An optimal velocity estimation (OVE) model based on non-empirical formula

In many research of optimal velocity model, the optimal velocity is estimated by empirical formulas. There are several aspects of this approach that need to be improved: On the one hand, the physical significance of such empirical formulas is not clear enough. On the other hand, the empirical formula of macro results is not detailed enough at the micro level. In this paper, we derived an equation to estimate the optimal velocity from two basic assumptions. Based on this equation, the optimal velocity estimation (OVE) model was established. To verify the rationality of OVE model, we conducted two single-file pedestrian experiments. From the results of experiments, we find that pedestrians pursue a consistent velocity and a comfortable distance between pedestrians in single-file movement. And the comfortable distance is proportional to the square of the steady velocity. These conclusions provide support for our assumptions. In addition, we simulated the experiments with the OVM model and a traditional OV model. By comparison, the OVM model can reproduce macro results very well. Further, the OVM model has a better performance than traditional OV model in micro level. In view of the clear physical meanings, our OVM model has an important significance in studying the influencing factors of pedestrian movement.