  Traffic breakdown, as one of the most puzzling traffic flow phenomena, is
characterized by sharply decreasing speed, abruptly increasing density and in
particular suddenly plummeting capacity. In order to clarify its root
mechanisms and model its observed properties, this paper proposes a
car-following model based on the following assumptions: (i) There exists a
preferred time-varied and speed-dependent space gap that cars hope to maintain;
(ii) there exists a region R restricted by two critical space gaps and two
critical speeds in the car following region on the speed-space gap diagram, in
which cars' movements are determined by the weighted mean of the space-
gap-determined acceleration and the speed-difference-determined acceleration;
and (iii) out of region R, cars either accelerate to the free flow speed or
decelerate to keep safety. Simulation results show that this model is able to
simultaneously reproduce traffic breakdown and the transition from the
synchronized traffic flow to wide moving jams. To our knowledge, this is the
first car-following model that is able to fully depict traffic breakdown,
spontaneous formation of jams, and the concave growth of the oscillations.
