# Lightweight Path Recovery in IPv6 Internet-of-Things Systems
## 5 Performance Evaluation and Analysis
### Comparison of the Gain-Loss Ratio  
Figure 8 compares the gain-loss ratio of the three algorithms in different network scenarios. The gain-loss ratio is a composite performance metric that reflects the ratio of the gain (i.e., the numerical metric of correctly recovered paths) to the overhead (i.e., the sum of the additional storage overhead used for recovery), which is defined in Equations (2)-(4). In other words, this measurement covers not only the accuracy but also the length of the recovered path and overhead. A larger gain-loss ratio for an algorithm means that it has a higher accuracy or a smaller overhead, or both.  
As shown in Figure 8a, when the number of nodes is 300, and the percentage of fault nodes is 5%, the gain-loss ratio of the 3 algorithms improves as the active ratio of nodes changes. The overhead of the three algorithms is constant individually, so their accuracy determines the trend of their respective gain-loss ratios. The gain-loss ratio of LiPa grows in a high range because its accuracy rate also grows in an increased range. CSPR's gain-loss ratio grows to a certain point and remains stable because CSPR's accuracy has stabilized when the node activity rate is more significant than 50%. Furthermore, the accuracy of the LiPa algorithm is consistently higher than iPath and CSPR. The difference among their gain-loss ratios is affected by both accuracy and overhead. Among them, LiPa and iPath have smaller overheads, requiring only 6 bits of extra overhead per packet. However, CSPR, with low accuracy, has an extra overhead of 8 bits per packet, which makes its gain-loss ratio much lower than the other two algorithms. As shown in Figure 8b, when the percentage of fault nodes is 5%, and the active ratio of nodes is 30%, the gain-loss ratios of the 3 algorithms start fluctuating after improving to a certain level. Their respective accuracy rates influence this. Meanwhile, the gain-loss ratio of LiPa is still consistently higher than that of the other two algorithms. Among them, LiPa's higher gain-loss ratio than iPath is due to its higher accuracy rate, and LiPa's higher gain-loss ratio than CSPR is due to the former's higher accuracy rate and its more negligible overhead. As shown in Figure 8c, when the number of nodes is 300, and the active ratio of nodes is 30%, LiPa and iPath are more stable, while CSPR has a specific downward trend, which is also influenced by their individual accuracy rates. Moreover, the gain-loss ratio of LiPa is still consistently higher than that of iPath and CSPR. For similar reasons, in this network scenario, LiPa has higher accuracy than iPath and CSPR while having a lower additional overhead than CSPR.  
We can conclude that: LiPa's gain-loss ratio consistently outperforms iPath and CSPR in the above network scenarios. This is because, on the one hand, LiPa's higher accuracy  
Figure 7: Comparison of the _Accuracy_: (**a**) Variation in _accuracy_ rate with different node activity; (**b**) Variation in _accuracy_ rate with the number of nodes; (**c**) Variation in _accuracy_ rate with the different node failure rate.  
rate leads to more significant gains; on the other hand, LiPa's overhead is not larger than CSPR and iPath. Thus, the higher gain ratio of LiPa is reflected.