The Effect of absorbing sites on the one-dimensional cellular automaton traffic flow with open boundaries

Abstract

The effect of the absorbing sites with an absorbing rate ${\beta }_0$, in both one absorbing site (one way out) and two absorbing sites (two ways out) in a road, on the traffic flow phase transition is investigated using numerical simulations in the one-dimensional cellular automaton traffic flow model with open boundaries using parallel dynamics.In the case of one way out, there exist a critical position of the way out $i_{c1}$ below which the current is constant for ${\beta }_0$$<$${\beta }_{0c2}$ and decreases when increasing ${\beta }_0$ for ${\beta }_0$$>$${\beta }_{0c2}$. When the way out is located at a position greater than $i_{c2}$, the current increases with ${\beta }_0$ for ${\beta }_0$$<$${\beta }_{0c1}$ and becomes constant for any value of ${\beta }_0$ greater than ${\beta }_{0c1}$. While, when the way out is located at any position between $i_{c1}$ and $i_{c2}$ ($i_{c1}$$<$$i_{c2}$), the current increases, for ${\beta }_0$$<$${\beta }_{0c1}$, with ${\beta }_0$ and becomes constant for ${\beta }_{0c1}$$<$${\beta }_0$$<$${\beta }_{0c2}$ and decreases with ${\beta }_0$ for ${\beta }_0$$>$${\beta }_{0c2}$. In the later case the density undergoes two successive first order transitions; from high density to maximal current phase at ${\beta }_0$$=$${\beta }_{0c1}$ and from intermediate density to the low one at ${\beta }_0$$=$${\beta }_{0c2}$. In the case of two ways out located respectively at the positions $i_1$ and $i_2$, the two successive transitions occur only when the distance $i_2$-$i_1$ separating the two ways is smaller than a critical distance $d_c$. Phase diagrams in the ($\alpha ,{\beta }_0$), ($\beta ,{\beta }_0$) and ($i_1,{\beta }_0$) planes are established. It is found that the transitions between Free traffic, Congested traffic and maximal current phase are first order.

References in corpus (1)

• Traffic and Related Self-Driven Many-Particle Systems