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# Modeling and Analyzing for a Novel Continuum Model Considering Self-Stabilizing Control on Curved Road with Slope

Li Lei1, Zihao Wang2,*, Yong Wu3

1 School of Energy and Power Engineering, Shandong University, Jinan, 250061, China
2 School of Control Science and Engineering, Shandong University, Jinan, 250061, China
3 Department of Logistics Management, Ningbo University of Finance and Economics, Ningbo, 315175, China

* Corresponding Author: Zihao Wang. Email:

(This article belongs to this Special Issue: Numerical Methods in Engineering Analysis, Data Analysis and Artificial Intelligence)

Computer Modeling in Engineering & Sciences 2022, 131(3), 1815-1830. https://doi.org/10.32604/cmes.2022.019855

## Abstract

It is essential to fully understand master the traffic characteristics of the self-stabilizing control effect and road characteristics to ensure the regular operation of transportation. Traffic flow on curved roads and slopes is irregular and more complicated than that on the straight road. However, most of the research only considers the effect of self-stabilizing in the straight road. This study attempts to bridge this deficiency from the following three aspects. First, we review the potential influencing factors of traffic flow stability, which are related to the vehicle's steady velocity, history velocity, and the turn radius of the road and the slope of the road. Based on the above review, an extended continuum model accounting for the self-stabilizing effect on a curved road with slope is proposed. Second, the linear stability criterion of the new model is derived by applying linear stability theory, and the neutral stability curve is obtained in detail. The modified KdV equation describing the evolution characteristics of traffic congestion is derived by using the nonlinear analysis method. Upon the theoretical analysis, the third aspect focuses on simulating the self-stabilizing effect under different slopes and radius, which demonstrates that the self-stabilizing effect is conducive to reducing congestion of the curved road with slope.

## Keywords

Lei, L., Wang, Z., Wu, Y. (2022). Modeling and Analyzing for a Novel Continuum Model Considering Self-Stabilizing Control on Curved Road with Slope. CMES-Computer Modeling in Engineering & Sciences, 131(3), 1815–1830.

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