  We study heterogeneous traffic dynamics by introducing quenched disorders in
all the parameters of Newell's car-following model. Specifically, we consider
randomness in the free-flow speed, the jam density, and the backward wave
speed. The quenched disorders are modeled using beta distributions. It is
observed that, at low densities, the average platoon size and the average speed
of vehicles evolve as power-laws in time as derived by Ben-Naim, Krapivsky, and
Redner (BKR). No power-law behavior has been observed in the time evolution of
the second moment of density and density distribution function indicating no
equivalence between the present system and the sticky gas. As opposed to a
totally asymmetric simple exclusion process (TASEP), we found no power-law
behavior in the stationary gap distribution and the transition from the platoon
forming phase to the laminar phase coincides with the free-flow to congestion
transition and is always of first-order, independent of the quenched disorder
in the free-flow speed. Using mean-field theory, we derived the gap
distribution of vehicles and showed that the phase transition is always of
first-order, independent of the quenched disorder in the free-flow speed
corroborating the simulation results. We also showed that the transition
density is the reciprocal of the average gap of vehicles in the platoon in the
thermodynamic limit.
