## 5 Results and Discussion
Figure 4 shows that throughput performances \(S_{protocol}=3\) for \(protocol\in\) [MRTS, BACK, train] with \(W_{3}=31\) are higher than those with \(W_{3}=63\), respectively. It is because underwater sensor nodes utilizing these protocols with \(W_{3}=31\) can wait less time to access the underwater medium than those with \(W_{3}=63\). Figures 3 and 4 generally show the rank of normalized throughput as: the proposed underwater multi-DATA train protocol \(>\) the proposed underwater BACK protocol \(>\) the underwater multi-RTS reception protocol \(>\) the conventional CSMA/CA protocol. Figure 5 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 mean access delay with varying the number of underwater sensor nodes \(N_{r}\) when the contention window size \(W_{r}=31\). The analytical and simulation results show that the conventional CSMA/CA protocol with \(r=1\) may yield the worst delay performance among these protocols with varying the values of \(N_{r}\). The analytical and simulation results show that delay performances of the proposed underwater BACK protocol with \(r=2\) and \(r=3\) are better than those of the underwater multi-RTS reception protocol with \(r=2\) and \(r=3\), respectively. Since the proposed underwater BACK protocol transmits the BACK frame instead of multiple ACK frames, the proposed underwater BACK protocol can shorten the delay to acknowledge the reception of multiple DATA frames. The analytical and simulation results show that delay performances of the proposed underwater multi-DATA train protocol with \(r=2\) and \(r=3\) are better than those of the proposed underwater BACK protocol with \(r=2\) and \(r=3\), respectively. Since an underwater sink node utilizing the proposed underwater multi-DATA train protocol can receive a train of multiple successive DATA frames which has a short guard time between the successive DATA frames, the proposed underwater multi-DATA train protocol can shorten the delay for the underwater sink node to receive multiple DATA frames. The analytical and simulation results also show that more rings can yield better delay performance for the underwater multi-RTS reception protocol, the proposed underwater BACK protocol, and the proposed underwater multi-DATA train protocol, respectively. It is because these protocols in the case of more rings can make an underwater sink node recover more RTS frames transmitted simultaneously from multiple underwater sensor nodes which are not overlapped at the underwater sink node due to long underwater acoustic propagation delay. Figure 6 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 mean access delay with varying the number of underwater sensor nodes \(N_{r}\) and the contention window size \(W_{r}\). When the number of underwater sensor nodes is 18, 21, 24, and 27, the results show that the delay performance of the conventional CSMA/CA protocol with \(W_{1}=63\) is better than that with \(W_{1}=31\). It is because the conventional CSMA/CA protocol with \(W_{1}=63\) can cause  
less collisions of RTS frames transmitted from underwater sensor nodes than that with \(W_{1}=31\) when the number of underwater sensor nodes is large. When the number of underwater sensor nodes is 9, 12, and 15, the results show that the delay performance of the conventional CSMA/CA protocol with \(W_{1}=31\) is better than that with \(W_{1}=63\).