The effect of mixture lenghts of vehicles on the traffic flow behavior in one-dimensional cellular automaton

Abstract

The effect of mixture lengths of vehicles on the asymmetric exclusion model is studied using numerical simulations for both open and periodic boundaries in parallel dynamics. Densities are calculated as a function of the injecting rates $\alpha1$ and $\alpha2$ of vehicles type 1 and type 2 respectively, and the phase diagram ($\alpha1$,$\alpha2$) is presented for a fixed value of the extracting rate $\beta$. In this case the first order transition from low to high density phases occurs at $\alpha1+\alpha2=\beta$ and disappears for $\alpha2>\beta$. While, in the case of one entry the gap which is a characteristic of the first order transition vanishes with increasing $\alpha$ for n $\neq 0$.However, the first order transition between high and low densities exhibit an end point above which the global density undergoes a continuous passage. The end point coordinate depends strongly on the value of n. In the periodic boundaries case, the presence of vehicles type2 in the chain leads to a modification in the fundamental phase diagram (current, density). Indeed, the maximal current value decreases with increasing the concentration of vehicles type 2, and occurs at higher values of the global density in contrast with what was found by Schadschneider et al \cite{20}.