On How Traffic Signals Impact the Fundamental Diagrams of Urban Roads
Chao Zhang, Yechen Li, Neha Arora, Carolina Osorio
TL;DR
This paper addresses how traffic signal settings shape the urban fundamental diagram (FD) by making the FD parameters explicit functions of signal factors. It introduces a parsimonious FD form $v = v_{max} \left( 1 - \left( \frac{q}{q_{cap}} \right)^{\alpha} \right)^{\beta}$ and imposes linear dependencies on the green split $g$ through $\beta = \theta_0 + \theta_1 g$ and $(\beta/\alpha) = \theta_2 + \theta_3 g$, enabling a signal-aware, scalable FD across segments. The approach is validated with actuated-signal data from Salt Lake City, showing that increasing $g$ shifts the FD upward, consistent with increased capacity and altered congestion patterns, with common parameter values across segments. This yields a practical tool for predicting how changes in signal plans influence macroscopic traffic behavior and congestion.
Abstract
Being widely adopted by the transportation and planning practitioners, the fundamental diagram (FD) is the primary tool used to relate the key macroscopic traffic variables of speed, flow, and density. We empirically analyze the relation between vehicular space-mean speeds and flows given different signal settings and postulate a parsimonious parametric function form of the traditional FD where its function parameters are explicitly modeled as a function of the signal plan factors. We validate the proposed formulation using data from signalized urban road segments in Salt Lake City, Utah, USA. The proposed formulation builds our understanding of how changes to signal settings impact the FDs, and more generally the congestion patterns, of signalized urban segments.