A comprehensive review of dynamic modeling methods for extended optimal velocity car-following models in traffic flow

This article reviews the state-of-the-art achievements in traffic dynamic modeling methods for extended optimal velocity (OV) car-following models across a variety of complex environments. Existing extended OV modeling approaches are categorized into four key types: incorporating spatial interactions, incorporating temporal interactions, setting different parameters and combining both the spatial interactions and the temporal interactions. By analyzing numerous models, we identified various stimuli and introduced a stimulus matrix (S Matrix), including both existing and potential stimuli. Each element within S Matrix has an explicit meaning, and stimuli of the same type can be summed up in different ways to construct various interactions within complex environments. The article also summarizes existing and potential summation operators. Based on S Matrix, the stimulus combinations of a number of extended OV models are detailed, illustrating how these combinations define the function of traffic dynamics equations and facilitate a rapid comprehension of the similarities and differences among various models. The paper proposes several valuable recommendations for future research on OV modeling and analysis using S Matrix. To standardize future modeling efforts, principles for stimulus incorporating are suggested. It is expected that the application of S Matrix will improve car-following modeling and promote understanding of the evolution mechanism of traffic flow dynamics.