## 5 Performance Evaluation
### The Balance of Energy  
(1) Energy variance  
Figure 7 shows the variance of residual energy of nodes in the network as the network size changes at the end of network operation of three algorithms. It can be seen that the energy balance of MCRP is poor, followed by DS-EERA. The energy balance of EBRA-NLE proposed in this paper is the proposing, and its energy variance is always kept at a low level under different network size. This is because in the decision-making indexes, \"energy balance factor\" and \"buffer idleness\" of EBRA-NLE consider the current energy and traffic of the forward neighbors, and send the data to the forward neighbor node with high energy and light load as the next hop. Therefore, the energy consumption between nodes is relatively balanced, and the network can work for a longer time.  
(2) Energy distribution  
Figure 8 shows the distribution of the residual energy of nodes over time with 100 nodes randomly distributed in the monitoring area of \(100\times 100\) m\({}^{2}\). The figure in the upper left shows the energy distribution at the initial moment of network operation, the energy of all nodes is full and equal. In the lower left, the network reaches its lifetime after 1404 h of network operation. It can be seen from the Figure 8 that the energy of the nodes in the network is consumed evenly over time, the residual energy between the nodes is balanced, and there is no energy hole problems.  
(3) Network lifetime  
Figure 6: The average energy consumption comparisons with varying network size.  
Figure 9 shows the comparison of the network lifetime of the three algorithms with the change of network size. It can be seen that the network lifetime of the EBRA-NLE proposed in this paper is always the highest, and is more than 50% higher than that of DS-EERA and MCRP in most cases. For example, when N = 100, the network lifetime of MCRP, DS-EERA, and EBRA-NLE is 340 h, 817 h, and 1404 h, which means that EBRA-NLE is improved about 313% and 72% more than that of MCRP and DS-EERA respectively. This is because according to Figures 7 and 8, the energy of nodes in the data transmission path  
(4)Node survival rate  
The survival rate of nodes in the network can also reflect the effectiveness and balance of energy utilization in a certain extent. Figure 10 shows the curve of node survival rate of three algorithms with varying time when the number of nodes in the network is 100. It can be seen that the first node death time of MCRP, DS-EERA, and EBRA-NLE is 340 h, 817 h, and 1404 h respectively. When all nodes in the MCRP and DS-EERA are dead, EBRA has not yet seen the first node death. Obviously, the curve of EBRA-NLE is the steepest, and that of MCRP is more smoothly after they reach their first node death. This is because the difference of residual energy between nodes in MCRP is large. When the first node in the network dies, the residual energy of other nodes is still sufficient, thus reaching the network lifetime prematurely. It is evident that the energy balance between the EBRA-NLE proposed in this paper is promising, which can effectively extend the network lifetime.  
Figure 10: The node survival rate with varying time.  
Figure 9: The network lifetime with varying network size.