Fuzzy cellular automata with complete number-conserving rule as traffic-flow models with bottleneck

Vector-valued fuzzy cellular automata (VFCA) are dynamical systems that are the continuous counterparts of cellular automata (CA). As such, continuous-valued traffic-flow models can be defined as VFCA that conserve the number of particles. In this study, a VFCA-based traffic model with obstacles on the road is presented. The proposed VFCA model exhibits asymptotic behavior, in the fundamental diagram, similar to a totally asymmetric simple-exclusion process. This observation was also investigated using the mean-field theory by comparing the equations of the two models.