## 5 Results and Discussion
Figures 3-6 show that the analytical results of \(S_{protocol}\), and \(D_{protocol}\) for \(protocol\in\) {CONV, MRTS, BACK, train} agree very well with the simulation results, respectively, for various values of \(N_{r}\) and input parameters. Figure 3 shows the analytical results and the simulation results of the proposed underwater multi-DATA train protocol with \(r=2\) and \(r=3\), the proposed underwater BACK protocol with \(r=2\) and \(r=3\), the underwater multi-RTS reception protocol with \(r=2\) and \(r=3\), and the conventional CSMA/CA protocol with \(r=1\) in terms of the normalized throughput with varying the number of underwater sensor nodes \(N_{r}\) when the contention window size \(W_{r}=31\). Figure 3 shows that the proposed underwater BACK protocol with \(r=2\) and \(r=3\) outperforms the underwater multi-RTS reception protocol with \(r=2\) and \(r=3\), respectively, in terms of the normalized throughput. It is because the proposed underwater BACK protocol can save more time to acknowledge the reception of multiple DATA frames than the underwater multi-RTS reception protocol. Figure 3 also shows that the proposed underwater multi-DATA train protocol with \(r=2\) and \(r=3\) outperforms the proposed underwater BACK protocol with \(r=2\) and \(r=3\), respectively, in terms of the normalized throughput. It is because the proposed underwater multi-DATA train protocol can save more time to transmit multiple DATA frames than the proposed underwater BACK protocol. The analytical results and the simulation results show that the conventional CSMA/CA protocol with \(r=1\) may yield the lowest normalized throughput among these protocols. It is because the conventional CSMA/CA protocol with \(r=1\) cannot provide the multi-RTS reception capability for an underwater sink node. The analytical and simulation results also show that larger number of rings \(r\) can yield larger normalized throughput for the proposed underwater multi-DATA train protocol, the proposed underwater BACK protocol, and the underwater multi-RTS reception protocol, respectively. It is because an underwater sink node utilizing these protocols with more rings can recover more RTS frames transmitted simultaneously from underwater sensor nodes which are not overlapped at the underwater sink node due to long underwater acoustic propagation delay. Figure 6: Mean access delay of the proposed underwater multi-DATA train protocol, the proposed underwater BACK protocol, and the underwater multi-RTS reception protocol with \(W_{3}=31\) and \(W_{3}=63\), and the conventional CSMA/CA protocol with \(W_{1}=31\) and \(W_{1}=63\). Figure 4 shows the analytical results and the simulation results of the proposed underwater multi-DATA train protocol with \(r=3\), the proposed underwater BACK protocol with \(r=3\), the underwater multi-RTS reception protocol with \(r=3\), and the conventional CSMA/CA protocol with \(r=1\) in terms of the normalized throughput with varying the number of underwater sensor nodes \(N_{r}\) and the contention window size \(W_{r}\). The analytical and simulation results show that the normalized throughput of the conventional CSMA/CA protocol with \(W_{1}=31\) is larger than that with \(W_{1}=63\) when the number of underwater sensor nodes is 9, 12, and 15. It is because underwater sensor nodes using the conventional CSMA/CA protocol with \(W_{1}=63\) can wait more time to access the underwater medium than those with \(W_{1}=31\) when the number of underwater sensor nodes is small. The analytical and simulation results show that the normalized throughput of the conventional CSMA/CA protocol with \(W_{1}=31\) is smaller than that with \(W_{1}=63\) when the number of underwater sensor nodes is 18, 21, 24, and 27. It is because the conventional CSMA/CA protocol with \(W_{1}=31\) can cause more collisions due to more RTS frames transmitted simultaneously from underwater sensor nodes than that with \(W_{1}=63\) when the number of underwater sensor nodes is large.