edges. We put the available information in a matrix form $$\mathbb{A}\left( 1\right) =\left( 
\begin{array}{rrrr}
3000 & 1500 & 2500 & 3000 \\ 
500 & 1000 & 500 & 500 \\ 
3000 & 1500 & 4000 & 2500 \\ 
4000 & 1500 & 3000 & 4500\end{array}\right) \ , \label{B0}$$ where in the diagonal entries one finds the number of vehicles in each site and the off-diagonal entries stand for the number of those traveling from one site (line $i$) to another (column $j$), and $\left( \mathbb{A}\left(
1\right) \right) = 12\ 500$ is the number of vehicles still at the sites. The number of vehicles in each row ($U_{k}\left( 0\right) $) are given by the vector ([B02]{}).

The Stochastic Matrix
---------------------

We assume that the matrix (\[B0\]) is the seed that permits to construct another matrix, in a suited form, to be used to forecast the circulation of the vehicles in future moments. This hypothesis is framed formally by normalizing each row. The result is the SM $$\mathbb{M}=\left( 
\begin{array}{cccc}
3/10 & 3/20 & 1/4 & 3/10 \\ 
1/5 & 2/5 & 1/5 & 1/5 \\ 
3/11 & 3/22 & 4/11 & 5/22 \\ 
4/13 & 3/26 & 3/13 & 9/26\end{array}\right)\ ,  \label{D1}$$ 