Discontinuous-Galerkin-Based Analysis of Traffic Flow Model Connected with Multi-Agent Traffic Model

As the number of automobiles continues to increase year after year, the associated problem of traffic congestion has become a serious societal issue. Initiatives to mitigate this problem have considered methods for optimizing traffic volumes in wide-area road networks, and traffic-flow simulation has become a focus of interest as a technique for advance characterization of such strategies. Classes of models commonly used for traffic-flow simulations include microscopic models based on discrete vehicle representations, macroscopic models that describe entire traffic-flow systems in terms of average vehicle densities and velocities, and mesoscopic models and hybrid (or multiscale) models incorporating both microscopic and macroscopic features. Because traffic-flow simulations are designed to model traffic systems under a variety of conditions, their underlying models must be capable of rapidly capturing the consequences of minor variations in operating environments. In other words, the computation speed of macroscopic models and the precise representation of microscopic models are needed simultaneously. Thus, in this study we propose a multiscale model that combines a microscopic model-for detailed analysis of subregions containing traffic congestion bottlenecks or other localized phenomena of interest-with a macroscopic model enabling simulation of wide target areas at a modest computational cost. In addition, to ensure analytical stability with robustness in the presence of discontinuities, we discretize our macroscopic model using a discontinuous Galerkin finite element method (DGFEM), while to conjoin microscopic and macroscopic models, we use a generating/absorbing sponge layer, a technique widely used for numerical analysis of long-wavelength phenomena in shallow water, to enable traffic-flow simulations with stable input and output regions.