Ultra-discrete Optimal Velocity Model: a Cellular-Automaton Model for Traffic Flow and Linear Instability of High-Flux Traffic

Abstract

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.

9 pages, 6 figures

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Cited by in corpus (5)

• Two-lane traffic-flow model with an exact steady-state solution
• Calibration of the Particle Density in Cellular-Automaton Models for Traffic Flow
• Mean-Field Theory of Meta-Learning
• Exact Solutions and Flow--Density Relations for a Cellular Automaton Variant of the Optimal Velocity Model with the Slow-to-Start Effect
• A CA Hybrid of the Slow-to-Start and the Optimal Velocity Models and its Flow-Density Relation