Nonlocal Calculus-Based Macroscopic Traffic Model: Development, Analysis, and Validation

Abstract

Nonlocal calculus-based macroscopic traffic models overcome the limitations of classical local models in accurately capturing traffic flow dynamics. These models incorporate “nonlocal” elements by considering the speed as a weighted mean of downstream traffic density, aligning it more closely with realistic driving behaviors. The primary contributions of this research are manifold. Firstly, we choose a nonlocal LWR model and Greenshields fundamental diagram and prove that this traffic flow model satisfies the well-posed conditions. Furthermore, we prove that the chosen model maintains bounded states, laying the groundwork for developing numerically stable schemes. Subsequently, the efficacy of the proposed nonlocal model is evaluated through extensive field validation using real traffic data from the NGSIM dataset and developing a stable numerical scheme. These validation results highlight the superiority of the nonlocal model in capturing traffic characteristics compared to its local counterpart and establish its enhanced accuracy in reproducing complex traffic behavior. Therefore, this research expands both the theoretical constructs within the field and substantiates its practical applicability.

Keywords

• Macroscopic traffic model
• nonlocal calculus
• nonlocal LWR model