Traffic Dynamics on a Rotary

Summary

We present a simple cellular automaton model to study the traffic dynamics on a 4-ramp rotary. Vehicles can move in and out of the rotary through on-ramp and off-ramp, respectively. On the rotary, vehicles move deterministically; while the ramps operate stochastically. We show that, both numerically and analytically, the traffic states on the rotary are completely determined by the ramps. The ramps provide a means to stabilize the density difference on the rotary and to support the maximum flow as a distinct phase. We are able to obtain exact solutions in the full parameter space. The complete phase diagram can be derived. We compare the results between a closed system and an open system. We show that the bulk density is not a good parameter. The traffic states are better characterized by the stochastic rates in the boundaries.