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Modeling stochastic traffic behaviors at the microscopic level, such ascar-following and lane-changing, is a crucial task to understand theinteractions between individual vehicles in traffic streams. Leveraging arecently developed theory named physics regularized Gaussian process (PRGP),this study presents a stochastic microscopic traffic model that can capture therandomness and measure errors in the real world. Physical knowledge fromclassical car-following models is converted as physics regularizers, in theform of shadow Gaussian process (GP), of a multivariate PRGP for improving themodeling accuracy. More specifically, a Bayesian inference algorithm isdeveloped to estimate the mean and kernel of GPs, and an enhanced latent forcemodel is formulated to encode physical knowledge into stochastic processes.Also, based on the posterior regularization inference framework, an efficientstochastic optimization algorithm is developed to maximize the evidencelower-bound of the system likelihood. To evaluate the performance of theproposed models, this study conducts empirical studies on real-world vehicletrajectories from the NGSIM dataset. Since one unique feature of the proposedframework is the capability of capturing both car-following and lane-changingbehaviors with one single model, numerical tests are carried out with twoseparated datasets, one contains lane-changing maneuvers and the other doesn't.The results show the proposed method outperforms the previous influentialmethods in estimation precision.

Modeling Stochastic Microscopic Traffic Behaviors: a Physics Regularized Gaussian Process Approach