# Self-Organized Fast Routing Protocol for Radial Underwater Networks
## 7 Computer Simulation Results
### Discussion of Results  
If we analyze the results, we can see that the convergence delay was due to the long propagation delay of the underwater acoustic channel. In order to avoid collisions, some kind of time synchronization must be used in this protocol. For example, it is possible that RR packets sent  
Figure 19: Comparison of Time Slots for Collision Rate and Convergence Delay.  
Figure 20: Energy Consumption vs. Number of Time Slots.  
Figure 18: Collision Rate vs. Convergence Delay.  
by the first nodes of the side strings have been successfully received by the second nodes but we have to wait for a period equal to three transmissions of RR and RR_ACK packets before the side nodes transmit the CF_RR packet to the intermediate nodes. The reason is that the two side nodes do not know about each other transmission's state. If one side node has successfully sent the RR packet but the other one needs one more transmission, then synchronization will be lost, which may cause collisions at later stages.  
Figure 14 shows that the convergence delay increases linearly with the number of nodes in the strings. In Figure 13, we see that the convergence delay changed only when the number of strings increased from even to odd. Figure 16 shows that the collision rate also increased substantially when the number of strings grew from odd to even, whereas there is a trivial increase in the collision rate when the number of strings grows from even to odd. However, Figure 16 shows that, when the number of nodes increased, the collision rate remained almost the same with an average of 2.325% and standard deviation of \(\sigma=0.135\).  
The percentage of retransmitted packets increased with the probability of packet loss but it was not high (see Figure 15). Under normal channel conditions, we may expect low packet loss probability and hence a small number of packet retransmissions.  
We can compare our proposal with the location-free protocols described in Section 2.1. Both NLPU [16] and SOFRP are proactive protocols, using a probe message to establish the path and their topology has one gateway node. However, there are two main differences: (a) NLPU does not replicate the physical topology, thus paths may be longer than required; and (b) the channel is split into several sub-channels, thus decreasing the available bandwidth per node.  
Assume a network that has 30 nodes, organized in 5 strings and 6 rows. The distance between the nodes is 1000 m and data rate is 10 kbps. The communication channel is divided into seven subchannels, each with a data rate of 1428 bps. If we analyze the end-to-end delay achieved with NLPU and SOFRP when the farthest node transmits, we find that for NLPU, this value is 20.3 s, while SOFRP achieves an end-to-end delay of 4.3 s. Overall, an improvement of roughly 75%.  
It is not possible to carry out a proper comparison with the other location free protocol, LFLSR, as the results shown in Reference [17] do not describe the network configuration and information on the number of hops each packet requires is missing. However, the use of periodic Hello packets imposes an additional burden that increases the end-to-end delay of packets. Hence, LFLSR would at least require 0.667 s more than SOFRP per each Hello packet transmission that the data packet encountered along the way.