We present the analytical results in a simple traffic model describing a single-lane highway with ramps. Both on-ramps and off-ramps are considered. Complete classification of distinct phases is achieved. Exact phase diagrams are derived. In the case of a single ramp (either on-ramp or off-ramp), the bottleneck effect is absent. The traffic conditions of congestion before the ramp and free-flowing after the ramp cannot be realized. In the case of two consecutive ramps, the bottleneck emerges when the on-ramp is placed before the off-ramp and the flow in between the ramps saturates.

• Received 17 March 2005

DOI:https://doi.org/10.1103/PhysRevE.72.016102