Phase transition and critical phenomenon in the power-law model of traffic

A power-law model of traffic is proposed to extend the optimal velocity model of traffic. The phase transition and critical phenomenon are investigated by computer simulation. It is shown that the phase transition among the freely moving phase, the coexisting phase, and the homogeneous congested phase occurs below the critical point. The dependence of the phase transition upon the power of model is derived from numerical simulation. It is found that the headway, the car velocity, and the jam propagation velocity scale, respectively, as (ac − a)α, (ac − a)β, and (ac − a)γ with α = β and γ = 2α, where a is the sensitivity parameter and ac is its critical value. The simulation results is compared with that obtained by the generalized traffic flow model. The universality class of this model is definitely different from the generalized traffic flow model.