  Microscopic traffic simulation provides a controllable, repeatable, and
efficient testing environment for autonomous vehicles (AVs). To evaluate AVs'
safety performance unbiasedly, ideally, the probability distributions of the
joint state space of all vehicles in the simulated naturalistic driving
environment (NDE) needs to be consistent with those from the real-world driving
environment. However, although human driving behaviors have been extensively
investigated in the transportation engineering field, most existing models were
developed for traffic flow analysis without consideration of distributional
consistency of driving behaviors, which may cause significant evaluation
biasedness for AV testing. To fill this research gap, a distributionally
consistent NDE modeling framework is proposed. Using large-scale naturalistic
driving data, empirical distributions are obtained to construct the stochastic
human driving behavior models under different conditions, which serve as the
basic behavior models. To reduce the model errors caused by the limited data
quantity and mitigate the error accumulation problem during the simulation, an
optimization framework is designed to further enhance the basic models.
Specifically, the vehicle state evolution is modeled as a Markov chain and its
stationary distribution is twisted to match the distribution from the
real-world driving environment. In the case study of highway driving
environment using real-world naturalistic driving data, the distributional
accuracy of the generated NDE is validated. The generated NDE is further
utilized to test the safety performance of an AV model to validate its
effectiveness.
