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 $β_{0}$, 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 $β_{0}$$<$$β_{0c2}$ and decreases when increasing $β_{0}$ for $β_{0}$$>$$β_{0c2}$. When the way out is located at a position greater than $ i_{c2}$, the current increases with $β_{0}$ for $β_{0}$$<$$β_{0c1}$ and becomes constant for any value of $β_{0}$ greater than $β_{0c1}$. While, when the way out is located at any position between $ i_{c1}$ and $ i_{c2}$ ($ i_{c1}$$<$$ i_{c2}$), the current increases, for $β_{0}$$<$$β_{0c1}$, with $β_{0}$ and becomes constant for $β_{0c1}$$<$$β_{0}$$<$$β_{0c2}$ and decreases with $β_{0}$ for $β_{0}$$>$$β_{0c2}$. In the later case the density undergoes two successive first order transitions; from high density to maximal current phase at $β_{0}$$=$$β_{0c1}$ and from intermediate density to the low one at $β_{0}$$=$$β_{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 ($α,β_{0}$), ($β,β_{0}$) and ($i_{1},β_{0}$) planes are established. It is found that the transitions between Free traffic, Congested traffic and maximal current phase are first order.