Non-ergodicity and non-Markovianity of some simple traffic flow models
The celebrated Nagel–Schreckenberg model allows to study a reasonably
large class of one-dimensional traffic flow models with parallel updates.
Unfortunately further generalizations of this construction turn out
to be not especially fruitful. Namely, numerical simulations of such
generalizations did not demonstrate stable behavior qualitatively
different from the original model, and more to the point their
mathematical treatment is still not available even up to nowadays.
I'll discuss several features of these models which partially explain
the failure of both numerical and mathematical attempts to study
generalizations of the Nagel–Schreckenberg model.