can be verified that $ \left( \begin{array}{ccc} 11/27 & 2/9 & 10/27 \end{array} \right) 
\mathbb{M} =\left( \begin{array}{ccc} 11/27 & 2/9 & 10/27 \end{array}\right)$.

A generic vector $\mathbb{X}_{0}^{\mathrm{T}}=\left( \begin{array}{ccccc}
x_{1} & x_{2} & \cdots & x_{N-1} & x_{N}\end{array}\right) $ evolves as $\mathbb{X}_{n}^{\mathrm{T}}=\mathbb{X}_{0}^{\mathrm{T}}\mathbb{M}^{n}$ and asymptotically becomes $\mathbb{X}_{\infty }^{\mathrm{T}}=\mathbb{X}_{0}^{\mathrm{T}}\mathbb{C}_{1} $; thus it “looses memory” about its components but keeps the sum $\sum_{i=1}^{N}x_{i}=Y$ as a recollection, i.e., $\mathbb{X}_{0}^{\mathrm{T}} \Rightarrow \mathbb{X}_{\infty }^{\mathrm{T}}
=Y\mathbb{Z}^{\mathrm{T}}$.

**(6)** In the numerical examples to be worked out below the eigenvalues of the matrices have multiplicity $1$, nevertheless the math and the physical analysis can be extended to the situation where eigenvalues have multiplicity higher than $1$. As an illustration about this point we consider here an interesting behavior that affects the time decay in the case of occurrence of a degenerate eigenvalue (in comparison with the situation of no degeneracy). Pointedly, within a closed network, it causes a delay in the time the flux of vehicles takes to evolve to the stationary matrix $\lim_{n \rightarrow 
\infty}\mathbb{M}^n$. In this case, the diagonalization of the matrix $\mathbb{M}$ – the decomposition (\[A8\]) – that produces the diagonal matrix $\mathbb{D}$ is not anymore possible because there are fewer linearly independent eigenvectors than the dimension 