Gas-kinetic traffic flow modeling including continuous driver behavior models

A modeling technique is presented that analytically bridges the gap between microscopic behavior of individual drivers and the macroscopic dynamics of traffic flow. The basis of this approach is the (gas-) kinetic or mesoscopic modeling principle that considers the dynamics of traffic density and generalizations thereof as a probability density function of vehicles in different driving states. In contrast to traditional kinetic models, deceleration of individual vehicles due to slower traffic is treated as a continuous adaptive process rather than a discrete event. An analytic procedure is proposed to aggregate arbitrarily refined individual driver behavior to a macroscopic expected acceleration or deceleration of flow as a whole that can be used in macroscopic differential equations for traffic flow. The procedure implicitly accounts for the anisotropy of information flow in traffic, for anticipation behavior of drivers, and for the finite space requirement of vehicles, as long as these properties have been specified at the level of individual driver behavior. The procedure is illustrated for a simple car-following model with overtaking opportunity. The results show that the procedure yields micro-based aggregate traffic flow models that capture the essential properties of traffic dynamics. The techniques presented can contribute to the development of traffic flow models with driver behavior and driver psychology as important explanatory factors of congestion formation and propagation. Moreover, the approach allows building macroscopic traffic flow equations from future traffic flows for which no empirical speed-flow-density relations are available yet.