An Algebraic Evaluation Framework for a Class of Car-Following Models

Car-following models describe how a driver follows the leading vehicle in the same lane. They serve as the cornerstone of microscopic traffic-flow simulations and play an essential role in analyzing human factors in traffic casualty, congestion, efficiency, and emissions. An extensive and continuously growing number of car-following models in the literature raises the requirement to evaluate and compare different models objectively. Generally, a car-following model is evaluated after model parameter calibration: the optimal residual between the calibrated model output and the measured counterpart is used as a metric to assess a car-following model's performance. However, model parameter calibration, usually formed as a numerical optimization problem, suffers from several issues, such as local optimality and heavy computational burden. More importantly, different formulations of the cost function can lead to distinct calibration outcomes and contradictory conclusions of the model evaluation results. This paper proposes instead a purely algebraic framework for evaluating a class of car-following models whose parameters can be linearly identified. Car-following models with nonlinear relationships among parameters, e.g., the behavioral car-following models, are out of the scope of analysis in this paper. Algebraic manipulations performed on a model finally produce a system error index, which is a uniform metric for evaluating and comparing different car-following models. During the whole process, no cost function needs to be designed a priori, and no computationally expensive numerical optimization is involved. Three car-following models are evaluated and compared under the proposed algebraic framework.