An Extreme Value Theory Approach for Understanding Queue Length Dynamics in Adaptive Corridors

TL;DR

The paper addresses understanding the long-term behavior of cycle-to-cycle maximum queue lengths in signalized corridors under adaptive control. By applying extreme value theory, it demonstrates that the cycle maxima follow a Generalized Extreme Value (GEV) distribution, with asymptotic forms for the maximum queue length expressed as $L^*(t) \sim \gamma(\log t + \log \beta + Z)$ where $Z$ has a Gumbel distribution. Empirical analysis across nine intersections in the Alafaya Trail corridor provides evidence that EVT, and specifically GEV/Gumbel fits, describe the extreme queue-length behavior after removing seasonality and trend. The findings enable reliability-oriented corridor management and spillover risk assessment, and point to future work on threshold-exceedance approaches to improve data efficiency and predictive capability.

Abstract

This paper introduces a novel approach employing extreme value theory to analyze queue lengths within a corridor controlled by adaptive controllers. We consider the maximum queue lengths of a signalized corridor consisting of nine intersections every two minutes, roughly equivalent to the cycle length. Our research shows that maximum queue lengths at all the intersections follow the extreme value distributions. To the best knowledge of the authors, this is the first attempt to characterize queue length time series using extreme value analysis. These findings are significant as they offer a mechanism to assess the extremity of queue lengths, thereby aiding in evaluating the effectiveness of the adaptive signal controllers and corridor management. Given that extreme queue lengths often precipitate spillover effects, this insight can be instrumental in preempting such scenarios.

Figures (7)

• Figure 1: Location of intersections on Alafaya corridor (left) and illustration of the corridor as a dynamical system (right). Northbound (NB) through queue length at each intersection is measured in distance units.
• Figure 2: Illustrates the original queue length time series and adjusted time series after removing seasonal and trend components from the original queue length time series.
• Figure 3: Illustrates the residual part computed after removing seasonal and trend components from the original queue length time series.
• Figure 4: Illustrates the RSS score of some popular distributions. The general extreme value distribution is the best fit for most intersections.
• Figure 5: Illustrates the probability distribution of the residual part of the queue length time series. Gumbel and Fréchet distributions are fitted into the histogram