Long-lived states in synchronized traffic flow: empirical prompt and dynamical trap model

The present paper proposes an interpretation of the widely scattered states (called synchronized traffic) stimulated by Kerner's hypothesis about the existence of a multitude of metastable states in the fundamental diagram. Using single-vehicle data collected at the German highway A1, temporal velocity patterns have been analyzed to show a collection of certain fragments with approximately constant velocities and sharp jumps between them. The particular velocity values in these fragments vary in a wide range. In contrast, the flow rate is more or less constant because its fluctuations are mainly due to the discreteness of traffic flow. Subsequently, we develop a model for synchronized traffic that can explain these characteristics. Following previous work [I. A. Lubashevsky and R. Mahnke, Phys. Rev. E 62, 6082 (2000)] the vehicle flow is specified by car density, mean velocity, and additional order parameters h and a that are due to the many-particle effects of the vehicle interaction. The parameter h describes the multilane correlations in the vehicle motion. Together with the car density it determines directly the mean velocity. The parameter a, in contrast, controls the evolution of h only. The model assumes that a fluctuates randomly around the value corresponding to the car configuration optimal for lane changing. When it deviates from this value the lane change is depressed for all cars forming a local cluster. Since exactly the overtaking maneuvers of these cars cause the order parameter a to vary, the evolution of the car arrangement becomes frozen for a certain time. In other words, the evolution equations form certain dynamical traps responsible for the long-time correlations in the synchronized mode.