面向混合自动驾驶交通的具有前视效应的各向异性交通流模型

关于具有非局部前瞻相互作用的Aw-Rascle-Zhang交通模型

On the Aw-Rascle-Zhang traffic models with nonlocal look-ahead interactions

本文提出一类含非局部前瞻相互作用的ARZ二阶交通流模型，证明其全局适定性，并利用相平面分析和新比较原理，表明非局部作用可缓解激波形成。

Sharp critical thresholds for a class of nonlocal traffic flow models

We study a class of traffic flow models with nonlocal look-ahead interactions. The global regularity of solutions depend on the initial data. We obtain sharp critical threshold conditions that distinguish the initial data into a trichotomy: subcritical initial conditions lead to global smooth solutions, while two types of supercritical initial conditions lead to two kinds of finite time shock formations. The existence of non-trivial subcritical initial data indicates that the nonlocal look-ahead interactions can help avoid shock formations, and hence prevent the creation of traffic jams.

Entropy Admissibility of the Limit Solution for a Nonlocal Model of Traffic Flow

We consider a conservation law model of traffic flow, where the velocity of each car depends on a weighted average of the traffic density $ρ$ ahead. The averaging kernel is of exponential type: $w_\varepsilon(s)=\varepsilon^{-1} e^{-s/\varepsilon}$. For any decreasing velocity function $v$, we prove that, as $\varepsilon\to 0$, the limit of solutions to the nonlocal equation coincides with the unique entropy-admissible solution to the scalar conservation law $ρ_t + (ρv(ρ))_x=0$.

On Traffic Flow with Nonlocal Flux: a Relaxation Representation

We consider a conservation law model of traffic flow, where the velocity of each car depends on a weighted average of the traffic density $ρ$ ahead. The averaging kernel is of exponential type: $w_\varepsilon(s)=\varepsilon ^{-1} e^{-s/\varepsilon}$. By a transformation of coordinates, the problem can be reformulated as a $2\times 2$ hyperbolic system with relaxation. Uniform BV bounds on the solution are thus obtained, independent of the scaling parameter $\varepsilon $. Letting $\varepsilon\to 0$, the limit yields a weak solution to the corresponding conservation law $ρ_t + ( ρv(ρ))_x=0$. In…

含时滞的非局部交通流模型：适定性与数值逼近

Non-local traffic flow models with time delay: well-posedness and numerical approximation

本文研究含时滞的标量非局部交通流模型，利用有限体积格式收敛性与 Kruzkov 型变量加倍技术证明弱熵解的存在性及 L1 稳定性，并通过数值测试验证格式效率和参数影响。

Traveling Waves for a Microscopic Model of Traffic Flow

We consider the follow-the-leader model for traffic flow. The position of each car $z_i(t)$ satisfies an ordinary differential equation, whose speed depends only on the relative position $z_{i+1}(t)$ of the car ahead. Each car perceives a local density $ρ_i(t)$. We study a discrete traveling wave profile $W(x)$ along which the trajectory $(ρ_i(t),z_i(t))$ traces such that $W(z_i(t))=ρ_i(t)$ for all $i$ and $t>0$; see definition 2.2. We derive a delay differential equation satisfied by such profiles. Existence and uniqueness of solutions are proved, for the two-point boundary value problem wher…

在物理信息神经网络中融入非局部交通流模型

Incorporating Nonlocal Traffic Flow Model in Physics-informed Neural Networks

针对经典LWR模型难以准确表征真实交通流的问题，本研究提出融入非局部LWR模型的新型物理信息深度学习框架，经多数据集评估验证其性能优于基线方法，可提升交通状态估计效果。

非局部Follow-the-Leader模型的连续极限

The continuum limit of non-local Follow-the-Leader models

本文研究驾驶员同时考虑前方多车和后方紧邻车辆位置的广义Follow-the-Leader模型，证明其在交通密集时收敛于经典Lighthill-Whitham-Richards模型，从而验证了该经典模型的鲁棒性。