Empirical Investigation of Markovian and Uniformity Property in Human and Autonomous Driving

In the realm of mixed traffic dynamics analysis, Autonomous Vehicles (AVs) control, and AVs safety evaluation, the prevailing practice leans heavily on the utilization of Markovian and uniformity assumptions and models to characterize driving behavior. Markovian properties imply that driving actions depend solely on the present environmental conditions, while uniformity properties suggest uniform driving behaviors across various drivers and scenarios. The legitimacy of these fundamental assumptions is subject to critical examination. This study conducts an in-depth analysis of Car-Following (CF) behaviors concerning the Markovian and uniformity characteristics, emphasizing the distinctions between Human-Driven Vehicles (HVs) and AVs. Leveraging a linear CF model incorporating speed, speed difference, and spacing, we meticulously scrutinize CF trajectories within dedicated HV platoons, AV platoons, and mixed HV-AV platoons. Our dataset encompasses diverse drivers and a variety of commercial autonomous vehicle models, offering insights into a multitude of CF scenarios encompassing stable cruising and oscillatory patterns.

To validate Markovian properties, we introduce the concept of memory length, which assesses the extent to which historical information is likely to influence CF decisions, particularly accelerations. Our findings disclose that AV trajectories strongly adhere to Markovian properties, with decisions intricately linked to temporally proximate state variables. Conversely, HV trajectories fail to exhibit Markovian characteristics, with accelerations displaying weaker correlations with nearby states. To provide a more comprehensive explanation for HV decisions, historical states extending over a more extended timeframe prove necessary. Notably, AVs exhibit memory lengths of 1-2 seconds, while HVs' memory lengths span a range of 60-80 seconds. Furthermore, our study unveils that HVs display shorter memory lengths in oscillating CF scenarios compared to cruising, underscoring the capacity of human drivers to adapt their CF behavior dynamically in response to evolving environments during oscillations. In stark contrast, the memory length of AVs remains consistent across scenarios. For the validation of uniformity properties, an examination of AV trajectory data sourced from various brands, models, and scenarios reveals strikingly similar memory lengths, indicative of uniformity in AVs' CF behavior. Notably, the memory of HVs displays substantial variations across different drivers, further underscoring the absence of uniformity in HV behavior.

Collectively, our findings underscore that AVs consistently exhibit Markovian and uniform CF behaviors, while HVs' behaviors lack Markovian and uniformity. This investigation not only elucidates the fundamental disparities in CF behavior between HVs and AVs, concerning Markovian and uniformity properties but also contributes to a more profound understanding of mixed traffic dynamics, as well as the development and evaluation of AV technologies.