## 4 The Design of Routing Protocol
### Data Packet Forwarding
The energy tax: The average amount of energy expended by each node in forwarding a data packet towards the sink node. ### Performance Comparison

To comprehensively evaluate the performance of the proposed ASVMR protocol, four routing protocols are selected for comparison, namely (1) the DBR protocol [16], (2) the HH-VBF routing protocol [12], (3) the flooding routing protocol [34], and (4) the RLOR protocol [25]. Here, the DBR and HH-VBF protocols are the representative depth-aware and location-aware routing protocols, respectively. Additionally, to better demonstrate the performance of the proposed ASVMR protocol, the flooding routing protocol and the RLOR protocol in underwater networks are also included in the comparison. Table 3 provides a comparison of these five routing protocols. First, the impact of node density on the performance of the five routing protocols is simulated and compared. Figure 8 shows the impact of node density on the performance of the five routing protocols, where the node density changes as the number of sensor nodes varies from 100 to 500; the moving velocity of sensor nodes is set as 0; the discount factor is set as 0.8; and the routing pipe radius is set as \(R\). The PDR, the hop count, the end-to-end delay, and the energy tax are shown in Figure 8a-d, respectively. From Figure 8a, we observe that as the node density increases, the PDR of the five routing protocols increases gradually. This is due to the reduction in the number of void regions resulting from the deployment of nodes from sparse to dense, which allows more nodes to participate in packet forwarding and mitigates packet loss. Moreover, the proposed ASVMR protocol outperforms the others since it utilizes opportunistic routing and a recovery mechanism to enhance the success probability at each hop. Additionally, in a sparse network, the ASVMR protocol expands its pipeline radius to its maximum value (i.e., as the communication range) to eliminate constraints on the pipeline. From Figure 8b, one finds that as the node density increases, the hop count decreases progressively across the five routing protocols. In a sparse network, sensor nodes may not cover the shortest path between the source and the sink node, resulting in multiple triggering of the recovery mode and a high average hop count. Nonetheless, in a densely populated network, the presence of additional nodes leads to a reduced number of void nodes and an increased likelihood of node coverage along the shortest path, resulting in a decreased hop count. In a sparse network, the RLOR protocol exhibits a higher hop count compared to the DBR protocol due to a smaller number of nodes. This limitation hinders reinforcement learning from acquiring additional valuable information, thereby leading to a degradation in performance. Additionally, the hop count of the proposed ASVMR protocol outperforms that of the others since it integrates an adaptive pipe radius and the SVM mechanism to identify the globally optimal next hop. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Protocol** & **Year** & **Advantage** & **Disadvantage** \\ \hline DBR [16] & 2008 & Only deep information is required, with high PDR & Easy to cause energy hole problem and consume a lot of energy \\ HH-VBF [12] & 2007 & Robustness improved & Significant signaling overhead \\ Flooding [34] & 2017 & Simple, link reliability & Poor performance, high overhead \\ RLOR [25] & 2021 & High energy efficiency & Computational complexity \\ ASVMR & 2023 & Minimizes end-to-end & Node location information needed \\  & & delay and prolongs the network lifetime & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of routing protocols. The proposed ASVMR protocol demonstrates effective performance in terms of hop count, which results in low end-to-end delay and energy consumption, as illustrated in Figure 8c,d, respectively. By defining a pipeline, the ASVMR protocol ensures that data are exclusively transmitted along the shortest path from the current sensor node to the sink node.