## 5 Results and Discussion  
In this section, we compare and discuss analytical results and simulation results of the normalized throughput \(S_{protocol}\) and the mean access delay \(D_{protocol}\) for \(protocol\in\{\text{CONV, MRTS, BACK, train}\}\) in the case of \(r\) rings with various values of input parameters. For the analytical results and the simulation results, we consider the number of underwater sensor nodes as \(N_{1}=N_{2}=N_{3}\) and \(n_{i}=N_{r}/r\), for \(i=1,\dots,r\) when the number of rings is \(r\). Each ring \(i=1,\dots,r\) has the boundary \([l_{i-1},l_{i})\) where \(l_{0}=0\) and the ring \(i\) has two radii \(l_{i-1}\) and \(l_{i}\). We consider \(l_{i}=i\cdot l_{1}\) for \(i=1,\dots,r\). We set \(l_{r}=r_{C}\) where \(r_{C}\) is a cell radius. We consider the transmission probability \(p_{\text{T}|r}\) as \(2/(W_{r}+2)\) where denotes a contention window size when the number of rings is \(r\). We consider \(\text{PROP}_{\text{ifr}}=i\cdot\text{PROP}_{\text{1I}}\) for \(i=1,\ldots,r\) when the number of rings is \(r\). In our simulation, the condition (1) for two underwater sensor nodes is satisfied when the two underwater sensor nodes are located in different rings. In our simulation, the condition (1) for two underwater sensor nodes is not satisfied when the two underwater sensor nodes are located in the same ring. The input parameters and values for the analytical and simulation results are shown in Table 1 based on [2; 3; 4; 5; 6; 17]. Figures 3-6 show the analytical results (lines) and the simulation results (marks) of our proposed underwater multi-DATA train protocol, our proposed underwater BACK protocol, the underwater multi-RTS reception protocol [17], and the conventional CSMA/CA protocol based on [6; 14], respectively, in terms of the normalized throughput and the mean access delay with varying the number of underwater sensor nodes \(N_{r}\) when the number of rings is \(r\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Data rate \(R_{\text{UWA}}\) & 660 [bps] \\ Duration of PHY header \(T_{\text{PHY}}\) & \(128/R_{\text{UWA}}\) [s] \\ Duration of MAC header \(T_{\text{MAC}}\) & \(272/R_{\text{UWA}}\) [s] \\ Duration of RTS frame \(T_{\text{RTS}}\) & \(T_{\text{PHY}}+(160/R_{\text{UWA}})\) [s] \\ Duration of CTS frame \(T_{\text{CTS}}\) & \(T_{\text{PHY}}+(112/R_{\text{UWA}})\) [s] \\ Duration of DATA payload \(T_{\text{P}}\) & \(8184/R_{\text{UWA}}\) [s] \\ Duration of ACK frame \(T_{\text{ACK}}\) & \(T_{\text{PHY}}+(112/R_{\text{UWA}})\) [s] \\ Duration of BACK frame \(T_{\text{BACK}}\) & \(T_{\text{PHY}}+(112/R_{\text{UWA}})\) [s] \\ Underwater acoustic speed \(v_{\text{UWA}}\) & 1500 [m/s] \\ Cell radius \(r_{\text{C}}\) & 2500 [m] \\ Maximum propagation delay \(\text{PROP}_{\text{max}}\) & \(2r_{\text{C}}/v_{\text{UWA}}\) [s] \\ SIFS & 0.1 [s] \\ DIFS & \(\text{PROP}_{\text{max}}+\text{SIFS}\) [s] \\ EIFS & \(\text{SIFS}+T_{\text{ACK}}+\text{DIFS}\) [s] \\ Slot time \(T_{\text{I}}\) & \(\text{PROP}_{\text{max}}\) [s] \\ Contention window size \(W_{r}\) & 31, 63 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Input parameters and values for analytical and simulation results. Figure 3: Normalized throughput of the proposed underwater multi-DATA train protocol, the proposed underwater BACK protocol, and the underwater multi-RTS reception protocol with \(r=2\) and \(r=3\), and the conventional CSMA/CA protocol with \(r=1\). Figure 4: Normalized throughput 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 5: Mean access delay of the proposed underwater multi-DATA train protocol, the proposed underwater BACK protocol, and the underwater multi-RTS reception protocol with \(r=2\) and \(r=3\), and the conventional CSMA/CA protocol with \(r=1\).