Numerical and Theoretical Analysis of a New One-Dimensional Cellular Automaton Model for Bidirectional Flows

Abstract

In recent years, research on mathematical models describing crowd dynamics has become increasingly important. Among this research, a two-dimensional mathematical model with the effect of body rotation describing bidirectional flows has been constructed, and its fundamental diagram has been shown to be qualitatively consistent with real experimental data from the perspective of flow rate inversion. However, this property has not been mentioned in one-dimensional mathematical models. In this paper, we introduce a new, simpler, one-dimensional cellular automaton model to focus on the direction of particles and the effect of flipping instead of body rotation by extending the well-known TASEP as a solvable lattice model. Our model was found to be qualitatively consistent with the actual phenomenon of flow rate inversion, both numerically and theoretically.