whose eigenvalues are approximately $$\begin{tabular}{|c||c|c|c|c|}
\hline
$k$ & $1$ & $2$ & $3$ & $4$ \\ \hline
\multicolumn{1}{|l||}{$\lambda _{k}$} & \multicolumn{1}{l|}{${\ 1.0}$} & 
\multicolumn{1}{l|}{${\ 0.27}$} & \multicolumn{1}{l|}{${\ 0.13}$} & 
\multicolumn{1}{l|}{${\ 0.01}$} \\ \hline
\end{tabular}\ .  \label{D1.1}$$ The eigenvalue $\lambda _{1}=1.0$ is the PF while the others are quite smaller than $1$, this is an indication that under this kind of evolution the traffic should stabilize after very few steps. As $\det \mathbb{M}=\left({2600}\right)^{-1}<1$, then $\lim_{n\rightarrow \infty }$$\det \left( 
\mathbb{M}^{n}\right) =0$ and $\lim_{n\rightarrow \infty }\mathrm{Tr}\left( 
\mathbb{M}^{n}\right) =1$.

Now we calculate the number of vehicles in each site plus those that left (in a period of 24 hours). The prediction of the distribution for the following days is given by Eq. (\[A24\]), and the total number of vehicles is a conserved quantity, $\lim_{n\rightarrow \infty }\sum_{i}U_{i}\left( n\right) =36\,500 = Y$. The distribution changes with $n$ until the stabilization of the flow is attained swiftly in less than $4$ steps. This trend could be guessed due to the wide difference between the PF eigenvalue ($\lambda _{1}$=1) and $\lambda _{2}$, see the frame (\[D1.1\]). The vehicular circulation presents three characteristic decay times towards the stationary distribution $$\begin{tabular}{|c||c|c|c|c|}
\hline
$i$ & ${\ 1}$ & ${\ 2}$ & 