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.