Analytical results of asymmetric exclusion processes with ramps

Phase diagrams of the Katz-Lebowitz-Spohn process on lattices with a junction

This paper studies the Katz-Lebowitz-Spohn (KLS) process on lattices with a junction, where particles move on parallel lattice branches that combine into a single lattice at the junction. It is shown that 11 kinds of phase diagrams could be observed, depending on the two parameters ε and δ in the KLS process. We have investigated the phase diagrams as well as bulk density analytically based on flow rate conservation and the extremal current principle. Extensive Monte Carlo computer simulations are performed, and it is found that they are in excellent agreement with theoretical prediction.

Introduction of frictional and turning function for pedestrian outflow with an obstacle

In this paper, two important factors which affect the pedestrian outflow at a bottleneck significantly are studied in detail to analyze the effect of an obstacle setup in front of an exit. One is a conflict at an exit when pedestrians evacuate from a room. We use floor field model for simulating such behavior, which is a well-studied pedestrian model using cellular automata. The conflicts have been taken into account by the friction parameter. However, the friction parameter so far is a constant and does not depend on the number of the pedestrians conflicting at the same time. Thus, we have improved the friction parameter by the frictional function, which is a function of the number of the pedestrians involved in the conflict. Second, we have presented the cost of turning of pedestrians at the exit. Since pedestrians have inertia, their walking speeds decrease when they turn and the pedestrian outflow decreases. The validity of the extended model, which includes the frictional function and the turning function, is supported by the comparison of a mean-field theory and real experiments. We have observed that the pedestrian flow increases when we put an obstacle in front of an exit in our real experiments. The analytical results clearly explains the mechanism of the effect of the obstacle, i.e., the obstacle blocks pedestrians moving to the exit and decreases the average number of pedestrians involved in the conflict. We have also found that an obstacle works more effectively when we shift it from the center since pedestrians go through the exit with less turning.

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.