## 5 Performance Evaluation
### Performance Evaluation  
We evaluate RRSS performance using the following three parameters. The packet delivery ratio is the ratio of the number of data packets received successfully by all sink nodes to the number of data packets transmitted by the source nodes. The data packets received by many sink nodes are counted only once when calculating the packet delivery ratio. The average end-to-end delay represents the average time taken by a packet from the source node to a sink node. The total energy consumption includes all the energy consumption of all the nodes in the transmitting, receiving and idling states in the UWSNs. (1) delivery ratio vs. time interval of the beacon signal  
The curves of the delivery ratio vs. the time interval of the beacon signal are shown in Figure 11. T represents the propagation time from a sender to a communication radius \((T=\frac{R}{v_{0}})\). We can see the delivery ratio decreases as the interval increases when the speed of water current is 0. When the speed of nodes is 1 m/s and the beacon signal interval is less than 6 T, the delivery ratio is almost same; when the interval is greater than 6 T, the delivery rate decreases significantly. When the speed of nodes is 3 m/s, the delivery ratio starts to decrease at the point of 5 T of the interval of the beacon signal. When the speed of the nodes' movement is 5 m/s, the point of delivery ratio decrease is 3.5 T. This is because the routing table is unable to be updated in a timely way with the movement of the nodes. In other words, the best next-hop selected may not be the qualified node. In addition, the interval of the beacon signal should be decreased with the increase of the speed of the nodes. So, in the following simulation, the speed of water current is 1-5 m/s and the time interval of the beacon signal is set as 5 T. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter Name** & **Value** \\ \hline Communication radius & 100 m \\ Data packet payload size & 50 byte \\ Hello packet size & 6 byte \\ Transmission power & 2 w \\ Receive power & 0 w \\ Idle power & 0 w \\ Bit rate & 10 kbps \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter setting. Effect of Data Rate  
The packet delivery ratio, energy consumption and end-to-end delay at different data rates are shown in Figure 12. From Figure 12a we can see the delivery ratio increases with the number of nodes when the data rate is 0.5 packets per second and 1 packet per second. The number of candidate next-hop nodes increases as the total number of sensor nodes increases, which results in a better next-hop and a higher delivery ratio. When the data rate is 2 packets per second, the delivery ratio is less than 80%. A high data rate leads to much collision. Figure 12b shows that end-to-end delay decreases as the number of sensor nodes increases, since a more optimized path can be chosen. Figure 12c indicates that the energy consumption is proportional to the number of packets delivered when the data rate is 0.5 and 1 packet per second. When the data rate is 2 packets per second, the energy consumption is more than double that of 1 packet per second, which is due to excessive collisions and retransmission. Figure 11: Delivery ratio vs. time interval of the beacon signal. Figure 12: Effect of data rate. (**a**) Delivery ratio vs. the number of nodes; (**b**) end-to-end delay vs. the number of nodes; (**c**) energy consumption vs. the number of nodes. (3) Performance Comparison  
In Figure 13, we compare the RRSS with the VBF and DBR routing protocols. Firstly, the delivery ratio is compared in networks with one sink node and five sink nodes, respectively. Figure 13a shows the delivery ratio in the network with five sink nodes is higher than the delivery ratio in the network with one sink node in DBR as well as RRSS. The delivery ratio of RRSS is higher than VBF and DBR, which results from both VBF and DBR being a greedy routing algorithm; and data packets may be forwarded to nodes in void area or without enough residual energy.