Oversaturated intersections: A real-world assessment of polynomial fluid queue models

Abstract

This paper investigates the challenges of quantifying stochasticity and dynamics in traffic states, crucial to efficient transportation systems, particularly during oversaturated conditions at signalized intersections. We build upon Newell's polynomial fluid queuing-theoretic ordinary differential equation (ODE) model as an example of model order reduction, with a focus on time-dependent stochastic arrival rates and departure rates. These assumptions facilitate dynamic arrival rate approximation using polynomial functions, which, when integrated with queue lengths, yield total delay per episode. Validation of Newell's polynomial fluid-queue based dynamic patterns is sought by analyzing cumulative cycles during peak periods, segmented based on residual queue values. A comprehensive real-world experiment employs emerging high resolution video detector cameras to capture various queue lengths, revealing recurring congestion patterns. Real-time arrival and departure count during peak periods further allow for the creation of cumulative curves, enhancing our understanding of congestion dynamics at signalized intersections under partially oversaturated conditions. This foundational understanding is essential for applying deep reinforcement learning in such environments, where the goal is to observe environment states to maximize expected long-term reward.