Load asymptotics and dynamic speed optimization for the greenest path problem: a comprehensive analysis

We study the effect of using high-resolution elevation data on the selection of the most fuel-efficient (greenest) path for different trucks in various urban environments. We adapt a variant of the Comprehensive Modal Emission Model (CMEM) to show that the optimal speed and the greenest path are slope dependent (dynamic). When there are no elevation changes in a road network, the most fuel-efficient path is the shortest path with a constant (static) optimal speed throughout. However, if the network is not flat, then the shortest path is not necessarily the greenest path, and the optimal driving speed is dynamic. We prove that the greenest path converges to an asymptotic greenest path as the payload approaches infinity and that this limiting path is attained for a finite load. In a set of extensive numerical experiments, we benchmark the \(\hbox {CO}_{2}\) ${\text{CO}}_2$ emissions reduction of our dynamic speed and the greenest path policies against policies that ignore elevation data. We use the geo-spatial data of 25 major cities across 6 continents. We observe numerically that the greenest path quickly diverges from the shortest path and attains the asymptotic greenest path even for moderate payloads. Based on an analysis of variance, the main determinants of the \(\hbox {CO}_{2}\) ${\text{CO}}_2$ emissions reduction potential are the variation of the road gradients along the shortest path as well as the relative elevation of the source from the target. Using speed data estimates for rush hour in New York City, we test \(\hbox {CO}_{2}\) ${\text{CO}}_2$ emissions reduction by comparing the greenest paths with optimized speeds against the fastest paths with traffic speed. We observe that selecting the greenest paths instead of the fastest paths can significantly reduce \(\hbox {CO}_{2}\) ${\text{CO}}_2$ emissions. Additionally, our results show that while speed optimization on uphill arcs can significantly help \(\hbox {CO}_{2}\) ${\text{CO}}_2$ reduction, the potential to leverage gravity for acceleration on downhill arcs is limited due to traffic congestion.