Assessing Markov property in driving behaviors: Insights from statistical tests

The Markov property serves as a foundational assumption in most existing work on vehicle driving behavior, positing that future states depend solely on the current state, not the series of preceding states. This study validates the Markov properties of vehicle trajectories for both Autonomous Vehicles (AVs) and Human-driven Vehicles (HVs). A statistical method used to test whether time series data exhibits Markov properties is applied to examine whether the trajectory data possesses Markov characteristics. Kolmogorov–Smirnov test and Brown–Forsythe test are additionally introduced to characterize the differences in Markov properties between AVs and HVs. Based on several public trajectory datasets, we investigate the presence and order of the Markov property of different types of vehicles through rigorous statistical tests. Our findings reveal that AV trajectories generally exhibit stronger Markov properties compared to HV trajectories, with a higher percentage conforming to the Markov property and lower Markov orders. In contrast, HV trajectories display greater variability and heterogeneity in decision-making processes, reflecting the complex perception and information processing involved in human driving. These results have significant implications for the development of driving behavior models, traffic flow models, and traffic simulation systems. Our study also demonstrates the feasibility of using statistical methods to test the presence of Markov properties in driving trajectory data.