Neighborhood-five cellular automaton model for pedestrian flow

We discuss a certain type of 1 + 1 dimensional cellular automata with five neighbors of which state values are binary and evolve by deterministic rules. The sum of state values is conserved on time, they can be considered particle moving systems. We call them neighborhood-five particle cellular automata (PCA5) and focus on two specific systems, PCA5-40 and PCA5-59, in this article. Asymptotic behaviors of solutions and fundamental diagrams are discussed by numerical simulations for PCA5-40 and PCA5-59. From the exact pattern analysis on PCA5-40, we show that they reproduce important properties of the pedestrian crowd dynamics such as the presence of a double hump in the fundamental diagram. Furthermore, this paper gives a new insight into the mechanism of the double hump by comparing PCA5-40 with a model that includes a delay effect.