Rule 184 fuzzy cellular automaton as a mathematical model for traffic flow

The rule 184 fuzzy cellular automaton is regarded as a mathematical model of traffic flow because it contains the two fundamental models, and Burgers equation, special cases. We show that diagram (flux–density diagram) this consists three parts: free-flow part, congestion part two-periodic part. which may correspond to synchronized mode region, two-dimensional area in diagram, boundary parts. prove any state both parts stable, but not asymptotically while unstable. Transient behaviour bottle-neck effects are also examined by numerical simulations. Furthermore, investigate low or high density limit, we consider ultradiscrete limit turns travelling wave velocity one finite time steps for generic initial conditions.