## 6 Numerical Results and Analysis
### Simulation Results and Analysis
The reason is that NCFM exploits the encoding function to cut down the wireless resource redundancy with more information. Under some \(SDR\) levels, the destination can still receive sufficient packets to restore the original packets. Therefore, this proactive NCFM algorithm outperforms the 1:N and 1 + 1 protection mechanisms. The 1:N method in lossy networks can guarantee the reliability of data transmission to some degree, but the latency caused by path switching and packet retransmission is  
Figure 9: Comparison of successful delivery ratios. longer than those of the other two fault-tolerant mechanisms. Therefore, the conclusion can be drawn that the 1:N fault-tolerant mechanism is not suitable if network users have strict real-time demands. The proactive NCFM method can make full use of limited bandwidth resources to supply fast recovery for delay-sensitive traffic. Figure 12 displays the analysis of the degrees of resource redundancy for the three fault-tolerant mechanisms when the link failure probability is increased. As the link failure probability increases, the degrees of resource redundancy continue to rise, as shown in Figure 12. With the deterioration of channel conditions, packet loss frequently occurs in certain nodes. Partial nodes need to resend the missing packets to ensure that all destination nodes can receive their packets error-free. A large number of retransmissions can cause many redundant packets in WSNs. As depicted in Figure 12, the cost of an elastic transmission mechanism and resource redundancy protection mechanism in terms of the degree of resource redundancy seems to be less than that of a backup path protection mechanism. This is because many different packets are encouraged to mix together into one packet before transmission. This operation can decrease the number of packet transmissions or retransmissions as much as possible, and improve wireless resource utilization. Although some packets are lost, the  
Figure 11: Comparison of ED with the number of packets sent forNetwork Coding-based Fault-tolerant Mechanism (NCFM), 1 + 1 and 1:N.  
Figure 10: Comparison of average end-to-end delay. destination can still exploit the received encoded packets to recover the original packets without retransmission. In particular, the \(RRD\) of the 1:N method rises sharply after the link error rate reaches 0.1. This is because poor channel quality causes much retransmission, resulting in network congestion, which incurs many more redundant packets. To a certain extent, \(RRD\) is similar to the energy consumption efficiency. We can conclude that the elastic transmission mechanism is more economical than the \(1+1\) and 1:N mechanisms. Although NCFM increases the data processing burden of nodes, energy consumption in the computer hardware is much smaller than that needed to process packet transmission, so this part of energy consumption can be ignored. Figure 13 presents an analysis of the degree of resource redundancy for the three fault-tolerant mechanisms as the network traffic continues to increase. The simulation experiments ran with a link failure probability of 10%. As the injected network traffic grows, the \(RRD\)s of the three fault-tolerant mechanisms trend steadily upward. When the link failure probability is relatively low, it can be observed that the expense of NCFM in the degree of resource redundancy is smaller than that of the 1:N and \(1+1\) protection mechanisms. The reason for this is similar to the analysis for Figure 12. Therefore, we can conclude that for identical link error rates, the NCFM is the most economical fault-tolerant scheme for network resources. Figure 12: Comparison of resource redundancy degrees. Figure 13: Comparison of RRD with the number of packets sent for NCFM, \(1+1\) and 1:N.  
Figure 14 shows the analysis of the useful throughput ratio for the three fault-tolerant mechanisms. The simulations were conducted with a link failure probability of 8%.