Probabilistic breakdown phenomenon at on-ramp bottlenecks in three-phase traffic theory

A nucleation model for the breakdown phenomenon at an on-ramp bottleneck is presented. This model is based on Kerner's three-phase traffic theory. In this theory, traffic breakdown is associated with a first-order phase transition from the free-flow phase to the synchronized-flow phase. It is suggested that because of merging of a flow on the main road with an on-ramp inflow, free flow is spatially nonhomogeneous in the neighborhood of a bottleneck. This permanent and motionless nonhomogeneity can be considered a deterministic vehicle cluster localized at the bottleneck. Because of the deterministic cluster, the breakdown phenomenon can also occur if there were no fluctuations in free flow. At a lower flow rate, traffic breakdown nucleation occurs through a random increase in vehicle number within the deterministic vehicle cluster. The mean time delay and the associated nucleation rate of traffic breakdown at the bottleneck were found and investigated. The model and a nucleation rate of traffic breakdown exhibit qualitatively different features compared with previous results.