Do traffic flow states follow Markov properties? A high-order spatiotemporal traffic state reconstruction approach for traffic prediction and imputation

Assessing traffic states accurately is challenging due to the complex, high-dimensional, and nonlinear nature of traffic systems. This study introduces the innovative High-Order Spatiotemporal Traffic State Reconstruction (HOSTSR) algorithm, designed to track and predict traffic flow dynamics effectively. It combines phase space reconstruction with time delays and high-order neighborhood concepts from graph theory to improve traffic state assessments' accuracy. The algorithm's effectiveness is validated using chi-square tests and the Chapman-Kolmogorov equation to confirm the Markovian properties of traffic flows. A lean autoencoder, informed by prior Markov knowledge of traffic states, is developed for mapping traffic states to real traffic data, proving highly effective for traffic data imputation due to the Markov model's memoryless property. Experimental results from the PeMSD04 and PeMSD08 datasets show that HOSTSR outperforms traditional state reconstruction methods based on delayed coordinate embedding in predicting future traffic flow state based on four key metrics. The autoencoder framework, guided by prior Markov knowledge, shows significant advantages in addressing traffic data gaps in different cases over six baseline models. Gradient sensitivity analysis further evaluates the impact of prior knowledge on improving the autoencoder's interpretability for interpolation efforts.