# Self-Organized Fast Routing Protocol for Radial Underwater Networks
## 3 Overview of Self Organized Fast Routing Protocol (SOFRP)
### Network Topology  
It is well understood that the larger the number of sensor nodes deployed in an area the more complete the area monitoring and characterization. Therefore, deploying the large number of sensors in a grid or hexagonal form is preferred for more accurate monitoring. This relationship between nodes density and information accuracy is valid for all kind of monitoring systems, whether terrestrial or underwater, wired or wireless. However, such high accuracy is not always required for all kind of monitoring systems. High density deployment of the nodes has a substantial effect on the cost. Compared to terrestrial monitoring systems, the costs of the underwater sensor nodes and their deployment are very high, especially in deep waters [48]. Therefore, monitoring systems having a low density of sensor nodes are preferred (whenever high accuracy is not required) to reduce the costs. Underwater monitoring systems such as an early warning system for tsunamis [49] and volcanic eruption monitoring [50; 51] will perform well enough with low density sensor networks. In such cases, radial topology, with a larger density at the core, is more suitable to reduce the costs of the monitoring system. Our protocol is proposed for a kind of hybrid radial/linear topology as shown in Figure 2. The reason is that this particular topology is very much suited for monitoring river plumes, where sediments are carried away from a river mouth into the sea, whose scattering follows a triangular pattern, moving sideways with the sea current. It can also be used for monitoring oil spills, coral reefs and habitats along the coastal area. In general, the topology serves to monitor an area and collect all the information in a single point that connects the network to the outside world. We consider that the network contains an indeterminate number of nodes and a gateway (GW), with \(N\) radii, where \(N=\{1,2,\ldots,n\}\). From now on, we will use the name of string for the radial lines. The strings are shown in vertically in Figure 2, but they can be organized as radii departing from the gateway in all directions, distributed over the circle (2D) or the sphere (3D). This topology fits any 3D region shape when only one sink node is possible. \begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol** & **Description** \\ \hline DCFRR & Delay for CF\_RR and CFRR\_ACK packets delivery \\ DCFRRBACK & Delay for CFRR\_BACK and CFRRBACK\_ACK packets delivery \\ DGWRR & Delay for RR packet delivery to the gateway \\ DRR & Delay for RR packet delivery start at first layer \\ D\_RALL & Total delay for RR packet to be delivered to all nodes \\ DRRRSP & Delay for RR\_RSP and RRRSP\_ACK packets delivery \\ DGGN & Delay for SGN packet delivery \\ DBHN & Delay for SHN and SHN\_ACK packets delivery \\ DSHNRSP & Delay for SHNRF and SHN\_ACK packets delivery \\ DTotal & Total delay for RR\_RSP packet to reach the gateway \\ DR & Data rate (bits/sec.) \\ DT & Distance between two nodes (m) \\ GT & Guard time (sec.) \\ LTS & Duration of a wait period (sec.) \\ ND & Number of nodes in a string \\ PKD & Packet transmission delay (sec.) \\ PROD & Propagation delay (sec.) \\ PS & Packet size (bits) \\ RPH & Repetition of RR packet forwarding within a layer \\ RPV & Repetition of RR packet forwarding through all layers \\ SPS & Sound Propagation Speed (m/s) \\ ST & Number of strings \\ TS & Duration of a timeslot (sec.) \\ TTS & Number of timeslots in a wait period \\ WP & Wait Period \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of the symbols used in the equations. In terms of interference, the worst case is when adjacent strings are parallel to each other, and this will be the case considered. For the purpose of the analysis in this paper, we have considered an equal distance among the nodes in each radius. Varying distances can be considered by setting an appropriate guard time in the transmissions, within a limit. Finally, we consider that nodes adapt their transmission power so that only neighbor nodes can be reached.