  A nucleation model for the breakdown phenomenon in freeway free traffic flow
at an on-ramp bottleneck is presented. This model, which can explain empirical
results on the breakdown phenomenon, is based on assumptions of three-phase
traffic theory in which the breakdown phenomenon is related to a first-order
phase transition from the "free flow" phase to the "synchronized flow" phase.
The main idea of this nucleation model is that random synchronized flow
nucleation occurs within a metastable inhomogeneous steady state associated
with a deterministic local perturbation in free flow, which can be considered
"deterministic vehicle cluster" in free flow at the bottleneck. This
deterministic vehicle cluster in free flow is motionless and exists permanent
at the bottleneck due to the on-ramp inflow. In the nucleation model, traffic
breakdown nucleation occurs through a random increase in vehicle number within
this deterministic vehicle cluster, if the amplitude of the resulting random
vehicle cluster exceeds some critical amplitude. The mean time delay and the
associated nucleation rate of speed breakdown at the bottleneck are found and
investigated. The nucleation rate of traffic breakdown as a function of the
flow rates to the on-ramp and upstream of the bottleneck is studied. The
nucleation model and the associated results exhibit qualitative different
characteristics than those found earlier in other traffic flow nucleation
models. Boundaries for speed breakdown in the diagram of congested patterns at
the bottleneck are found. These boundaries are qualitatively correlated with
numerical results of simulation of microscopic traffic flow models in the
context of three-phase traffic theory.
