  This paper firstly show that a recent model (Tian et al., Transpn. Res. B 71,
138-157, 2015) is not able to well replicate the evolution concavity in traffic
flow, i.e. the standard deviation of vehicles increases in a concave/linear way
along the platoon. Then we propose an improved model by introducing the safe
speed, the logistic function of the randomization probability, and small
randomization deceleration for low-speed vehicles into the model. Simulations
show that the improved model can well reproduce the metastable states, the
spatiotemporal patterns, the phase transition behaviors of traffic flow, and
the evolution concavity of traffic oscillations. Validating results show that
the empirical time series of traffic speed obtained from Floating Car Data can
be well simulated as well.
