  Microscopic traffic simulation provides a controllable, repeatable, and
efficient testing environment for autonomous vehicles (AVs). To evaluate AVs'
safety performance unbiasedly, the probability distributions of environment
statistics in the simulated naturalistic driving environment (NDE) need 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 considering the distributional consistency of
driving behaviors, which could cause significant evaluation biasedness for AV
testing. To fill this research gap, a distributional consistent NDE modeling
framework is proposed in this paper. Using large-scale naturalistic driving
data, empirical distributions are obtained to construct the stochastic human
driving behavior models under different conditions. To address the error
accumulation problem during the simulation, an optimization-based method is
further designed to refine the empirical behavior 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. The framework is evaluated in the case study of a multi-lane
highway driving simulation, where the distributional accuracy of the generated
NDE is validated and the safety performance of an AV model is effectively
evaluated.
