# An Energy Balanced and Lifetime Extended Routing Protocol for Underwater Sensor Networks
## 5 Simulations
### Random Node Distribution  
In this part, we value the performance among different protocols under random node distribution as shown in Figure 5b. At each sending round, each node generates \(X\) data packets randomly using Possion distribution. The probability distribution function is given in Equation (22). Here we set \(\lambda=0.5\), so each node send 0.5 packets on average per sending round. The number of sensor nodes are 40 and the network radius is 2 km. \[P\left(X=k\right)=\frac{\lambda^{k}}{k!}e^{-\lambda},k=0,1,\cdots \tag{22}\]  
Figure 13 shows the percentage of residual energy at different circular rings for EBLE, direct transmission, BTM and BEAR. There is a significant difference in energy consumption at different rings for direct transmission protocol (Figure 13b). Both BTM and BEAR improve the unbalanced energy consumption to some extent but the difference is still large. As the sensor nodes are not deployed evenly, nodes in some areas may deal with heavy data loads and BTM/BEAR fails to balance the energy consumption between these areas. Our proposed EBLE outperforms other protocols in terms of energy balancing. This is because that EBLE can balance the energy consumption with more candidate forwarding nodes. Once the most energy efficient path is energy limited, a suboptimal route can be chosen and the direct one-hop transmission only happens when all candidate forwarding nodes lack battery power. Figure 12: The overall network consumed energy per sending round for different protocols. Figure 14 shows the percentage of dead nodes at different sending round for direct transmission, EBLE, BTM and BEAR. In this random node distribution case, EBLE can send the greatest number of packets before a first node in the network is dead. When a first node is dead because of low power, EBLE can have 90 more sending rounds than BTM. The performance of BEAR is even worse than the direct transmission in this case. This is because BEAR uses regular zones to choose the next forwarder. Only nodes in the same zone can be selected as next hop forwarders and this limits the choice of forwarders. When the nodes in the network are distributed randomly, there may not be enough nodes in some zones and BEAR has to choose to send data to the sink node directly. The energy cost for broadcasting residual energy also aggravates the energy consumption. It can also be seen that when 35% of the sensor nodes are dead, BTM can send more packets compared with EBLE. This is because BTM uses more direct transmissions than EBLE and some nodes in BTM may have few data loads, which makes the network keep a lot of energy when some nodes are unable to work any more. In network protocol design, we believe that the principle is to keep as many sensor nodes alive as possible because we are unwilling to lose the information of any interested area. Figure 13: Percentage of residual energy: (**a**) EBLE, (**b**) Direct transmission, (**c**) BTM, (**d**) BEAR. In order to make the simulation results more reliable, we change the random seed to conduct simulations on 10 different random node distributions. Figure 15 shows the number of overall transmitted packets in the network when a first node is depleted of its battery power. The direct one-hop transmission protocol has almost the same number of transmitted packets over different node distributions. This is because the network life performance for direct transmission is always determined by the node farthest from the sink. Other protocols use energy balancing scheme to distribute the data load evenly. It is clearly seen that EBLE outperforms other protocols in terms of \(FirstNodeDead\) network life. This is mainly due to our proper design of cost function and intelligent choice of next forwarders. In BTM, only one node has a unique optimal forwarder. If this forwarder is in low battery power state, BTM has to send data directly to the sink. However, EBLE selects the next hop forwarders by comparing their energy consumption per effective distance.