The effect of off-ramp on the one-dimensional cellular automaton traffic flow with open boundaries

The effect of the position of the off-ramp (way out), 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. When the off-ramp is located between two critical positions i(c1) and i(c2) the current increases with the extracting rate beta(0), for beta(0) < beta(0c1), and exhibits a plateau (constant current) for beta(0c1) < beta(0) < beta(0c2) and decreases with beta(0) for beta(0) > beta(0c2). However, the density undergoes two successive first order transitions: from high density to plateau current phase at beta(0) = beta(0c1); and from average density to the low one at beta(0) = beta(0c2). In the case of two off-ramps located respectively at i(1) and i(2), these transitions occur only when i(2) - i(1) is smaller than a critical value. Phase diagrams in the (alpha, beta(0)), (i(1), beta(0)) and (i(1), beta(0)) planes are established. It is found that the transitions between free traffic (FT), congested traffic (CT) and plateau current (PC) phases are of first order. The first order line transition in (i(1), beta(0))-phase diagram terminates by an end point above which the transition disappears.