Traffic flow is a very prominent example of a driven non-equilibrium system. A characteristic phenomenon of traffic dynamics is the spontaneous and abrupt drop of the average velocity on a stretch of road leading to congestion. Such a traffic breakdown corresponds to a boundary-induced phase transition from free flow to congested traffic. In this paper, we study the ability of selected microscopic traffic models to reproduce a traffic breakdown, and we investigate its spatiotemporal dynamics. For our analysis, we use empirical traffic data from stationary loop detectors on a German Autobahn showing a spontaneous breakdown. We then present several methods to assess the results and compare the models with each other. In addition, we will also discuss some important modeling aspects and their impact on the resulting spatiotemporal pattern. The investigation of different downstream boundary conditions, for example, shows that the physical origin of the traffic breakdown may be artificially induced by the setup of the boundaries.
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. A recently developed theory for boundary-induced phenomena in nonequilibrium systems predicts the existence of various steady-state phase transitions induced by the motion of a shock wave. We provide direct empirical evidence that a phase transition between a free flow and a congested phase occurring in traffic flow on highways in the vicinity of on- and off-ramps can be interpreted as an example of such a boundary-induced phase transition of first order. We analyse the empirical traffic data and give a theoretical interpretation of the transition in terms of the macroscopic current. Additionally we support the theory with computer simulations of the Nagel-Schreckenberg model of vehicular traffic on a road segment which also exhibits the expected second-order transition. Our results suggest ways to predict and to some extent to optimize the capacity of a general traffic network.  We present data from several German freeways showing different kinds of congested traffic forming near road inhomogeneities, specifically lane closings, intersections, or uphill gradients. The states are localized or extended, homogeneous or oscillating. Combined states are observed as well, like the coexistence of moving localized clusters and clusters pinned at road inhomogeneities, or regions of oscillating congested traffic upstream of nearly homogeneous congested traffic. The experimental findings are consistent with a recently proposed theoretical phase diagram for traffic near on-ramps [D. Helbing, A. Hennecke, and M. Treiber, Phys. Rev. Lett. 82, 4360 (1999)]. We simulate these situations with a continuous microscopic single-lane model, the intelligent driver model,'' using empirical boundary conditions. All observations, including the coexistence of states, are qualitatively reproduced by describing inhomogeneities with local variations of one model parameter. We show that the results of the microscopic model can be understood by formulating the theoretical phase diagram for bottlenecks in a more general way. In particular, a local drop of the road capacity induced by parameter variations has essentially the same effect as an on-ramp.