On the stochastic fundamental diagram: A general micro-macroscopic traffic flow modeling framework

IF 12.5 Q1 TRANSPORTATION
Xiaohui Zhang, Jie Sun, Jian Sun
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引用次数: 0

Abstract

The stochastic fundamental diagram (SFD), which describes the stochasticity of the macroscopic relations of traffic flow, plays a crucial role in understanding the uncertainty of traffic flow evolution and developing robust traffic control strategies. Although many efforts have been made to reproduce the SFD via various methods, few studies have focused on the analytical modeling of the SFD, particularly linking the macroscopic relations with microscopic behaviors. This study fills this gap by proposing a general micro-macroscopic modeling approach, which uses probabilistic leader–follower behavior to derive the macroscopic relations of a platoon and is referred to as the leader–follower conditional distribution-based stochastic traffic modeling (LFCD-STM) framework. Specifically, we first define a conditional probability distribution of speed for the leader‒follower pair according to Brownian dynamics, which is proven to be a general representation of the longitudinal interaction and compatible with classical car-following models. As a result, we can describe the joint distribution of vehicle speeds of the platoon through Markov chain modeling and further derive the macroscopic relations (e.g., the mean flow‒density relation and its variance) under equilibrium conditions. On the basis of this general micro-macroscopic framework, we utilize the maximum entropy approach to theoretically derive the SFD model, in which we provide a specific conditional distribution for longitudinal interaction and thus solve the analytical functions of the mean and variance of FD. The performance of the maximum entropy-based SFD model is thoroughly validated with the NGSIM I-80, US-101 and HighD datasets. The high consistency between the theoretical results and empirical results demonstrates the soundness of the LFCD-STM framework and the maximum entropy-based SFD model. Finally, the proposed SFD model has practical implications for promoting smoother driving behaviors to suppress stochasticity and improve traffic flow.
论随机基本图:一种通用的微观宏观交通流建模框架
随机基本图(SFD)描述了交通流宏观关系的随机性,对于理解交通流演化的不确定性和制定稳健的交通控制策略具有重要意义。尽管人们已经通过各种方法对SFD进行了再现,但很少有研究关注SFD的分析建模,特别是将宏观关系与微观行为联系起来。本研究提出了一种通用的微观宏观建模方法来填补这一空白,该方法利用概率leader-follower行为来推导队列的宏观关系,被称为基于leader-follower条件分布的随机交通建模(LFCD-STM)框架。具体地说,我们首先根据布朗动力学定义了领队-随从对速度的条件概率分布,并证明了这是纵向相互作用的一般表示,与经典的汽车跟随模型兼容。因此,我们可以通过马尔可夫链建模来描述车队车速的联合分布,并进一步推导出平衡条件下的宏观关系(如平均流量密度关系及其方差)。在这一宏观微观框架的基础上,利用最大熵方法从理论上推导出SFD模型,该模型为纵向相互作用提供了特定的条件分布,从而求解出FD的均值和方差的解析函数。利用NGSIM I-80、US-101和HighD数据集对基于最大熵的SFD模型的性能进行了验证。理论结果与实证结果的高度一致性证明了LFCD-STM框架和基于最大熵的SFD模型的合理性。最后,本文提出的SFD模型对于促进驾驶行为的平稳性以抑制随机性和改善交通流具有实际意义。
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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CiteScore
15.20
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0.00%
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