Stochastic boundary conditions in the deterministic Nagel-Schreckenberg traffic model

Open systems where cars move according to the deterministic Nagel-Schreckenberg rules are considered. The movement is with a maximum velocity which is an extension of the asymmetric exclusion process. The behavior of the system is dominated by the competition between the left and right boundary and the development of so-called `buffers'. There is a first-order phase transition between the free flow and the congested phase. In the free-flow regime the current does not depend on the injection rate.