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.
Currently, stationary loop detectors are still the most common source of traffic data. In their simplest form they count the number of passing vehicles and measure their velocity aggregated over intervals of one minute. These values already allow an empirical fundamental diagram of traffic flow to be drawn. A more detailed picture on inter-vehicle dynamics can be obtained if even single vehicle data are available. Knospe al @cite_20 , for instance, used data from loop detectors which also measured time-headways ( the time passing between two vehicles crossing a detector). They analyzed the distribution of time-headways depending on the density and studied the functional relation between speed and distance to the preceding car, known as optimal velocity function. In addition to that, they compared these data to seven traffic cellular automata (CA) models. Knospe al found significant differences between the examined models. In particular, the earlier and simpler models were not able to satisfyingly reproduce the empirical results. More advanced models like the comfortable driving model (CDM), which is one of the models to be studied in this paper, showed good agreement with the empirical data.
@cite_20
2067179438 2021002141 2057165483 2098304112
Based on a detailed microscopic test scenario motivated by recent empirical studies of single-vehicle data, several cellular automaton models for traffic flow are compared. We find three levels of agreement with the empirical data: (1) models that do not reproduce even qualitatively the most important empirical observations, (2) models that are on a macroscopic level in reasonable agreement with the empirics, and (3) models that reproduce the empirical data on a microscopic level as well. Our results are not only relevant for applications, but also shed light on the relevant interactions in traffic flow. With the increasing amount of traffic information collected through floating car data, it is highly desirable to find meaningful traffic patterns such as congestion patterns from the accumulated massive historical dataset. It is however challenging due to the huge size of the dataset and the complexity and dynamics of traffic phenomena. A novel floating car data analysis method based on data cube for congestion pattern exploration is proposed in this paper. This method is different from traditional methods that depend only on numerical statistics of traffic data. The view of the event or spatial-temporal progress is adapted to model and measure traffic congestions. According to a multi-dimensional analysis framework, the traffic congestion event is first identified based on spatial-temporal related relationship of slow-speed road segment. Then, it is aggregated by a cluster style to get the traffic pattern on a different level of detail of spatial-temporal dimension. Aggregated location, time period and duration time for recurrent and important congestions are used to represent the congestion pattern. The authors evaluate methods using a historical traffic dataset collected from about 12000 taxi-based floating cars for one week in a large urban area. Results show that the method can effectively identify and summarize the congestion pattern with efficient computation and reduced storage cost. 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. We introduce and analyze a simple probabilistic cellular automaton which emulates the flow of cars along a highway. Our Traffic CA captures the essential features of several more complicated algorithms, studied numerically by K. Nagel and others over the past decade as prototypes for the emergence of traffic jams. By simplifying the dynamics, we are able to identify and precisely formulate the self-organized critical evolution of our system. We focus here on the Cruise Control case, in which well-spaced cars move deterministically at maximal speed, and we obtain rigorous results for several special cases. Then we introduce a symmetry assumption that leads to a two-parameter model, described in terms of acceleration (α) and braking (β) probabilities. Based on the results of simulations, we map out the (α, β) phase diagram, identifying three qualitatively distinct varieties of traffic which arise, and we derive rigorous bounds to establish the existence of a phase transition from free flow to jams. Many other results and conjectures are presented. From a mathematical perspective, Traffic CA provides local, particle-conserving, one-dimensional dynamics which cluster, and converge to a mixture of two distinct equilibria.