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Based on cellular automaton traffic BML model, one-dimensional traffic Fukui-Ishibashi(FI)model is extended to urban traffic network. The two-dimensional FI model is proposed. Under the conditions of periodic boundary, the relationship of the average speed and the density of the traffic as well as the fundamental diagram of the traffic for size of traffic network and the maximum speed of the vehicle are obtained by simulation. The result shows that the maximum speed has a great impact on traffic congestion under different size of traffic networks, and reveals transition from free flow to local jamming and fully jamming with the increase of density. The transition point to induce traffic congestion is decreased when the maximum velocity increases in the same lattice. The corresponding patterns of traffic in several states confirm these research results further.

Two-dimensional Deterministic Cellular Automaton Traffic FI Model