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 vehi cular space requirements like increased interaction rates: and effects of v elocity correlations that reflect the bunching of cars, at least partially. From this gas-kinetic equation, we systematically derive the related macro scopic traffic equations. The corresponding partial differential equations for the vehicle density an d average velocity are directly related to the quantities characterizing in dividual driver-vehicle behavior, and, as we show by calibration of the mod el, their optimal values have the expected order of magnitude. Therefore: t he 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-loca l instead of diffusion or viscosity terms. This resolves some of the incons istencies found in previous models and allows for a fast and robust numeric al integration, so that several thousand freeway kilometers can be simulate d in real-time. It turns out that the model is in good agreement with the experimentally ob served properties of freeway traffic flow. In particular, it reproduces the characteristic outflow and dissolution velocity of traffic jams, as well a s the phase transition to "synchronized" congested traffic. We also reprodu ce 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 t hat congested states are often induced by perturbations in the traffic flow . Finally, we introduce generalized macroscopic equations for multi-lane an d multi-userclass traffic. With these, we investigate the differences betwe en multi-lane simulations and simulations of the effective one-lane model. (C) 2001 Elsevier Science Ltd. All rights reserved.