Calibration of a Family of Car-Following Models with Retarded Linear Regression Methods

Abstract

Microscopic traffic simulation tools have wide applications in transportation operations and management, and models inside these simulation tools should be carefully calibrated and validated in order to provide meaningful results. This paper proposes a systematic approach to calibrating parameters for a family of four car-following models: Newell’s model, Pipes’ model, an optimal velocity model, and the linear General Motors model, which can be derived from each other and share the same triangular fundamental diagram in equilibrium traffic. The authors first discretize all models and introduce calibration objective functions based on location, speed, or acceleration for each model. Since all of the original car-following models have delays, the authors can solve retarded linear regression problems to estimate parameters that yield the best fit between observed and calculated trajectories of following vehicles. Theoretically, the authors point out one prominent limitation of this and other calibration methods when the leading and following vehicles have parallel linear trajectories. With vehicle trajectories provided by Next Generation Simulation (NGSIM), the authors choose car-following pairs with significant variations in speeds to minimize the impacts of parallel linear trajectories and demonstrate that the proposed calibration methods yield consistent results across different models. Discussions on future studies are presented in the conclusion section.