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

Abstract

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.