Multi-Agent Reinforcement Learning for Traffic State Estimation on Highways Using Fundamental Diagram and LWR Theory

Traffic state estimation (TSE) is a core task in intelligent transportation systems (ITSs) that seeks to infer key operational parameters—such as speed, flow, and density—from limited observational data. Existing methods often face challenges in practical deployment, including limited estimation accuracy, insufficient physical consistency, and weak generalization capability. To address these issues, this paper proposes a hybrid estimation framework that integrates multi-agent reinforcement learning (MARL) with the Lighthill–Whitham–Richards (LWR) traffic flow model. In this framework, each roadside detector is modeled as an agent that adaptively learns fundamental diagram (FD) parameters—the free-flow speed and jam density—by fusing local detector measurements with global CAV trajectory sequences via an interactive attention mechanism. The learned parameters are then passed to an LWR solver to perform sequential (rolling) prediction of traffic states across the entire road segment. We design a reward function that jointly penalizes estimation error and violations of physical constraints, enabling the agents to learn accurate and physically consistent dynamic traffic state estimates through interaction with the physics-based LWR environment. Experiments on simulated and real-world datasets demonstrate that the proposed method outperforms existing models in estimation accuracy, real-time performance, and cross-scenario generalization. It faithfully reproduces dynamic traffic phenomena, such as shockwaves and queue waves, demonstrating robustness and practical potential for deployment in complex traffic environments.