# Self-Organized Fast Routing Protocol for Radial Underwater Networks
## 7 Computer Simulation Results  
The performance of the protocol is analyzed in terms of three parameters, i.e., convergence delay, probability of collision between packets and number of retransmitted packets in case of packet loss. Convergence delay is defined as the total time required to form the routing paths, which starts with the transmission of the beacon packets and ends when the gateway successfully receives the RR_RSP packets. For the simulations, we have assumed a topology with the structure shown in Figure 3. The distance between the gateway and its neighbor nodes is set at 500 m. Similarly, the distance between two adjacent nodes in a string is also set at 500 m. The number of nodes in all the strings is the same. Propagation speed is taken as 1500 m/s. The data rate is 5000 bits per second and the packet size is calculated using Equation (1). The transmission power considered for the simulations is 18 W (a value taken from Reference [52]), and the BER is \(10^{-6}\). The simulation parameters are summarized in Table 3. All these values are realistic in UW communication networks. The simulation tool is a proprietary MATLAB(r)-based simulator. First, we analyze the effect of increasing the number of strings on the convergence delay. Figure 13 shows the results of a simulation in which there are three nodes in each string, but the number of strings varies. It shows that the convergence delay remains the same when the number of strings  
Figure 14: Convergence Delay vs. No. of Nodes. Figure 13: Convergence Delay vs. No. of Strings. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline Sound speed & 1500 & m/s \\ Distance between nodes & 500 & m \\ Data rate & 5000 & bits/s \\ Header size & 37 & bits \\ Transmission power & 18 & Watts \\ Bit error rate & \(10^{-6}\) & \\ Number of runs & 500 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation Parameters. increases from odd to even, as for example from three to four or from five to six. This is due to the fact that the number of transmissions of RR packets and CF_RR packets remains the same when the number of strings increases from odd to the next even number. Hence, the delay remains the same for a number of strings (1, 2), (3, 4), (5, 6), and so on. The difference of delay between string 4 and 5 is 8.489754 min. Similarly, the difference between strings 6 and 7 is also 8.489754 min. The effect of increasing the number of nodes in a string is depicted in Figure 14. It shows that the convergence delay increased linearly with the number of nodes. This was as expected because the delay incurred by each layer is almost constant. The delay increased as the number of nodes grew due to the increase in the packet size. The difference in the packet delay transmission was constant (0.0016 s) for consecutive increases in the number of nodes (see Table 4). The impact of augmenting the network in one node per string in the total convergence delay was 0.091728 (see Table 5). We have analyzed the number of packet retransmissions when the probability of packet loss increases from 0 to 20% at intervals of 2% (Figure 15). The graph shows that, even at high packet loss probabilities, the number of retransmitted packets was in the range of 11-13%. The collision rate is also tested. Figure 16 shows the collision rate when the number of nodes is constant (three nodes in each string), whereas the number of strings increases from three to eight. The graph shows that the collision rate increases nonlinearly with the number of strings. It shows that there is a slight change in the collision rate when the increase in the number of strings is from an odd number to an even number. From even number of strings to the odd number of strings, the change is negligible.