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.
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