Additionally, we extend our analysis by examining a third model, (3) a nonlinear $n$-step process; by non-linearity we mean that some entries of matrix $\mathbb{M}$ depend on $n$. With a specific choice of periodic functions for the entries we verify the existence of several stationary régimes (instead of a single one as it occurs in the linear models), such that the vehicle distributions change cyclically instead of remaining constant. This nonlinear approach enables more detailed predictions about the traffic dynamics because it permits to slice, for instance, a 24-hour day into several sub-periods of traffic observation in the stationary régimes.

The present theoretical study was used to analyze the urban traffic in a selected sector of Tigre, a city located in the province of Buenos Aires, Argentina. The raw data are counts of circulating vehicles as recorded by cameras positioned in several intersections. The methodology, analysis and comparison between raw data and the utilized model are presented in a following paper, to be referred as Part II.

Model I: Inter-site circulation of vehicles between without input or output.
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The first model consists of four sites, to which we attribute the letters $A, B, C, D$, connected by arteries (roads, 