Figure 1: Traffic waves generated by human driving increase the energy consumption of traffic flow. A small fraction of wellcontrolled automated vehicles can smooth the flow and the reduce energy consumption.

Traffic waves can rise even from single lane car-following behaviour. To better understand and mitigate traffic waves, it is necessary to use analytical tools like mathematical models, data analysis, and micro-simulations that can capture the dynamics of real traffic flow. In this study, we isolate car-following dynamics and present a systematic hierarchy of tests that connect the microscopic scale with the meaningful macroscopic effective state in the presence of waves. This allows insights with precise attributable cause-to-effect relationships of specific observed traffic patterns. We establish a principled way of generating macroscopic flow quantities from microscopic models in the unstable regime. Those quantities are then used to study how the corresponding non-equilibrium wave structures manifest in the fundamental diagram, based on three basic scenarios that can serve as building blocks for understanding more complex micro-simulation studies. Finally, this study gives insight on the shapes of the reduced fundamental diagrams for different commonly used microscopic models.

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