Open boundaries in a cellular automaton model for traffic flow with metastable states

The effects of open boundaries in the velocity-dependent randomization (VDR) model, a modified version of the well-known Nagel-Schreckenberg (NaSch) cellular automaton model for traffic flow, are investigated. In contrast to the NaSch model, the VDR model exhibits metastable states and phase separation in a certain density regime. A proper insertion strategy allows us to investigate the whole spectrum of possible system states and the structure of the phase diagram by Monte Carlo simulations. We observe an interesting microscopic structure of the jammed phases, which is different from the one of the NaSch model. For finite systems, the existence of high flow states in a certain parameter regime leads to a special structure of the fundamental diagram measured in the open system. Apart from that, the results are in agreement with an extremal principle for the flow, which has been introduced for models with a unique flow-density relation. Finally, we discuss the application of our findings for a systematic flow optimization. Here some surprising results are obtained, e.g., a restriction of the inflow can lead to an improvement of the total flow through a bottleneck.