A rapid semi-analytical approach for modeling traffic flow on changing road conditions and its application

Road traffic conditions exhibit spatial and temporal variations influenced by factors such as construction, speed limits, and accidents. Accurate and efficient modeling of vehicular flow on changing road conditions is crucial for understanding intricate traffic phenomena and analyzing dynamic characteristics in real-world scenarios. In this paper, we develop a rapid numerical approach that computes traffic flow solutions for roads divided into multiple sections with varying traffic conditions, utilizing the Lighthill-Whitham-Richards model as the mathematical framework. The key aspect of our approach lies in solving the flow at the dividing point between consecutive road sections with different traffic conditions. For the two-section road scenario, we integrate the Hamilton-Jacobi formulation of the traffic model with the triangular fundamental diagram, capturing the explicit relationship between flow and density. This integration allows us to derive the spatiotemporal solution for a single dividing point. By accounting for the dynamic interaction between adjacent dividing points, we extend the applicability of our approach to an arbitrary number of road sections based on a semi-analytic Lax-Hopf formula. Our semi-analytical method is distinguished by grid-free computing, reducing computational demands and ensuring exceptional simulation speed. Particularly noteworthy is the formulation's remarkable efficacy in handling the complexities of heterogeneous road traffic conditions, marked by dynamic variations in both time and space, surpassing traditional macroscopic traffic flow simulations. To demonstrate its effectiveness, we apply the proposed approach to an optimization example involving traffic signal timing in a complex road environment. Additionally, we showcase its predictive capabilities by efficiently evaluating the impact of traffic accidents on the surrounding traffic flow. This research provides valuable insights for traffic management, optimization, and decision-making, enabling the analysis of complex scenarios and facilitating the development of strategies to enhance traffic efficiency and safety.