Analytical results of the Nagel-Schreckenberg model with stochastic open boundary conditions.

The deterministic Nagel-Schreckenberg model with stochastic open boundary conditions is investigated in a mostly analytical way. By means of the Markov Chain, we model the working process of the stochastic open boundaries. First, the analytical expression of the free-flow density profiles is derived. Then, we discuss theoretically how the right boundary determines the traffic capacity, global density, and density profiles. For these features, the analytical and numerical results agree well. This paper implies that the deterministic Nagel-Schreckenberg model with stochastic open boundaries is almost totally analyzable.