How the on-ramp inflow causes bottleneck

We study traffic dynamics in a simple system with three open boundaries. Traffic patterns in steady states are mainly controlled by boundary conditions. There are three distinct phases in the entire parameter space. We construct a phase diagram and develop a mean-field theory to derive the phase regimes. The influences of speed limit are also discussed. We identify three kinds of on-ramp bottleneck: localized bottleneck in free flow, severe bottleneck in congestion, and extended bottleneck in rush hours. The first two are steady and the third is dynamical. The on-ramp bottleneck can be enhanced significantly by the dynamical effects of rush hours