  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.
