## 2 Materials and Methods
### Modeling \(T\)  
#### 2.3.1 Procedure 1  
\(T\) values corresponding to \(sp_{1}=60\) km/h and \(p_{2}\) selections (second data column in Table 2 above) are stored in vector \(A_{60}=\left[0.23\times 10^{-3}\ 0.25\ldots 6.77\ 9.02\right]\). The same procedure can be used to construct a vector for each \(sp_{1}\) case. A vector content is accessed by position with index \(j=1\ldots\ 8\), for example \(A_{65}(1)=0.0116\). We construct vector \(B_{sp_{1}}\) with \(A_{sp_{1}}\) in such a way that, for \(j\geq 2\), \(B_{sp_{1}}(j-1)=A_{sp_{1}}(j)-A_{sp_{1}}(j-1)\), because the values of vectors \(B_{sp_{1}}\) might follow a linear pattern. Table 4 presents the values of vectors \(B_{sp_{1}}\). In the first column, we have the content of vector \(B_{60}\); in the second, the content of \(B_{65}\); and so on. The Pearson's linear correlation coefficient (\(r\)) between vector \(B_{sp_{1}}\) and vector \(J=\left[1\ 2\ldots\ 6\ 7\right]\) (the vector containing the \(j=1\ldots\ 7\) index values) is expressed as \(corr\big{(}B_{sp_{1}},J\big{)}\). As \(corr\big{(}B_{sp_{1}},J\big{)}\geq 0.95\) for \(sp_{1}\) values [60,65,75,85,90], each \(B_{sp_{1}}\) vector is modeled with a linear equation (Equation (4)). The equations presented in this section, and in the following ones, were solved with the least-squares technique. \[\tilde{B}_{sp_{1}}(j)=(a\cdot j)+b \tag{4}\]  
With Equation (4) (with index \(j\) being the independent term), we calculate parameters \(a\) (slope) and \(b\) (y-intercept) for modeling vectors in Table 4, resulting in vectors \(\tilde{B}_{sp_{1}}\). Table 5 presents parameters \(a\) and \(b\) to obtain each vector \(\tilde{B}_{sp_{1}}\). In the first column, the parameters' values for obtaining \(\tilde{B}_{sp_{1}=60}\) can be found; in the second, those for \(\tilde{B}_{65}\); and so on. Parameter \begin{table}
\begin{tabular}{c c c c c c} \hline \(\mathbf{p}_{2}\) & \(\mathbf{T}_{60}\) & \(\mathbf{T}_{65}\) & \(\mathbf{T}_{75}\) & \(\mathbf{T}_{85}\) & \(\mathbf{T}_{90}\) \\ \hline \(10\%\) & \(T_{60}^{10}=0.232\times 10^{-3}\) s & \(T_{65}^{10}=0.011688\) & \(T_{75}^{10}=0.066858\) & \(T_{85}^{10}=0.09583\) & \(T_{90}^{10}=0.052981\) \\ \hline \(20\%\) & \(T_{60}^{20}=0.255986\) & 0.335886 & 0.321614 & 0.393612 & 0.315841 \\ \hline \(30\%\) & \(T_{60}^{30}=0.915285\) & 0.813281 & 0.75368 & 0.823075 & 0.784827 \\ \hline \(40\%\) & \(T_{60}^{40}=1.944888\) & 1.609535 & 1.718255 & 1.379915 & 1.400379 \\ \hline \(50\%\) & \(T_{60}^{50}=3.237528\) & 2.881251 & 2.453064 & 2.20284 & 2.190038 \\ \hline \(60\%\) & \(T_{60}^{60}=4.812069\) & 4.316362 & 3.70371 & 3.239808 & 3.135533 \\ \hline \(70\%\) & \(T_{60}^{70}=6.774603\) & 6.005609 & 4.949776 & 4.394159 & 4.239621 \\ \hline \(80\%\) & \(T_{60}^{80}=9.029137\) & 7.842978 & 6.649683 & 5.68031 & 5.467405 \\ \hline \end{tabular}
\end{table} 
Table 2: Mean extra travel time data. \begin{table}
\begin{tabular}{c c c c c c} \hline \(\mathbf{p}_{2}\) & \(\mathbf{V}_{60}\) & \(\mathbf{V}_{65}\) & \(\mathbf{V}_{75}\) & \(\mathbf{V}_{85}\) & \(\mathbf{V}_{90}\) \\ \hline \(10\%\) & \(V_{60}^{10}=5.28\times 10^{-5}\) s & \(V_{65}^{10}=0.011465\) & \(V_{75}^{10}=0.082488\) & \(V_{85}^{10}=0.119821\) & \(V_{60}^{10}=0.072548\) \\ \hline \(20\%\) & \(V_{60}^{20}=0.375195\) & 0.452188 & 0.347738 & 0.409435 & 0.341801 \\ \hline \(30\%\) & \(V_{60}^{30}=0.89158\) & 0.681472 & 0.605966 & 0.583584 & 0.530159 \\ \hline \(40\%\) & \(V_{60}^{40}=1.194243\) & 0.888504 & 0.891808 & 0.768092 & 0.788808 \\ \hline \(50\%\) & \(V_{60}^{50}=1.666407\) & 1.207142 & 1.279672 & 1.250472 & 1.477645 \\ \hline \(60\%\) & \(V_{60}^{60}=1.350847\) & 1.152442 & 1.290058 & 1.167536 & 1.054867 \\ \hline \(70\%\) & \(V_{60}^{70}=1.612525\) & 1.612141 & 1.413731 & 1.062381 & 1.236766 \\ \hline \(80\%\) & \(V_{60}^{80}=1.31128\) & 1.257396 & 0.996451 & 1.23536 & 1.105068 \\