Ramp-induced transitions in traffic dynamics

We present the analytical results of ramp effects in asymmetric simple exclusion processes. Both on-ramp and off-ramp are included in between the two open boundaries. The ramps can be taken as the nontrivial boundaries to trigger the phase transitions. Exact phase diagrams are obtained analytically in the full parameter space. We find that the order of the two ramps is crucial. When the on-ramp is placed after the off-ramp along the traffic direction, there are only four distinct phases: free-free-free, free-free-jam, free-jam-jam, and jam-jam-jam. The other four phases from naive expectation cannot be realized, i.e., jam-free-free, jam-jam-free, jam-free-jam, and free-jam-free are all absent. The free flow will not follow the congestion. When the on-ramp is placed before the off-ramp, we observe an interesting phase: jam-max.-free. The bottleneck emerges as the flow in between the two ramps saturates to its maximum. We further show that the roadway configuration is equivalent to a nonstandard intersection. Applications to a traffic rotary are discussed.