are on their way to arrive at it. So, we may consider that matrix (\[A1\]) represents a continuous observation for a 24-hour period, or an average over sub-periods of observations, for instance, six minutes sample at every two hours.

The Stochastic Matrix 
======================

By normalizing the rows of matrix (\[A1\]) we construct a stochastic matrix (SM) to be adopted as the generator of the evolution that could describe and forecast the number of vehicles in the sites plus those in transit. Writing the parameters for the first row as $$r_{1}=\frac{R_{1}}{U_{1}},\quad p_{1}=\frac{P_{1}}{U_{1}},\quad p_{5}=\frac{P_{5}}{U_{1}},\quad q_{4}=\frac{Q_{4}}{U_{1}},  \label{normline}$$ the same goes for the other rows, which are used to construct the transition probability matrix $$\mathbb{M}=\left( 
\begin{array}{cccc}
r_{1} & p_{1} & p_{5} & q_{4} \\ 
q_{1} & r_{2} & p_{2} & p_{6} \\ 
q_{5} & q_{2} & r_{3} & p_{3} \\ 
p_{4} & q_{6} & q_{3} & r_{4}\end{array}\right)\ .  \label{A2}$$ The sum of the (non-negative) entries of each row is $1$ whereas the sum of the entries of each column is not necessarily $1$, however, if additionally the sum of the entries of each column happens also to be $1$ then the matrix is said to be *doubly stochastic*. In more realistic instances the entries 