| Summary: | Macroscopic traffic models represent a promising tool to design strategies for ecological routing. To benefit from this tool, we must first characterize the relationship between path emissions and distance traveled or travel time on aggregated networks, i.e., a regional network. This paper investigates this relationship between two toy networks and a real urban network representing the city of Innsbruck (Austria). We utilize an accumulation-based model based on the Macroscopic Fundamental Diagram to mimic the traffic dynamics in the network and utilize the COPERT IV model to estimate the travel emissions, focusing on the carbon dioxide <inline-formula> <tex-math notation="LaTeX">$CO_{2}$ </tex-math></inline-formula>. We show that there is a linear relationship between the total emissions of <inline-formula> <tex-math notation="LaTeX">$CO_{2}$ </tex-math></inline-formula> and the average travel time of internal paths, i.e., paths that take place completely within a single region. We also show that in some cases, there is a linear relationship between the total emissions and the average travel distance or travel time of paths that cross multiple regions in the network. However, the latter is not always true as traffic dynamics play an important role in path emissions. In other words, eco-friendly paths on regional networks do not necessarily follow the shortest paths in terms of distance or time.
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