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Paper detail

Exact solution of a delay difference equation modeling traffic flow and their ultra-discrete limit

We consider a car-following model described by a delay difference equation and give its exact solutions that present propagation of a traffic jam. This model is a discrete-time version of the delayed optimal-velocity model; in the continuum limit, we recover the delay differential equation for this model and the exact solutions as well. We then work in the ultra-discrete limit, obtaining a delay cellular-automaton model, which successfully inherits the solutions. Also the dispersion relation for the present solutions suggests that a quick response of drivers does not always result in fast dissolution of a traffic jam.

preprint2015arXivOpen access
Keisuke MatsuyaMasahiro Kanai
math-phmath.MPnlin.CG
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Keisuke MatsuyaMasahiro Kanai

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