深入探讨基于区域占用率的多级交通连续模型:速度和密度梯度公式的稳定性

IF 3.1 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
Ranju Mohan , Shashvat Tripathi
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引用次数: 0

摘要

本文分析比较了以面积占用率(AO)作为交通集中度度量时多级交通流速度梯度公式和密度梯度公式的稳定性条件。在二阶连续体交通流模型中,驾驶员对前方交通的预期用速度梯度和密度梯度表示,并根据两种公式的方程组特征值分析了稳定性条件。特征值是交通流的特征速度,根据巴拿赫收缩原理和Hyers-Ulam稳定性概念进行检查,以检查模型的振荡性质,并了解受扰动系统解决方案与未受扰动系统解决方案的接近程度。对两种公式中的预期项进行概述,以解释交通中可能的实际情况下的稳定性。根据车辆类别之间的相互作用,逐个检查线性稳定性条件。通过波前展开技术推导了公式的非线性稳定性条件。此外,对不同拥堵情况下的假设路段的数值模拟结果表明,在两种公式中,车辆速度总是非负的,特征速度是真实的,表明模型方程系统具有双曲性。速度梯度公式很好地反映了交通的各向异性;然而,在密度梯度公式中经常观察到高于车辆速度的特征速度。本研究解决了一个基本问题:对于传统密度测量效果不佳的复杂非车道交通,经典的各向同性(密度梯度)还是各向异性(速度梯度)建模方法在物理上更真实。本文不仅从稳定性的角度对这两种表述进行了深入分析,同时也分享了在多类别交通建模中选择AO作为交通集中度度量的见解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Diving deep into area occupancy based continuum models for multi-class traffic: Stability of speed and density gradient formulations
The paper analyses and compare the stability conditions of speed and density gradient formulations of multi-class traffic flow when using area occupancy (AO) as the traffic concentration measure. In a second-order continuum model of traffic flow, driver’s anticipation to traffic ahead is expressed in terms of speed and density gradient, and stability conditions are analysed based on the eigenvalues from the system of equations in both the formulations. Eigenvalues, which are characteristics speeds of traffic flow, are checked against the Banach contraction principle and the Hyers–Ulam Stability concept to check model’s oscillatory nature and to understand how well a perturbed system solution remains close to that of an unperturbed system. Anticipation terms in both formulations are overviewed to interpret stability in possible practical scenarios in traffic. Linear stability conditions are checked case by case defined based on interactions among vehicle classes. Non-linear stability conditions for the formulations are derived through wavefront expansion techniques. Further, results from numerical simulations on a hypothetical road section in various congestion scenarios show that the vehicle speeds are non-negative always in both the formulations, and characteristics speeds are real, indicating hyperbolicity of the model’s equation systems. Anisotropic behaviour of traffic is well captured in speed gradient formulation; however, characteristics speeds higher than the vehicle speeds are frequently observed in density gradient formulation. This study addresses a fundamental question: whether the classic isotropic (density gradient) or anisotropic (speed gradient) modelling approach is more physically realistic for complex, non-lane-based traffic where traditional density measure under performs. The paper is an in-depth analysis of both formulations, not only from a stability perspective, but also shares insights on the choice of AO as traffic concentration measure while multi-class traffic modelling.
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来源期刊
CiteScore
7.20
自引率
9.10%
发文量
852
审稿时长
6.6 months
期刊介绍: Physica A: Statistical Mechanics and its Applications Recognized by the European Physical Society Physica A publishes research in the field of statistical mechanics and its applications. Statistical mechanics sets out to explain the behaviour of macroscopic systems by studying the statistical properties of their microscopic constituents. Applications of the techniques of statistical mechanics are widespread, and include: applications to physical systems such as solids, liquids and gases; applications to chemical and biological systems (colloids, interfaces, complex fluids, polymers and biopolymers, cell physics); and other interdisciplinary applications to for instance biological, economical and sociological systems.
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