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

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2002. Vol. 66. Article 016117.

Lubashevsky I., Mahnke R., Wagner P., Kalenkov S.

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.

Keywords: traffic flow, dynamical trap, synchronized traffic flow