CRII: III: Effective Geometry of Urban Travel Patterns

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The speed and scale of urbanization brings tremendous challenges in developing sustainable cities. Half of the global population already lives in cities, and by 2050 two-thirds of the world’s people are expected to live in urban areas. This project aims to address open challenges in urban planning, such as traffic congestions and accessibility, using novel mathematical and computational tools. Specifically, the project combines the mathematics of Riemannian geometry with large-scale computer simulations of urban travel in road networks. The work will result in new algorithms to extract the geometrical features and rules of urban travel, which facilitate the design of urban mobility solutions for the sustainable development of cities. Furthermore, this research will support the training of STEM researchers, and the development of open-source software that will make this new line of research more accessible to other researchers. The technical aims of the project are divided into two thrusts. The first thrust develops theoretical and algorithmic tools to compute a Riemanian metric such that flows on the network are distance-minimizing geodesics for that metric. One can imagine a road map where instead of having a fixed scale (for example, every inch on the map corresponds to 1 mile), all roads have the same speed. Thus, distances on the map represent travel time rather than actual distances. The main idea is to represent network flows by vector fields attaching a vector to every node in the network, which shows the direction and speed of flow from that node to some fixed target node. The researchers will develop strategies to infer a metric tensor from these vector fields and show connections between geometric features (such as curvature and volume) and topological features of the original network. The second thrust will focus on analyzing real road maps and travel time data in cities around the world, and use the framework to classify cities based on their geometry and how it varies with time. The work will demonstrate how geometrical tools can be used to address open challenges in urban transportation systems such as traffic congestions and accessibility.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.