  The essential distinction between the fundamental diagram approach and
three-phase theory is the existence of the unique space-gap-speed relationship.
In order to verify this relationship, empirical data are analyzed with the
following findings: (1) linear relationship between the actual space gap and
speed can be identified when the speed difference between vehicles approximates
zero; (2) vehicles accelerate or decelerate around the desired space gap most
of the time. To explain these phenomena, we propose that, in homogeneous
congested traffic flow, the space gap between two vehicles will oscillate
around the desired space gap in the noiseless limit. This assumption is
formulated in terms of a cellular automaton. Simulations under periodic and
open boundary conditions reproduce the empirical findings of three-phase
theory. Finally, the model is calibrated and validated. All verification
results are acceptable and better than that of previous studies.
