## 5 Results and Discussion
It is because underwater sensor nodes using the conventional CSMA/CA protocol with \(W_{1}=31\) can wait less time to access the underwater medium than those with \(W_{1}=63\) when the number of underwater sensor nodes is small. The analytical and simulation results show that delay performances \(S_{protocol\in\{\text{MRTS, BACK, train}\}}\) with \(W_{3}=31\) are better than those with \(W_{3}=63\), respectively. It is because underwater sensor nodes utilizing these protocols with \(W_{3}=31\) can shorten average waiting time to access the underwater medium than those with \(W_{3}\) = 63. Figures 5 and 6 generally show the rank of mean access delay as: the conventional CSMA/CA protocol \(>\) the underwater multi-RTS reception protocol \(>\) the proposed underwater BACK protocol \(>\) the proposed underwater multi-DATA train protocol. Figure 7 shows the simulation results of the proposed underwater multi-DATA train protocol with \(r=2\) and \(r=3\), and the proposed underwater BACK protocol with \(r=2\) and \(r=3\) in terms of expected response time with varying the number of underwater sensor nodes \(N_{r}\) when the contention window size \(W_{r}=31\). In our simulation, we obtain the expected response time as an additional performance metric, where the expected response time is defined as the expected time from when an underwater sensor node transmits its RTS frame to when the underwater sensor node completes the reception of the acknowledgement for its DATA frame. The simulation results show that the expected response times of the proposed underwater multi-DATA train protocol with \(r=2\) and \(r=3\) are shorter than those of the proposed underwater BACK protocol with \(r=2\) and \(r=3\), respectively. 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 simulation results also show that larger number of rings \(r\) can yield a longer expected response time for the proposed underwater multi-DATA train protocol and the proposed underwater BACK 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 7: Expected response time of the proposed underwater multi-DATA train protocol with \(r=2\) and \(r=3\), and the proposed underwater BACK protocol with \(r=2\) and \(r=3\) when \(W_{r}=31\). Figure 8 shows successful transmission probabilities for the proposed underwater multi-DATA train protocol with \(r=2\) and \(r=3\) for various numbers of underwater sensor nodes when the contention window size \(W_{r}=31\). The analytical results in the case of \(r=2\) show \(p_{5,1|r=2}/p_{5|r=2}\) and \(p_{5,2|r=2}/p_{5|r=2}\) where \(p_{5|r=2}=\sum_{m=1}^{2}p_{5,m|r=2}\). As the number of underwater sensor nodes increases, \(p_{5,1|r=2}/p_{5|r=2}\) decreases and \(p_{5,2|r=2}/p_{5|r=2}\) increases. It can yield that the expected response time of the proposed underwater multi-DATA train protocol with \(r=2\) and \(W_{2}=31\) increases as the number of underwater sensor nodes increases as shown in Figure 7. The analytical results in the case of \(r=3\) show \(p_{5,1|r=3}/p_{5|r=3}\), \(p_{5,2|r=3}/p_{5|r=3}\), and \(p_{5,3|r=3}/p_{5|r=3}\) where \(p_{5|r=3}=\sum_{m=1}^{3}p_{5,m|r=3}\). As the number of underwater sensor nodes increases, \(p_{5,1|r=3}/p_{5|r=3}\) decreases, \(p_{5,2|r=3}/p_{5|r=3}\) increases, and \(p_{5,3|r=3}/p_{5|r=3}\) increases.