unique stationary matrix. And (c), we construct a nonlinear model because the formal structure permits the existence of several ($L$) stationary states for the distribution of vehicles at each site, that alternate cyclically with time. Each state represents the traffic for $L$ different moments. These models were used to analyze the traffic in a sector of the city of Tigre, located in the province of Buenos Aires, Argentina. The results are presented in a following paper.'
author:
- 'D. Otero$^{1}$, D. Galetti$^{2}$, and S. S. Mizrahi$^{3}$'
title: 'Modeling a vehicular traffic network. Part I'
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Introduction
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Understanding the structure and systematic of the flow of vehicles along a network of arteries is a crucial point for planning the construction of connections (roads and highways) linking sites, as is the need to forecast the vehicular flow for traffic control. For that aim the observation and the gathering of data are essential practices that have to go along with theoretical approaches. Mathematical modeling and numerical simulations are essential procedures to grasp at the traffic flow and jam problems in order to recommend solutions for the urban and inter-city vehicular mobility. Methods have been developed since the 1940 decade, see for instance 