matrix $$\mathbb{A}=\left( 
\begin{array}{cccc}
R_{1} & P_{1} & P_{5} & Q_{4} \\ 
Q_{1} & R_{2} & P_{2} & P_{6} \\ 
Q_{5} & Q_{2} & R_{3} & P_{3} \\ 
P_{4} & Q_{6} & Q_{3} & R_{4}\end{array}\right) ,  \label{A1}$$ whose entries are the number vehicles observed and counted in an *ad hoc* interval of time or an average over several previous observations.

Assuming that we want to forecast the evolution of the distribution of vehicles in the network at a daily basis, for instance, we adopt the causal interpretation based on the hypothesis that the vehicles distribution evolves according to a $n$-step process: (*a*) The entries in the main diagonal in matrix (\[A1\]), $A_{ii}=R_{i}$, stand for the number of vehicles at site $i$; (*b*) the off diagonal entries $A_{ij}$ ($i\neq j$) are for the number of vehicles that left site $i$ and are on their way to site $j$. For a period of 24 hours the sum of the entries of row $i$, $U_{i}=\sum_{j}A_{ij}$ represents the number of vehicles that remained in or left the site $i$ for the other sites. Complementarily, $T_{j}=\sum_{i}A_{ij}$ represents the number of vehicles that are in site $j$ plus those that have departed from the other sites and 