LAUSR

Abstract We propose three models for the traffic of vehicles within a network formed by sites (cities, car-rental agencies, parking lots, etc.) and connected by two-way arteries (roads, highways), that allow forecasting the vehicular flux in a sequence of n consecutive steps, or units of time. An essential approach consists in using, as an a priori information, previous observations and measurements. The formal tools used in our analysis consists in: (1) associating a digraph to the network where the edges correspond to arteries and the vertices with loops represent the sites. (2) From a distribution of vehicles within the network, we construct a matrix from which we derive a stochastic matrix (SM). This matrix becomes the generator of the evolution of the traffic flow. And (3), we use the Perron–Frobenius theory for a formal analysis. We investigate three models: (a) a closed network with conserved number of vehicles; (b) to this network we add an influx and an outflux of vehicles to picture an open system. And (c), we construct a nonlinear model whose formal structure exhibits 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 are hybridized and compared numerically to the effective vehicular traffic in a sector of the city of Tigre, localized in the province of Buenos Aires, Argentina. The empirical data and the traffic modelization are presented in a following paper, referred as Part II.