## 4 Discussion  
### Discussion for Explaining \(T\)  
Table 26 presents the error (obtained in procedure 1, 2, and 3) between a vector with data for modeling (\(A_{sp_{1}}\)) and the directly modeled vector (\(\bar{A}_{sp_{1}}\)). It also shows the mean of the errors \(E_{sp_{1}}(A_{sp_{1}},\bar{A}_{sp_{1}})\) for \(sp_{1}\) cases {60,65,75,85,90}, i.e., \(\overline{E}=mean([E_{60}\ E_{65}\ E_{75}\ E_{85}\ E_{90}\ ])\). The lower mean error is presented by procedure 1, followed closely by procedure 3. Similarly, Table 27 presents the error between a vector with data for validating (\(A_{sp_{1}}\)) and the indirectly modeled vector (\(\bar{A}_{sp_{1}}\)). It also shows the mean of the errors \(E_{sp_{1}}(A_{sp_{1}},\bar{A}_{sp_{1}})\) for \(sp_{1}\) cases {70,80}. The lower \(\overline{E}\) is presented by procedure 3, followed closely by procedure 1. Thus, the techniques presented in procedures 3 and 1 are the most suitable for modeling and explaining \(T\). We notice that, for procedures 1, 2, and 3, \(E_{80}>E_{70}\), meaning that \(\bar{A}_{70}\) is easier to explain than \(\bar{A}_{80}\). Moreover, for procedures 1 and 3, \(E_{65}\) and \(E_{75}\) are higher than \(E_{60}\), \(E_{85}\), and \(E_{90}\). It follows that \(\bar{A}_{60}\), \(\bar{A}_{85}\), and \(\bar{A}_{90}\) are easier to model than \(\bar{A}_{65}\) and \(\bar{A}_{75}\). In procedures 1 and 3, \(E_{90}\) presents the lowest error and \(E_{75}\) presents the highest, thus \(\bar{A}_{90}\) is the most easily modeled vector and \(\bar{A}_{75}\) is the hardest to model. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Procedure** & \begin{tabular}{c} - \\ \(E_{60}(A_{60}\bar{A}_{60})\) \\ \end{tabular} & \begin{tabular}{c} \(E_{65}(A_{65}\bar{A}_{65})\) \\ \end{tabular} & \begin{tabular}{c} \(E_{75}(A_{75}\bar{A}_{75})\) \\ \end{tabular} & \begin{tabular}{c} - \\ \(E_{85}(A_{85}\bar{A}_{85})\) \\ \end{tabular} & \
\begin{tabular}{c} - \\ \(E_{90}(A_{90}\bar{A}_{90})\) \\ \end{tabular} &
\begin{tabular}{c} \(E\) \\ \(E\) \\ \end{tabular} \\ \hline Procedure 1 & 0.0222 s & 0.0519 & 0.0550 & 0.0238 & 0.0128 & 0.0332 \\ \hline Procedure 2 & 0.4151 & 0.3944 & 0.2957 & 0.2390 & 0.2497 & 0.3188 \\ \hline Procedure 3 & 0.0226 & 0.0552 & 0.0617 & 0.0264 & 0.0116 & 0.0355 \\ \hline \end{tabular}
\end{table} 
Table 26: Error between \(A_{sp_{1}}\) and \(\bar{A}_{sp_{1}}\) (procedures 1, 2, and 3). Figure 6: \(p_{2}\) vs. \(V\) (procedure 6). In Figure 3, we observe that, for the \(sp_{1}\)\(\{70,80\}\) cases, the last two points of vectors \(\hat{A}_{sp_{1}}\) are clearly distant from the corresponding points of vectors \(A_{sp_{1}}\) (in contrast with the other six points). The last two points are the \(T\) when the percentage of slow vehicles is 70% and 80%. Hereafter, \(\overline{E}^{x,y}\) is the mean error of the \(x\) {1,2,...,5,6} procedure and the \(y\) {1,2} comparison, where \(y\) = 1 indicates a comparison between the directly modeled and observed data (Table 26 or Table 28), and \(y\) = 2 indicates a comparison between the not directly modeled and observed data (Table 27 or Table 29). Then, \(\overline{E}^{3,2}=mean\big{(}[E_{70}(A_{70},\hat{A}_{70})\ E_{80}(A_{80}, \hat{A}_{80})]\big{)}=0.2132\) s is the mean error of procedure 3 and \(sp_{1}\)\(\{70,80\}\) cases. With procedure 1, the mean error between the directly modeled and observed data, i.e., \(\overline{E}^{1,1}=0.0332\) s, is lesser that the mean error between the not directly modeled and observed data, i.e., \(\overline{E}^{1,2}=0.2162\) s. This holds for the three procedures. Figure 1 shows that, for \(A_{sp_{1}}\) vs. \(\hat{A}_{sp_{1}}\), the first six points of \(\hat{A}_{70}\) and \(\hat{A}_{80}\) are visible close to the corresponding points of \(A_{70}\) and \(A_{80}\), respectively. The last two points of \(\hat{A}_{70}\) are above those of \(A_{70}\), and the last two points of \(\hat{A}_{80}\) are below those of \(A_{80}\).