Micro- and macro-simulation of freeway traffic

We present simulations of congested traffic in circular and open systems with a non-local, gas-kinetic-based model and a novel car-following model. The model parameters are all intuitive and can be easily calibrated. Micro-and macro-simulations with these models for identical vehicles on a single lane produce the same traffic states, which also qualitatively agree with empirical traffic observations. Moreover, the phase diagrams of traffic states in the presence of bottlenecks for the microscopic car-following model and the macroscopic gas-kinetic-based model almost agree. In both cars, we found metastable regimes, spatially coexistent states, and a small region of tristability. The distinction of different types of vehicles (cars and long vehicles) yields additional insight and allows us to reproduce empirical data even more realistically, including the observed fluctuation properties of traffic flows like the wide scattering of congested traffic data. Finally, as an alternative to the gas-kinetic approach, we propose a new scheme for deriving non-local macroscopic traffic models from given microscopic car-following models. Assuming identical (macroscopic) initial and boundary conditions, we show that there are microscopic models for which the corresponding macroscopic version displays an almost identical dynamics. This enables us to combine micro- and macro-simulations of road sections by simple algorithms, and even to simulate them simultaneously.