Assessing Markov Property in Driving Behaviors: Insights from Statistical Tests

TL;DR

This work tackles whether driving trajectories obey the Markov property by formulating a statistical testing framework that uses conditional independence via the Conditional Characteristic Function and a doubly robust MDN-based estimator to detect Markov memory and order. It then compares autonomous and human-driven trajectories using two public datasets (Lyft Level-5 and CATS Lab ACC) and employs a two-sample $t$-test and an $F$-test to assess differences in Markov order and variability. The results show that AV trajectories more consistently satisfy the Markov property and exhibit lower Markov orders, while HV trajectories display greater heterogeneity and longer memory effects, with some scenario-dependent variations. These findings have practical implications for driving behavior models, AV controllers, and traffic simulators, and illustrate the feasibility of statistically validating Markov properties in driving data.

Abstract

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. t test and F test are additionally introduced to characterize the differences in Markov properties between AVs and HVs. Based on two 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, AV controllers, 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.

Figures (5)

• Figure 1: Problem description. This study investigates the Markov property in car-following behavior by analyzing time series trajectories. We consider the leading vehicle's speed, the following vehicle's speed, and the distance between leading and following vehicle as state variables, and the following vehicle's acceleration as the decision variable. Our goal is to determine if the car-following driving process is a Markov process (MP) or a high-order Markov process (HOMP). If it is a HOMP, we also determine the order of the process based on the number of influential historical states to current action and future states.
• Figure 2: Distribution of Markov orders for car-following trajectories in the Lyft Level-5 dataset. The first two plots (blue bars) show the Markov orders for AVs, and the last two plots (orange bars) show the Markov orders for HVs. The statistical test results with both $p>0.01$ and $p>0.05$ are presented.
• Figure 3: Box plots of Markov orders for car-following trajectories in the Lyft Level-5 dataset. The first and third columns, with blue boxes, represent the Markov orders of AVs. The second and fourth columns, with orange boxes, represent the Markov orders of HVs. The first two columns show the orders for the combined trajectory set of MP and HOMP. The last two columns show the orders for HOMP trajectories only. The first row shows the results for $p > 0.01$, and the second row shows the results for $p > 0.05$.
• Figure 4: Distribution of Markov orders for car-following trajectories in the CATS lab ACC dataset. The first two rows (blue bars) of the distribution plots show the Markov orders for AVs, and the last two rows (orange bars) show the Markov orders for HVs. The statistical test results with both $p>0.01$ and $p>0.05$ are presented.
• Figure 5: Box plot of Markov orders for car-following trajectories in the CATS lab ACC dataset. The columns with blue boxes represent the Markov orders of AVs. The other columns with orange boxes, represent the Markov orders of HVs. The first six columns show the orders for the combined trajectory set of MP and HOMP. The last six columns show the orders for HOMP trajectories only. The first row shows the results for $p > 0.01$, and the second row shows the results for $p > 0.05$.

Theorems & Definitions (1)

• Definition 1