The effect of mixture lengths of vehicles on the traffic flow behaviour 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 deterministic parallel dynamics. The vehicles are filed according to their length, the small cars type 1 occupy one cell whereas the big ones type 2 takes two. In the case of open boundaries two cases are presented. The first case corresponds to a chain with two entries where 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 situation the first order transition from low to high density phases occurs at $\alpha1 + \alpha2 = \beta$ and disappears for $\alpha2 > \beta$. The second case corresponds to a chain with one entry, where $\alpha$ is the injecting rate of vehicles independent of their nature. Type 2 are injected with the conditional probability $\alpha\alpha2$, where $0\leq\alpha2 = n\alpha\leq\alpha$ and n is the concentration of type 2. Densities are calculated as a function of the injecting rates $\alpha$, and the phase diagrams ($\alpha$,$\beta$) are established for different values of n. In this situation 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 type 2 in the chain leads to a modification in the fundamental 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.