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

The effect of the absorbing sites with an absorbing rate β0 , 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. It is found that the behavior of density and current depends strongly on the value of β0 , the position of the way(s) out from the entering and the distance between the ways out. Indeed, in the case of one way out, there exist a critical position of the way out ic1 below which the current is constant for β0 β0c2 When the way out is located at a position greater than i c2 , the current increases with β0 for β0 β0c2 . In the later case the density undergoes two successive first order transitions; from high density to maximal current phase at β0 =β0c1 and from intermediate density to the low one at β0 =β0c2 . In the case of two ways out located respectively at the positions i1 and i2, the two successive transitions occur only when the distance i2 - i1 seating the two ways is smaller than a critical distance dc , otherwise the traffic flow increases with β0, passes through a maximum at β0 =βmax and decreases for any value of β0 greater than βmax. The values of β0c1, β0c2, ic1, ic2 and dc depend on the injecting rate α, the extracting rate β and the position(s) of the way(s) out in the road. Moreover ic1 and ic2 , depend on the size of the system. Phase diagrams in the (α, β0 ), ( β, β0 ) and (i1 ,β0 ) planes are established. It is found that the transitions between Free traffic, Congested traffic and maximal current phase are first order.The effect of the absorbing sites with an absorbing rate β0 , 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. It is found that the behavior of density and current depends strongly on the value of β0 , the position of the way(s) out from the entering and the distance between the ways out. Indeed, in the case of one way out, there exist a critical position of the way out ic1 below which the current is constant for β0 β0c2 When the way out is located at a position greater than i c2 , the current increases with β0 for β0 β0c2 . In the later case the density undergoes two successive first order transitions; from high density to maximal current phase at β0 =β0c1 and from intermediate density to the low one at β0 =β0c2 . In the case of two ways out located respectively at the positions i1 and i2, the two successive transitions occur only when the distance i2 - i1 seating the two ways is smaller than a critical distance dc , otherwise the traffic flow increases with β0, passes through a maximum at β0 =βmax and decreases for any value of β0 greater than βmax. The values of β0c1, β0c2, ic1, ic2 and dc depend on the injecting rate α, the extracting rate β and the position(s) of the way(s) out in the road. Moreover ic1 and ic2 , depend on the size of the system. Phase diagrams in the (α, β0 ), ( β, β0 ) and (i1 ,β0 ) planes are established. It is found that the transitions between Free traffic, Congested traffic and maximal current phase are first order

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

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