Congested Traffic States in Empirical Observations and Microscopic Simulations

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. {\bf 82}, 4360 (1999)]. We simulate these situations with a novel continuous microscopic single-lane model, the ``intelligent driver model'' (IDM), using the 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 practically the same effect as an on-ramp.Comment: Now published in Phys. Rev. E. Minor changes suggested by a referee are incorporated; full bibliographic info added. For related work see http://www.mtreiber.de/ and http://www.helbing.org

Derivation, Properties, and Simulation of a Gas-Kinetic-Based, Non-Local Traffic Model

We derive macroscopic traffic equations from specific gas-kinetic equations, dropping some of the assumptions and approximations made in previous papers. The resulting partial differential equations for the vehicle density and average velocity contain a non-local interaction term which is very favorable for a fast and robust numerical integration, so that several thousand freeway kilometers can be simulated in real-time. The model parameters can be easily calibrated by means of empirical data. They are directly related to the quantities characterizing individual driver-vehicle behavior, and their optimal values have the expected order of magnitude. Therefore, they allow to investigate the influences of varying street and weather conditions or freeway control measures. Simulation results for realistic model parameters are in good agreement with the diverse non-linear dynamical phenomena observed in freeway traffic.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.html and http://www.theo2.physik.uni-stuttgart.de/treiber.htm

MASTER: macroscopic traffic simulation based on a gas-kinetic, non-local traffic model

We present a gas-kinetic (Boltzmann-like) traffic equation that is not only suited for low vehicle densities, but also for the high-density regime, as it takes into account the forwardly directed interactions, effects of vehicular space requirements like increased interaction rates, and effects of velocity correlations that reflect the bunching of cars, at least partially. From this gas-kinetic equation, we systematically derive the related macroscopic traffic equations. The corresponding partial differential equations for the vehicle density and average velocity are directly related to the quantities characterizing individual driver-vehicle behavior, and, as we show by calibration of the model, their optimal values have the expected order of magnitude. Therefore, the model allows to investigate the influences of varying street and weather conditions or freeway control measures. We point out that, because of the forwardly directed interactions, the macroscopic equations contain non-local instead of diffusion or viscosity terms. This resolves some of the inconsistencies found in previous models and allows for a fast and robust numerical integration, so that several thousand freeway kilometers can be simulated in real-time. It turns out that the model is in good agreement with the experimentally observed properties of freeway traffic flow. In particular, it reproduces the characteristic outflow and dissolution velocity of traffic jams, as well as the phase transition to "synchronized" congested traffic. We also reproduce the five different kinds of congested states that have been found close to on-ramps (or bottlenecks) and present a "phase diagram" of the different traffic states in dependence of the main flow and the ramp flow, showing that congested states are often induced by perturbations in the traffic flow. Finally, we introduce generalized macroscopic equations for multi-lane and multi-userclass traffic. With these, we investigate the differences between multi-lane simulations and simulations of the effective one-lane model.