This paper shows, via computational evidence, that two specific stochastic car following models can either display 1-phase/1-state or 2-phase/3-state traffic, depending on the choice of parameters. With 2-phase parameters, the two phases are: ``laminar'', and ``jammed''. These phases also correspond to two of the three states. Those states are homogeneous. The third state, at intermediate densities, is a coexistence state, consisting of sections with jammed and sections with laminar traffic.
The transition to a 1-phase/1-state model happens via the densities of the laminar and of the jammed phase approaching each other until they become the same. Beyond this point, there is only one homogeneous phase of traffic.
Some of these findings can be understood by looking at deterministic models for traffic, either car-following or fluid-dynamical. However, the stochastic elements of the transition cannot be explained by deterministic models. An important stochastic element is meta-stability, which means that a ``super-critical'' homogeneous state can survive for long times before it ``breaks down'' and reorganizes into stop-and-go traffic. Another important stochastic element is that structure formation and strong variability can also happen in a 1-phase model as long as the parameters are close to the 2-phase model - a deterministic model would converge to a homogeneous solution here.
It is important to understand this possibility of stochastic models to be in different regimes if one considers to enter discussions of traffic breakdown probabilities into the Highway Capacity Manual. If traffic is best described by a 1-phase model, then there is, in our view, no theoretical justification for such probabilities. If, however, traffic is best described by a 2-phase model, then the 2-phase model could give theoretical predictions for breakdown probabilities. A discussion of breakdown probabilities in 2-phase models can be found in Ref. (43).