Kerner's Three-phase Traffic Theory Research Articles

An empirical study of phase transitions from synchronized flow to jams on a single-lane highway

In this paper we study empirical data for traffic flow at low velocities in single-lane traffic and compare them with those for multi-lane traffic. It is found that the traffic dynamics are quite different. When the velocities are low in multi-lane traffic, the traffic flow always becomes unstable and develops into jams. In single-lane traffic, some drivers drive in a more relaxed way and stay further back from the preceding car, as they know they cannot overtake the slow vehicle in front of them or at the front of the line. It may also be because they prefer not to follow the preceding vehicle too closely in single-lane traffic, to avoid the incessant deceleration and acceleration. This strategy is feasible because even if the space in front is large, no vehicle could ‘cut in’ in the single lane traffic. This phenomenon is called the ‘moderating effect’, and it harmonizes the traffic flow at low velocities. It is shown that the data points of synchronized flow in single-lane traffic are usually to the left and below those for multi-lane traffic in the flow–density plane. Thus, it is more difficult for the phase transition from synchronized flow to jams to occur in single-lane traffic, as pointed out in Kerner's three-phase traffic theory.

On the modeling of synchronized flow in cellular automaton models

In this paper, we further analyze our cellular automaton (CA) traffic flow model. By changing some parameters, the characteristics of our model can be significantly varied, ranging from the features of phase transitions to the number of traffic phases. We also review the other CA models based on Kerner's three-phase traffic theory. By comparisons, we find that the core concepts for modeling the synchronized flow in these models are similar. Our model can be a good candidate for modeling the synchronized flow, since there is enough flexibility in our framework.

Simple cellular automaton model for traffic breakdown, highway capacity, and synchronized flow

We present a simple cellular automaton (CA) model for two-lane roads explaining the physics of traffic breakdown, highway capacity, and synchronized flow. The model consists of the rules "acceleration," "deceleration," "randomization," and "motion" of the Nagel-Schreckenberg CA model as well as "overacceleration through lane changing to the faster lane," "comparison of vehicle gap with the synchronization gap," and "speed adaptation within the synchronization gap" of Kerner's three-phase traffic theory. We show that these few rules of the CA model can appropriately simulate fundamental empirical features of traffic breakdown and highway capacity found in traffic data measured over years in different countries, like characteristics of synchronized flow, the existence of the spontaneous and induced breakdowns at the same bottleneck, and associated probabilistic features of traffic breakdown and highway capacity. Single-vehicle data derived in model simulations show that synchronized flow first occurs and then self-maintains due to a spatiotemporal competition between speed adaptation to a slower speed of the preceding vehicle and passing of this slower vehicle. We find that the application of simple dependences of randomization probability and synchronization gap on driving situation allows us to explain the physics of moving synchronized flow patterns and the pinch effect in synchronized flow as observed in real traffic data.

Cellular automaton model with time gap dependent randomisation under Kerner's three-phase traffic theory

In this article, a new cellular automaton traffic flow model, in which randomisation effect is enhanced with the decrease of time gap and the long time stopped vehicle has large randomisation probability, is presented. Both periodic and open boundary conditions are considered. Under periodic boundary condition, the fundamental diagram and the properties of synchronised flow are studied in detail. Under open boundary condition, different congested patterns induced by an on-ramp are analysed. The results are consistent with the well-known results of Kerner's three-phase traffic theory published before.

Cellular-automaton model with velocity adaptation in the framework of Kerner’s three-phase traffic theory

In this paper, we propose a cellular automata (CA) model for traffic flow in the framework of Kerner's three-phase traffic theory. We mainly consider the velocity-difference effect on the randomization of vehicles. The presented model is equivalent to a combination of two CA models, i.e., the Kerner-Klenov-Wolf (KKW) CA model and the Nagel-Schreckenberg (NS) CA model with slow-to-start effect. With a given probability, vehicle dynamical rules are changed over time randomly between the rules of the NS model and the rules of the KKW model. Due to the rules of the KKW model, the speed adaptation effect of three-phase traffic theory is automatically taken into account and our model can show synchronized flow. Due to the rules of the NS model, our model can show wide moving jams. The effect of "switching" from the rules of the KKW model to the rules of the NS model provides equivalent effects to the "acceleration noise" in the KKW model. Numerical simulations are performed for both periodic and open boundaries conditions. The results are consistent with the well-known results of the three-phase traffic theory published before.

Study of Freeway Speed Limit Control Based on Three-Phase Traffic Theory

Speed limit control at freeway bottlenecks is numerically studied on the basis of the Kerner-Klenov microscopic stochastic traffic flow model in the context of Kerner's three-phase traffic theory. It turns out that in some cases speed limit control, rather than preventing traffic breakdown, leads to induced congested pattern emergence at the bottleneck, whereas there is free flow at the bottleneck without speed limitation. In other cases, speed limit control can suppress moving jam emergence, which occurs without speed limitation. It is found that these effects are associated with the probabilistic character of traffic breakdown at a bottleneck as well as with complex spatiotemporal congested pattern features.

Empirical test of a microscopic three-phase traffic theory

A review of dynamic nonlinear features of spatiotemporal congested patterns in freeway traffic is presented. The basis of the review is a comparison of theoretical features of the congested patterns that are shown by a microscopic traffic flow model in the context of the Kerner's three-phase traffic theory and empirical microscopic and macroscopic pattern characteristics measured on different freeways over various days and years. In this test of the microscopic three-phase traffic flow theory, a model of an "open" road is applied: Empirical time-dependence of traffic demand and drivers' destinations are used at the upstream model boundaries. At downstream model boundary conditions for vehicle freely leaving a modeling freeway section(s) are given. Spatiotemporal congested patterns emerge, develop, and dissolve in this open freeway model with the same types of bottlenecks as those in empirical observations. It is found that microscopic three-phase traffic models can explain all known macroscopic and microscopic empirical congested pattern features (e.g., probabilistic breakdown phenomenon as a first-order phase transition from free flow to synchronized flow, moving jam emergence in synchronized flow rather than in free flow, spatiotemporal features of synchronized flow and general congested patterns at freeway bottlenecks, intensification of downstream congestion due to upstream congestion at adjacent bottlenecks). It turns out that microscopic optimal velocity (OV) functions and time headway distributions are not necessarily qualitatively different, even if local congested traffic behavior is qualitatively different. Model performance with respect to spatiotemporal pattern emergence and evolution cannot be tested using these traffic characteristics. The reason for this is that important spatiotemporal features of congested traffic patterns are lost in these and many other macroscopic and microscopic traffic characteristics, which are widely used as the empirical basis for a test of traffic flow models.

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.

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 ...