A Hierarchy of Kinetic Discrete-Velocity Models for Traffic Flow Derived from a Nonlocal Prigogine–Herman Model

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-01-30 DOI:10.1137/23m1583065

R. Borsche, A. Klar

引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 139-164, February 2024.
Abstract. Starting from a nonlocal version of the Prigogine–Herman traffic model, we derive a natural hierarchy of kinetic discrete-velocity models for traffic flow consisting of systems of quasi-linear hyperbolic equations with relaxation terms. The hyperbolic main part of these models turns out to have several favorable features. In particular, we determine Riemann invariants and prove richness and total linear degeneracy of the hyperbolic systems. Moreover, a physically reasonable invariant domain is obtained for all equations of the hierarchy. Additionally, we investigate the full relaxation system with respect to stability and persistence of periodic (stop-and-go-type) solutions and derive a condition for the appearance of such solutions. Finally, numerical results for various situations are presented, illustrating the analytical findings.

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从非局部普里戈金-赫尔曼模型推导出的交通流离散速度动力学模型层次结构

SIAM 应用数学杂志》第 84 卷第 1 期第 139-164 页，2024 年 2 月。摘要从普里戈金-赫尔曼交通模型的非局部版本出发，我们推导出了由带松弛项的准线性双曲方程系统组成的交通流离散速度动力学模型的自然层次。事实证明，这些模型的双曲主体部分具有若干有利特征。特别是，我们确定了黎曼不变式，并证明了双曲系统的丰富性和总线性退化性。此外，我们还为层次结构的所有方程获得了物理上合理的不变域。此外，我们还研究了全松弛系统的稳定性和周期性（走走停停型）解的持久性，并推导出了此类解出现的条件。最后，我们给出了各种情况下的数值结果，以说明分析结果。

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

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.