Phase transition and scaling in the generalized traffic flow model

The optimal velocity traffic model is generalized to the power-law type of the optimal velocity. The phase transition among the freely moving phase, the coexisting phase, and the homogeneous congested phase is investigated by computer simulation and the linear stability theory. Phase diagrams are obtained for various values of the power. It is shown that the phase boundary and the critical point depend strongly upon the power. The scaling behaviors of the headway, the car velocity, and the propagation velocity of jams are studied near the critical point. It is found that the headway and the car velocity scale as (ac − a)α and (ac − a)βwith α = β = n(n + 1) and the propagation velocity of jams scales as (ac − a)γwith γ = 2n(n + 1)where a is the sensitivity, ac is its critical value, and n is the power of the model.