Autonomous vehicles will have to perform within the context of existing traffic patterns. We look at some traffic data from New York City from several three mathematical perspectives, with the goal of ways of identifying large-scale behavior. Some of these results are preliminary.
1. We look at nonnegative matrix factorization of traffic counts to decompose traffic data into behavioral signatures. We rearrange the results to propose a way of quantifying (dis)order in traffic behavior.
2. We combine traffic counts, speeds, and accident data and use a bi-objective routing problem to quantify how intertwined accidents are in traffic behavior. We find slightly different results by time of day.
3. We look at the topology of congestion from the standpoint of topological data analysis and persistent homology. We build a simplicial complex whose barcode helps capture regions of congestion surrounded by faster roads. We find several interesting specific results.
Parts of this work are in conjunction with Dan Work.
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