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Connected and automated vehicles (CAVs) are expected to reshape traffic flowdynamics and present new challenges and opportunities for traffic flowmodeling. While numerous studies have proposed optimal modeling and controlstrategies for CAVs with various objectives (e.g., traffic efficiency andsafety), there are uncertainties about the flow dynamics of CAVs in real-worldtraffic. The uncertainties are especially amplified for mixed traffic flows,consisting of CAVs and human-driven vehicles, where the implications can besignificant from the continuum-modeling perspective, which aims to capturemacroscopic traffic flow dynamics based on hyperbolic systems of partialdifferential equations. This paper aims to highlight and discuss some essentialproblems in continuum modeling of real-world freeway traffic flows in the eraof CAVs. We first provide a select review of some existing continuum models forconventional human-driven traffic as well as the recent attempts forincorporating CAVs into the continuum-modeling framework. Wherever applicable,we provide new insights about the properties of existing models and revisittheir implications for traffic flows of CAVs using recent empiricalobservations with CAVs and the previous discussions and debates in theliterature. The paper then discusses some major problems inherent to continuummodeling of real-world (mixed) CAV traffic flows modeling by distinguishingbetween two major research directions: (a) modeling for explaining purposes,where making reproducible inferences about the physical aspects of macroscopicproperties 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 andrecommends some future research topics.

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