Numerical analysis of stochastic PDEs in traffic flow: Investigating density-flow relations

Understanding traffic flow dynamics is crucial for modeling real-world scenarios, where stochastic factors often introduce variability and unpredictability. This study explores the impact of stochastic influences on traffic flow, focusing on the relationship between flow and density in both deterministic and stochastic models. Using the Lighthill-Whitham-Richards (LWR) framework, the study examines a stochastic partial differential equation (SPDE) to simulate traffic behavior under varying conditions. The lognormal random numbers are incorporated for the Brownian motion for stochasticity after analysing its normalitynusing various tests. Numerical solutions were obtained through Godunov’s scheme, incorporating boundary conditions to capture stochastic effects. The findings show that the stochastic approach enhances predictive accuracy by capturing real-world traffic uncertainties.