A fundamental property of vehicular traffic flow on our highways is that it may exhibit significant non-equilibrium behavior once the flow becomes sufficiently dense: vehicles do not move at steady speeds, but rather undergo acceleration and braking. This unsteadiness manifests in a multitude of ways; but in almost all situations it is undesirable (loss of efficiency; increased fuel consumption, emissions, accident risk). Understanding the causes and dynamics of non-equilibrium traffic flow via models, observations, and data is a crucial challenge in traffic flow theory; and it becomes even more important in light of ongoing and future (partial) automation of the vehicle fleet. We highlight important steps in developing phenomenological models for instabilities and nonlinear waves in traffic flow, both macroscopic and microscopic, and discuss how this modeling extends to heterogeneous flows composed of a mix of human-driven and (semi-)automated vehicles. In particular, we stress how automation can go both ways: it could make traffic run more smoothly; but also render it less efficient than it is under human control.
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