Fuzzy cellular automaton with slow-to-start property

IF 0.7 4区数学 Q3 MATHEMATICS, APPLIED

Japan Journal of Industrial and Applied Mathematics Pub Date : 2023-09-19 DOI:10.1007/s13160-023-00612-8

Kohei Higashi

引用次数: 0

Abstract

Abstract We propose a nonlinear discrete model which incorporates the effects of slow-to-start property into rule 184 fuzzy CA as a mathematical traffic flow model. The exact solutions corresponding to free-flow and congested states are given for the new model. The exact average fluxes of both states are also given. By studying the stability of the uniform solution corresponding to the congested state, the critical point at which congestion does not occur is obtained analytically. This may be the first analytical result on stability of congested states of the models with slow-to-start property. The stability of some typical free-flow states are also discussed analytically.

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具有慢启动特性的模糊元胞自动机

摘要提出了一种将慢启动特性的影响纳入184规则模糊CA的非线性离散模型作为交通流数学模型。给出了新模型在自由流动和拥挤状态下的精确解。给出了两种状态的精确平均通量。通过研究拥塞状态对应的均匀解的稳定性，解析得到了不发生拥塞的临界点。这可能是关于慢启动模型拥塞状态稳定性的第一个分析结果。对一些典型的自由流动状态的稳定性进行了分析讨论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Japan Journal of Industrial and Applied Mathematics 数学-应用数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Japan Journal of Industrial and Applied Mathematics (JJIAM) is intended to provide an international forum for the expression of new ideas, as well as a site for the presentation of original research in various fields of the mathematical sciences. Consequently the most welcome types of articles are those which provide new insights into and methods for mathematical structures of various phenomena in the natural, social and industrial sciences, those which link real-world phenomena and mathematics through modeling and analysis, and those which impact the development of the mathematical sciences. The scope of the journal covers applied mathematical analysis, computational techniques and industrial mathematics.