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 ic1 and ic2 the current increases with the extracting rate β0, for β0<β0c1, and exhibits a plateau (constant current) for β0c1<β0<β0c2 and decreases with β0 for β0>β0c2. However, the density undergoes two successive first order transitions: from high density to plateau current phase at β0=β0c1; and from average density to the low one at β0=β0c2. In the case of two off-ramps located respectively at i1 and i2, these transitions occur only when i2-i1 is smaller than a critical value. Phase diagrams in the (α,β0), (β,β0) and (i1,β0) 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 (i1,β0)-phase diagram terminates by an end point above which the transition disappears.
The effect of mixture lengths of vehicles on the traffic flow behaviour in one-dimensional cellular automaton
