## 4 Evaluation
### Results
#### 4.3.4 Summary  
The _accuracy improvement_ and _time interval between PSI changes_ of all experiments are summarized in Figures 7 and 8 and Tables 8 and 9. In Figure 8, each block represents the percentages of situations when the congestion in the backup path is _better or worse_ than the current path (light gray denotes _worse_, and dark gray _better_). The red dashed arrow indicates the changing trend after the PWI turns to 1, and it is obvious that the smallest _accuracy improvement_ is 200%, while the largest improvement is almost 360%, which evidences that the proposed PSI is able to relieve the congestion of the path by at least two and up to nearly four times. From Equations (11)-(14) and intuitively in Figure 7, it is also evident that each time the PSI changes its value, it can take effect for at least 760 s, and more than 3000 s at most. This is quite consistent compared to the route change time expense, which is less than 1 s according to technical reports of current vendors ([[https://docs.oracle.com/cd/E19934-01/html/E21707/z40004761412103.html](https://docs.oracle.com/cd/E19934-01/html/E21707/z40004761412103.html)]([https://docs.oracle.com/cd/E19934-01/html/E21707/z40004761412103.html](https://docs.oracle.com/cd/E19934-01/html/E21707/z40004761412103.html)) [[https://www.cisco.com/c/en/us/support/docs/ip/open-shortest-path-first-ospf/7039-1.html#6](https://www.cisco.com/c/en/us/support/docs/ip/open-shortest-path-first-ospf/7039-1.html#6)]([https://www.cisco.com/c/en/us/support/docs/ip/open-shortest-path-first-ospf/7039-1.html#6](https://www.cisco.com/c/en/us/support/docs/ip/open-shortest-path-first-ospf/7039-1.html#6)).) The efficiency and consistency of the PSI are further presented in Figures 3b-6b, by putting the value of the PSI at each time step against the latency difference between the OSPF selected path and the backup one. In Figures 3b-6b, the green dotted lines are the differences between the latency of the chosen path and the backup path. The grey lines denote the values of the PSI at each time step. When the green dot is above 0, the OSPF chosen path is more congested than the backup path; when below 0, the backup path has a better channel situation. In these experiments, the peak traffic rates have exceeded the bandwidth by far (up to 20 times the bandwidth); thus during busy hours, the latency difference can be as large as \(\pm\)60 milliseconds. As suggested intuitively from Figures 3b-6b, the latency differences are dynamic and vibrating. This deduction can also be proved by the variances of latency differences, according to Table 9, in these experiments, the largest variance of latency difference reaches 31.983, while the consistency of the PSI can still be as high as 761.5 s, with a channel improvement of 251%. As for the traffic with the smallest variance 12.16, the PSI can stay unchanged for as long as 1500 s, while still achieving a congestion improvement of 342.9%, as denoted in Table 8.  
In summary, we argue that it is evident that the metric _PSI_ proposed in this paper is able to predict the path situation with acceptable precision and considerable consistency during extremely \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & **True** & **False** & \begin{tabular}{c} **Accuracy** \\ **Improvement** \\ \end{tabular} \\ \hline Exp. 1 & \begin{tabular}{c} PSI = 1 \\ PSI = 0 \\ \end{tabular} & 60\% & 40\% & \multirow{2}{*}{251\%} \\  & PSI = 0 & 76.1\% & 23.9\% & \\ \hline Exp. 2 & \begin{tabular}{c} PSI = 1 \\ PSI = 0 \\ \end{tabular} & 64.1\% & 35.9\% & \multirow{2}{*}{337.36\%} \\  & PSI = 0 & 81\% & 19\% & \\ \hline Exp. 3\_1 & \
\begin{tabular}{c} PSI = 1 \\ PSI = 0 \\ \end{tabular} & 30\% & 70\% & \multirow{2}{*}{212.76\%} \\  & PSI = 0 & 85.9\% & 14.1\% & \\ \hline Exp. 3\_2 &
\begin{tabular}{c} PSI = 1 \\ PSI = 0 \\ \end{tabular} & 58.3\% & 41.7\% & \multirow{2}{*}{342.9\%} \\  & PSI = 0 & 83\% & 17\% & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The accuracy result of all experiments with corresponding PSI.