## 4 Simulation and Discussion
### Simulation Results
When the number of AUVs is smaller, in order to guarantee the network connections, the transmission power of each AUV in network is larger and the network interference, the retransmission, and the network competition are smaller; moreover, when the number of AUVs in the network is small, the transmission power will play a dominant role in the energy consumption performance, and when this number increases, the transmission power will decrease, so the residual energy increases when the number of AUVs is smaller than nine. However, when the number of AUVs is larger, the dominant parameters will be the network interference, the retransmission, and the network competition, so when the number of AUVs in network increases, the residual energy decreases. As mentioned in Section 3.2, the needed degree of AUVs in the PTC-FTC algorithm is dynamic and defined based on the conclusion in [33]; moreover, to get a fair simulation result, the AUVs' degree in the FTC algorithm is set to three, which is the same as that shown in [6]. The simulation results in Figure 14 illustrate this simulation setting. In Figure 14, when the number of AUVs in the network increases, the AUVs' degree of the PTC-FTC algorithm increases fast to guarantee network connectivity; moreover, the AUVs' degree of the FTC algorithm remains stable. When the number of AUVs in the network is less than three, the AUVs' degree in the PTC-FTC algorithm is smaller than that in the FTC algorithm. This can be explained by the different needed degree calculation algorithms used in the PTC and FTC. In the FTC algorithm, this needed degree is fixed; however, in the PTC algorithm, according to the conclusions in [33], this number is dynamic according to the different  
Figure 15: The average queue length of PTC-FTC and FTC. network conditions. Interesting conclusions can be found when comparing the simulation results in Figure 13 with those in Figure 14. In Figure 14, the average degree of an AUV in the PTC-FTC algorithm is larger than that in the FTC algorithm; however, the residual energy of the PTC-FTC algorithm is larger than that of the FTC algorithm. This can be explained by the conclusion in Figure 12. Since the probability adjustment ratio in the PTC-FTC algorithm is smaller than that in the FTC algorithm, the energy consumption for topology control and retransmission caused by network competition is smaller than in the FTC algorithm, so even though the transmission range in the PTC-FTC algorithm is larger than that in the FTC algorithm, the residual energy in the PTC-FTC algorithm is large. As shown in Figure 15, the queue length of the PTC-FTC algorithm is much smaller than that of the FTC algorithm, and with an increasing number of AUVs in the network, the queue lengths in both the PTC-FTC algorithm and FTC algorithm increase. This is because the more AUVs in network, the more data packets need to be transmitted; therefore, the queue length will increase when the number of AUVs increases. Additionally, due to the fact the transmission power ratio of the PTC-FTC algorithm is much smaller than that of the FTC algorithm (which can be seen in Figure 11), the control messages in the PTC-FTC algorithm are much smaller than in the FTC algorithm, which means the queue length in PTC-FTC algorithm is small, too. The results presented from Figures 11-15 have demonstrated that the PTC-FTC algorithm is efficient on improving network performance while reducing energy consumption for underwater cooperating AUV networks.