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 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 i_c1 below which the current is constant for β₀ <β_0c2 and decreases when increasing β₀ for β₀ >β₀c2 When the way out is located at a position greater than i _c2 , the current increases with β₀ for β₀ <β_0c1 and becomes constant for any value of β₀ 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 β₀< β_0c1 , with β₀ and becomes constant for β_0c1 < β₀ <β_0c2 and decreases with β₀ for β₀ > β_0c2 . In the later case the density undergoes two successive first order transitions; from high density to maximal current phase at β₀ =β_0c1 and from intermediate density to the low one at β₀ =β_0c2 . 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 d_c , otherwise the traffic flow increases with β₀, passes through a maximum at β₀ =β_max and decreases for any value of β₀ greater than β_max. The values of β₀c1, β₀c2, i_c1, i_c2 and d_c depend on the injecting rate α, the extracting rate β and the position(s) of the way(s) out in the road. Moreover i_c1 and i_c2 , 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.