Car-following models are essential for microscopic traffic simulation. While conventional models rely on parsimonious formulas with simplified assumptions, recent studies have focused on developing data-driven models with the help of high-resolution trajectory data. This paper presents a data-driven model based on a Bayesian Gaussian mixture model (GMM) for probabilistic forecasting of human car-following behaviors. By incorporating past and future information, our model captures the temporal dynamics of human car-following behaviors, providing accurate predictions of the following vehicle’s behavior and quantifying the forecast uncertainty. We demonstrate the interpretability of the Bayesian GMM in modeling car-following behaviors, providing valuable insights into the heterogeneity and uncertainty of driver behaviors. Additionally, we show that the proposed model can make probabilistic multi-vehicle simulations that reproduce natural traffic phenomena. Our results suggest that the proposed Bayesian GMM is a promising approach for modeling and forecasting car-following behaviors in various driving scenarios, contributing to the development of safer and more efficient transportation systems.

Spatiotemporal traffic data imputation is of great significance in intelligent transportation systems and data-driven decision-making processes. To perform efficient learning and accurate reconstruction from partially observed traffic data, we assert the importance of characterizing both global and local trends in time series. In the literature, substantial works have demonstrated the effectiveness of utilizing the low-rank property of traffic data by matrix/tensor completion models. In this study, we first introduce a Laplacian kernel to temporal regularization for characterizing local trends in traffic time series, which can be formulated as a circular convolution. Then, we develop a low-rank Laplacian convolutional representation (LCR) model by putting the circulant matrix nuclear norm and the Laplacian kernelized temporal regularization together, which is proved to meet a unified framework that has a fast Fourier transform (FFT) solution in log-linear time complexity. Through extensive experiments on several traffic datasets, we demonstrate the superiority of LCR over several baseline models for imputing traffic time series of various time series behaviors (e.g., data noises and strong/weak periodicity) and reconstructing sparse speed fields of vehicular traffic flow. The proposed LCR model is also an efficient solution to large-scale traffic data imputation over the existing imputation models.