Comparison of the anisotropic and isotropic macroscopic traffic flow models

Second-order macroscopic vehicular traffic flow models are categorized under two broad headings based on the direction of their characteristics. Faster-than-vehicle waves are often called isotropic models vis-\'{a}-vis anisotropic models with slower-than-vehicle characteristic speed. The dispute on the supremacy among these families of models is the motivation for this paper. This paper compares and contrasts six distinctive second-order macroscopic models using a numerical simulation and analysis. Three models are characterized by faster-than-vehicle waves with their corresponding anisotropic counterparts. Simulation results on the formation of deceleration waves and the dissolution of acceleration fans are presented to graphically compare the wave profiles of the selected isotropic and anisotropic traffic models. Observably, these opposing models can all characterize these physical traffic phenomena to the same degree. Thus, faster characteristic speed conceptualization of second-order macroscopic equations does not tantamount to model failure but rather lies in the explanation of this property.