Stochastic boundary conditions in the deterministic Nagel-Schreckenberg traffic model

We consider open systems where cars move according to the deterministic Nagel-Schreckenberg rules and with maximum velocity $v_{max}>1$, what is an extension of the Asymmetric Exclusion Process (ASEP). It turns out that the behaviour of the system is dominated by two features: a) the competition between the left and the right boundary b) the development of so-called “buffers” due to the hindrance an injected car feels from the front car at the beginning of the system. As a consequence, there is a first-order phase transition between the free flow and the congested phase accompanied by the collapse of the buffers and the phase diagram essentially differs from that of $v_{max}=1$ (ASEP).