Self-Similar Characteristics in Queue Length Dynamics: Insights from Adaptive Signalized Corridor

TL;DR

This study investigates the self-similar fractal characteristics of queue length dynamics at adaptive signalized intersections, revealing a $1/f$ power spectrum and linking local scaling exponents to congestion patterns.

Contribution

It introduces a novel analysis of queue length self-similarity using DFA, providing new insights into adaptive traffic signal system dynamics.

Findings

Queue lengths exhibit a $1/f$ power spectrum indicating self-similarity.

Local scaling exponents correlate positively with congestion levels.

Fractal analysis reveals evolving queue dynamics over time.

Abstract

Self-similarity, a fractal characteristic of traffic flow dynamics, is widely recognized in transportation engineering and physics. However, its practical application in real-world traffic scenarios remains limited. Conversely, the traffic flow dynamics at adaptive signalized intersections still need to be fully understood. This paper addresses this gap by analyzing the queue length time series from an adaptive signalized corridor and characterizing its self-similarity. The findings uncover a $1/f$ structure in the power spectrum of queue lengths, indicative of self-similarity. Furthermore, the paper estimates local scaling exponents $(\alpha)$, a measure of self-similarity computed via detrended fluctuation analysis (DFA), and identifies a positive correlation with congestion patterns. Additionally, the study examines the fractal dynamics of queue length through the evolution of scaling exponent. As a result, the paper offers new insights into the queue length dynamics of signalized intersections, which might help better understand the impact of adaptivity within the system.