## 4 The Design of Routing Protocol
### Data Packet Forwarding  
This part discusses the procedure of data packet forwarding in the proposed ASVMR protocol, as summarized in Algorithm 2. ```
1:\(\mathcal{A}\), \(\mathcal{B}\), \(\mathcal{C}\), \



nodes that simultaneously possess two characteristics, namely nodes above the sender and nodes in the routing pipe. Next, the sender calculates decision values for each potential forwarding set based on the obtained status information. The node with the maximum decision value is chosen as the next hop, and the remaining nodes in the candidate forwarding set assist in routing the data packet towards the most favorable next hop. The routing pipe radius controls the number of nodes in the candidate forwarding set. Before transmitting the data packet, the node modifies the packet header by incorporating its own status information and the details of the next hop. Upon reception of a data packet, a node retrieves the sender's status information from the packet header and updates the relevant neighboring information, regardless of its role as a qualified forwarder. Then, the node verifies whether it has previously forwarded the same data packet. If it has, the node directly discards the data packet; otherwise, it checks whether it is the receiver. If the node is the receiver, it forwards the packet following the above procedure. If the node is not the receiver, it calculates its distance from the receiver. If the distance exceeds the communication range, the node discards the data packet. Otherwise, the node initiates a waiting time. While waiting, if a node intercepts the same data packet, it refrains from forwarding it since another node has already taken the responsibility of transmission. If not, the node proceeds with the transmission of the data packet once the waiting time period has expired. Furthermore, the proposed



## 5 Simulation Results and Discussion

The performance of the proposed ASVMR protocol is evaluated by computer simulations. ### Simulation Setup

In the UASN, each sensor node in the network has a unique ID and limited energy. Moreover, it has the knowledge about the locations of sink nodes, the sender (via the packet header), one-hop neighboring nodes, and its own location through underwater localization algorithms [33]. The sensor nodes are uniformly distributed within a 3D area measuring 500 m \(\times\) 500 m \(\times\) 500 m. The sensor nodes only receive information from one-hop neighboring nodes. The sink nodes, which have unlimited energy and the ability to communicate using RF and acoustical modes, are fixed on the water surface. The source nodes, which have the ability to move horizontally, are deployed at the bottom. The locations of sensor nodes are illustrated in Figure 7. The parameters in the simulations are listed in Table 2.

In addition, four quantitative metrics are adopted in the simulations to evaluate the performance of the proposed ASVMR protocol. 1. The PDR: The proportion of data packets successfully received by the sink node compared to the total number of data packets transmitted by the source node. 2. The hop count: The average number of intermediate nodes traversed by a data packet from the source node to the sink node. \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Value** \\ \hline Simulation time & 5000 s \\ The number of sink nodes & 5 \\ The number of source nodes & 5 \\ Sound speed & 1500 m/s \\ Communication radius & 150 m \\ Carrier frequency & 25 kHz \\ Data generation rate & 1 packet/s \\ Transmission rate & 10 kbps \\ Power of transmission & 2 W \\ Power of reception & 0.1 W \\ Power of idle & 10 mW \\ Number of sensor nodes & 100–500 \\ Node moving velocity & 0–2 m/s \\ Discount factor \(\gamma\) & 0.1–1 \\ Routing pipe radius \(W\) & \(R/8\)–\(R\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter settings in simulations. Figure 7: Placement of sensor nodes in the UASN. 3. The end-to-end delay: The average latency of a data packet from the moment it is transmitted by the source node to its reception at the sink node. 4.