Saeed Mohammadian | Searcharxiv

arXiv2025

Central-Upwind Scheme for the Phase-Transition Traffic Flow Model

Phase-transition models are an important family of non-equilibrium continuum traffic flow models, offering properties like replicating complex traffic phenomena, maintaining anisotropy, and promising potentials for accommodating automated vehicles. However, their complex mathematical characteristics such as discontinuous solution domains, pose numerical challenges and limit their exploration in traffic flow theory. This paper focuses on developing a robust and accurate numerical method for phase-transition traffic flow models: We propose a second-order semi-discrete central-upwind scheme specifically designed for discontinuous phase-transition models. This novel scheme incorporates the projection onto appropriate flow domains, ensuring enhanced handling of discontinuities and maintaining physical consistency and accuracy. We demonstrate the efficacy of the proposed scheme through extensive and challenging numerical tests, showcasing their potential to facilitate further research and application in phase-transition traffic flow modeling. The ability of phase-transition models to embed the ``time-gap'' -- a crucial element in automated traffic control -- as a conserved variable aligns seamlessly with the control logic of automated vehicles, presenting significant potential for future applications, and the proposed numerical scheme now substantially facilitates exploring such potentials.

math.NA↗

arXiv2023

Continuum modeling of freeway traffic flows: State-of-the-art, challenges and future directions in the era of connected and automated vehicles

Connected and automated vehicles (CAVs) are expected to reshape traffic flow dynamics and present new challenges and opportunities for traffic flow modeling. While numerous studies have proposed optimal modeling and control strategies for CAVs with various objectives (e.g., traffic efficiency and safety), there are uncertainties about the flow dynamics of CAVs in real-world traffic. The uncertainties are especially amplified for mixed traffic flows, consisting of CAVs and human-driven vehicles, where the implications can be significant from the continuum-modeling perspective, which aims to capture macroscopic traffic flow dynamics based on hyperbolic systems of partial differential equations. This paper aims to highlight and discuss some essential problems in continuum modeling of real-world freeway traffic flows in the era of CAVs. We first provide a select review of some existing continuum models for conventional human-driven traffic as well as the recent attempts for incorporating CAVs into the continuum-modeling framework. Wherever applicable, we provide new insights about the properties of existing models and revisit their implications for traffic flows of CAVs using recent empirical observations with CAVs and the previous discussions and debates in the literature. The paper then discusses some major problems inherent to continuum modeling of real-world (mixed) CAV traffic flows modeling by distinguishing between two major research directions: (a) modeling for explaining purposes, where making reproducible inferences about the physical aspects of macroscopic properties is of the primary interest, and (b) modeling for practical purposes, in which the focus is on the reliable predictions for operation and control. The paper proposes some potential solutions in each research direction and recommends some future research topics.

math.AP↗