Displaying items by tag: traffic flow

Thomas Hamori and Changhui Tan

Abstract

We present a new family of second-order traffic flow models, extending the Aw-Rascle-Zhang (ARZ) model to incorporate nonlocal interactions. Our model includes a specific nonlocal Arrhenius-type look-ahead slowdown factor. We establish both local and global well-posedness theories for these nonlocal ARZ models.
In contrast to the local ARZ model, where generic smooth initial data typically lead to finite-time shock formation, we show that our nonlocal ARZ model exhibits global regularity for a class of smooth subcritical initial data. Our result highlights the potential of nonlocal interactions to mitigate shock formations in second-order traffic flow models.
Our analytical approach relies on investigating phase plane dynamics. We introduce a novel comparison principle based on a mediant inequality to effectively handle the nonlocal information inherent in our model.

This work is supported by NSF grants DMS #2108264 and DMS #2238219

Yi Sun and Changhui Tan

Physica D, Volume 446, 133657 (2023)

Abstract

This paper presents a class of one-dimensional cellular automata (CA) models on traffic flows, featuring nonlocal look-ahead interactions. We develop kinetic Monte Carlo (KMC) algorithms to simulate the dynamics. The standard KMC method can be inefficient for models with global interactions. We design an accelerated KMC method to reduce the computational complexity in the evaluation of the nonlocal transition rates. We investigate several numerical experiments to demonstrate the efficiency of the accelerated algorithm, and obtain the fundamental diagrams of the dynamics under various parameter settings.

	doi:10.1016/j.physd.2023.133657
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	This work is supported by NSF grant DMS #1853001 and DMS #2108264
	This work is supported by a UofSC VPR ASPIRE I grant

Thomas Hamori and Changhui Tan

Nonlinear Analysis: Real World Applications, Volume 73, 103899, (2023).

Abstract

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.

	doi:10.1016/j.nonrwa.2023.103899
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	This work is supported by NSF grant DMS #1853001 and DMS #2108264
	This work is supported by a UofSC VPR ASPIRE I grant