. Size of hello packet is 100 bytes while the sizes of all other packets are 150 bytes. Summary of these parameters is presented in Table 3.

### Simulation Results

Initial deployment of our model is presented in Figure 8. This is a 3D deployment which covers x-axis, y-axis, and z-axis, respectively. The x-axis represents the width of the deployed wireless network. Y-axis indicates the breadth and z-axis cover the depth of the network. From the Figure 8, red \"*\" and blue \"+\" are representing the sink nodes and source nodes, respectively. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Network dimensions & 1500 m \(\times\) 1500 m \(\times\) 1500 m \\ Number of sink nodes & 45 \\ Other nodes & 100 \\ Minimum transmission range & 245 m \\ Maximum transmission range & 270 m \\ Initial energy of nodes & 100 J \\ Velocity of acoustic waves & 1500 m/s \\ Bandwidth & 3000 kHz \\ Packet transmission energy & 2 W \\ Packet reception energy & 0.1 W \\ Idle time energy & 10 \(\times\) 10\({}^{-3}\) W \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Network parameters setting. In Figure 9, final deployment is presented. This final deployment is done after adjusting the transmission range and depth of all nodes. These transmission ranges and depths are only adjusted in case of void hole occurrence. When void hole occurs, first transmission range is enhanced for finding the next forwarder node using some extra energy. If none of the forwarder neighbors is found then depth adjustment occurs. Depth adjustment is done after enhancing transmission range because it consumes more energy. Figure 10 depicts the depth adjustment of nodes. We can see from the Figure 10 that most of the depth adjustment is done during the start of network deployment. Once the network is deployed and initial depth adjustments are done then there exist only a few occasions on which depth adjustment is required. A large amount of energy is dissipated during the process of depth adjustment. So, we make sure that the depth adjustment only occurs when it is necessary. Otherwise, try to avoid the nodes by enhancing the transmission range. It is clear from the Figure 10 that in GEDPAR routing protocol, the nodes require fewer depth adjustments as compare to GEDAR. This step further involved in lessening the energy dissipation. Figure 8: Initial deployment. Figure 9: Final deployment. The throughput of proposed routing protocols is compared with GEDAR and LMPC. Figure 11 shows this comparison and assures the efficiency of proposed schemes. According to simulation results, LMPC performs better than GEDAR while GEDPAR outperforms both GEDAR and LMPC. The efficiency of the proposed scheme is better than LMPC and GEDAR by the percentage of 13% and 37%, respectively. As we can see from the Figure 11 that the second proposed technique also outperforms the counterparts. Firstly, E2 EVHR performs poor during the end to end node finding process; however, when the proposed scheme finds the end to end routes than its throughput is improved drastically. Figure 12 shows the performance of GEDAR, GEDPAR, E2 EVHR and LMPC with respect to PAR. PAR is already defined in Section 5.3 as it is a ratio between packets received at sonobuoys to the packets sent from source nodes. We measure PAR from the range of 0 to 1.