## 3 Design of SROA
### SROA Protocol Description
In SROA, since the Q-value of sensor node is less than zero after packet forwarding, the Q-value of sink node is fixed at zero to ensure that the protocol converges. ## 4 Simulations and Analysis

In this section, our proposed protocol SROA is evaluated for the performance based on Matlab R2021a and NS 3.26 [31] from three aspects. First, simulation settings are introduced before evaluations. Afterwards, we assess the impact of various parameters on the SROA. The performance of on-site architecture is also evaluated with the same protocols. Finally, we evaluate the performance of SROA and compare it with the other three routing protocols for different metrics. ### Simulation Setting

Sensor nodes are randomly deployed in a \(5000\,\mathrm{m}\times 5000\,\mathrm{m}\times 5000\,\mathrm{m}\) three-dimensional space in our simulations. Any sensor node is the same in functional features, and each node near to the seafloor can generate the data packets independently as a source node. The sink node is deployed on the seabed, which is considered to be difficult to reposition once deployed. For analysis, we select a source node from the seabed. The propagation loss model for underwater acoustic channels is Thorp [32]. The acoustic transmission speed is set at \(v_{0}=1500\,\mathrm{m/s}\), and the network size ranges between 100 and 500. Table 2 displays the simulation parameters [9]. To evaluate the SROA, we employ the Carrier Sense Multiple Access (CSMA) as the underlying MAC protocol. Specifically, when the channel is not occupied, the forwarding node is able to broadcast the data packet; otherwise, it backs off and discards the packet after five times of backing off [22]. We mainly evaluate the SROA protocol in several quantitative metrics and scenarios against the two different parameters: Network size and transmission range. Network size is different for various demands and environments in reality, hence the routing protocol is significant to have the ability which scales up the network with stability. Hence, the test for network scalability, irrespective of variation in the number of nodes, is essential. However, the transmission range also impacts the metrics of the protocol. The larger the transmission range of the sensor nodes, the more energy is needed for communicating. Based on this, two different transmission ranges are tested to evaluate the effects on the performance of the network. Furthermore, the performance of SROA is evaluated using the following metrics: Average End-to-End Delay indicates the network latency, namely the average time consumption for forwarding a data packet to the sink node, including the waiting time, packet propagation time, and processing time; the Packet Delivery Ratio represents the ratio of delivered data packets; Energy Consumption is defined as the total energy consumed by all of the nodes for transmission, which includes the packet transmission and reception consumption [33]; Average Hop Count of Delivered Packets means the average number of hops from the source to the destination on the routing path. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Network size & 100 to 500 \\ Transmission power & 10 W \\ Receiving power & 3 W \\ Transmission rate & 1 kbps \\ Data packet size & 50 Bytes \\ Simulation rounds & 200 \\ Communication range & 1000 m, 1500 m \\ Idle power & 30 mW \\ Initial energy & 1000 J \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation settings. observed that the residual energy variance increases with the value of \(\alpha_{2}\) increasing, because link quality and end-to-end delay account for a greater portion in selecting forwarding nodes. Similarly, taking merely the globally optimum path into account cannot assure the uniform distribution of remaining energy. Therefore, a delay-limited routing approach cannot provide uniform distributions of energy. Furthermore, the residual energy variance diminishes as \(\alpha_{1}\) grows.