  Despite the availability of large empirical data sets and the long history of
traffic modeling, the theory of traffic congestion on freeways is still highly
controversial. In this contribution, we compare Kerner's three-phase traffic
theory with the phase diagram approach for traffic models with a fundamental
diagram. We discuss the inconsistent use of the term "traffic phase" and show
that patterns demanded by three-phase traffic theory can be reproduced with
simple two-phase models, if the model parameters are suitably specified and
factors characteristic for real traffic flows are considered, such as effects
of noise or heterogeneity or the actual freeway design (e.g. combinations of
off- and on-ramps). Conversely, we demonstrate that models created to reproduce
three-phase traffic theory create similar spatiotemporal traffic states and
associated phase diagrams, no matter whether the parameters imply a fundamental
diagram in equilibrium or non-unique flow- density relationships. In
conclusion, there are different ways of reproducing the empirical stylized
facts of spatiotemporal congestion patterns summarized in this contribution,
and it appears possible to overcome the controversy by a more precise
definition of the scientific terms and a more careful comparison of models and
data, considering effects of the measurement process and the right level of
detail in the traffic model used.
