Open boundaries in a cellular automata model for synchronized flow: effects of nonmonotonicity

Metastability due to a branching-merging structure in a simple network of an exclusion process

We investigate a simple network, which has a branching-merging structure, using the totally asymmetric simple exclusion process, considering conflicts at the merging point. For both periodic and open boundary conditions, the system exhibits metastability. Specifically, for open boundary conditions, we observe two types of metastability: hysteresis and a nonergodic phase. We analytically determine the tipping points, that is, the critical conditions under which a small disturbance can lead to the collapse of metastability. Our findings provide insights into metastability induced by branching-merging structures, which exist in all network systems in various fields.

Traffic-light boundary in the deterministic Nagel-Schreckenberg model

The characteristics of the deterministic Nagel-Schreckenberg model with traffic-light boundary conditions are investigated and elucidated in a mostly theoretically way. First, precise analytical results of the outflow are obtained for cases in which the duration of the red phase is longer than one step. Then, some results are found and studied for cases in which the red phase equals one step. The main findings include the following. The maximum outflow is "road-length related" if the inflow is saturated; otherwise, if the inbound cars are generated stochastically, multiple theoretical outflow volumes may exist. The findings indicate that although the traffic-light boundary can be implemented in a simple and deterministic manner, the deterministic Nagel-Schreckenberg model with such a boundary has some unique and interesting behaviors.

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.

Analytical investigation of the open boundary conditions in the Nagel-Schreckenberg model

We theoretically investigate the mechanism of the open boundary conditions in the deterministic Nagel-Schreckenberg model, which was studied mainly by numerical simulations before. Our studies concentrate on the open boundaries and have found an effective approach for deducing the analytical expression of inflow. We also raise a removal rule which is analyzable. These findings provide a theoretical explanation of the behaviors of the open boundaries and allow the exact prediction of the traffic state by using the injection rate and the removal rate.