Dynamic mode decomposition type algorithms for modeling and predicting queue lengths at signalized intersections with short lookback

Abstract

This article explores a novel data-driven approach based on recent developments in Koopman operator theory and dynamic mode decomposition (DMD) for modeling signalized intersections. On signalized intersections, vehicular flow and queue formation have complex nonlinear dynamics, making system identification, modeling, and controller design challenging. We employ a DMD-type approach to transform the original nonlinear dynamics into locally linear infinite-dimensional dynamics. The data-driven approach relies entirely on spatio-temporal snapshots of the traffic data. We investigate several key aspects of the approach and provide insights into the usage of DMD-type algorithms for application in adaptive signalized intersections. To validate the obtained linearized dynamics, we perform prediction of the queue lengths at the intersection and compare the results with the benchmark methods such as ARIMA and long short term memory (LSTM). The case study involves intersection pressure and queue lengths at two Orlando area signalized intersections during the morning and evening peaks. It is observed that DMD-type algorithms are able to capture complex dynamics with a linear approximation to a reasonable extent. The merits include faster computation times and significantly less requirement for a “lookback” (training) window.