Driver memory, traffic viscosity and a viscous vehicular traffic flow model

Abstract

This paper studies the linkage between microscopic car-following and macroscopic fluid-like behavior of traffic flow. We find that driver memory in car-following leads to viscous effects in continuum traffic flow dynamics. This linkage is further exploited to develop a second-order continuum model with viscosity. Further, we show that this viscous model contains practically every well-known continuum model as a special case (e.g., the Lighthill–Whitham–Richards model and the Payne–Whitham model), has a stable wave structure of first- and second-order waves, and controls the extent of non-anisotropic and diffusive influences through a dimensionless parameter called anisotropic factor.