Nonlinear Sciences – Cellular Automata and Lattice Gases
Scientific paper
2009-02-16
Phys. Rev. E 79, 056108 (2009).
Nonlinear Sciences
Cellular Automata and Lattice Gases
9 pages, 6 figures
Scientific paper
10.1103/PhysRevE.79.056108
In this paper, we propose the ultra-discrete optimal velocity model, a cellular-automaton model for traffic flow, by applying the ultra-discrete method for the optimal velocity model. The optimal velocity model, defined by a differential equation, is one of the most important models; in particular, it successfully reproduces the instability of high-flux traffic. It is often pointed out that there is a close relation between the optimal velocity model and the mKdV equation, a soliton equation. Meanwhile, the ultra-discrete method enables one to reduce soliton equations to cellular automata which inherit the solitonic nature, such as an infinite number of conservation laws, and soliton solutions. We find that the theory of soliton equations is available for generic differential equations, and the simulation results reveal that the model obtained reproduces both absolutely unstable and convectively unstable flows as well as the optimal velocity model.
Isojima Shin
Kanai Masahiro
Nishinari Katsuhiro
Tokihiro Tetsuji
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