the seminal papers [@pipes1953; @lighthill1955] and references therein. Further studies were done in several places uninterruptedly and many articles and reports were published on the subject, among which we cite, for instance, the Refs. [@bando1994; @bando19951; @bando19952; @kerner1997; @helbing1998; @nagatani1998; @deangelis1999; @aw2000; @helbing2001; @nagatani2002; @bellomo2002; @greenberg2004; @kisselev2004; @gasser2004; @orosz2005; @li2006; @siebel2006; @guanghan2009; @bressan2011; @bressan2012; @goh2012; @forstall2013; @bressan2014; @canec2015; @bressan2016; @piccoli; @morein], and the books [@kerner2004; @manhke2009].

The success of a model depends essentially on its capability to describe the present traffic dynamics as well as to forecast its trend. There are approaches that make use of fluid dynamics and differential equations [@bando19951; @helbing1998] whereas others utilize the $n$-step evolution of a stochastic matrix [@manhke2009; @ching2006; @woess-PF]. Here we consider the vehicular circulation occurring essentially inter-sites, and by sites we mean towns, parking lots, car-rental agencies, etc. In this study we do not describe the features of the vehicles, as mean size, mean speed, stopping distance nor the characteristics of the arteries as length, width and number of lanes. It consists in schematizing a traffic network imaged by a digraph, as shown in Fig. \[fig01\], that could be scaled up to higher complexity. The mathematical elements we utilize are essentially the 