Calibration and uncertainty quantification of macroscopic fundamental diagrams

TL;DR

This paper introduces a mathematical framework for calibrating the macroscopic fundamental diagram (MFD) and quantifying uncertainty in traffic network capacity, validated with empirical data, to improve traffic management and resilience strategies.

Contribution

It presents a novel calibration and uncertainty quantification method for MFDs, incorporating factors like congestion phases and driving behavior, advancing traffic network analysis.

Findings

Validated approach with empirical data from Chinese cities

Identified congestion loading and recovery as key uncertainty factors

Developed a method to assess capacity drop and traffic resilience

Abstract

Traffic congestion occurs as travel demand exceeds network capacity, necessitating a thorough understanding of network capacity for effective traffic control and management. The macroscopic fundamental diagram (MFD) provides an efficient framework for quantifying network capacity. However, empirical MFDs exhibit considerable data scatter and uncertainty. In this paper, we propose a mathematical program that simultaneously calibrates the MFD and quantifies the uncertainty associated with data scatter. We further investigate contributing factors of uncertainties regarding network capacity and traffic resilience. To be specific, we first include two conventional approaches for MFD calibration and uncertainty quantification as special cases. The proposed program is validated using empirical data from two cities in China. Subsequently, we identify how congestion loading and recovery contribute to data scatter. We develop a novel uncertainty quantification approach capable of capturing distinct congestion phases simultaneously. The gap between the upper and lower bounds of the calibrated MFDs, represented by a coefficient parameter, is regarded as the capacity drop induced by traffic congestion. Furthermore, the proposed approach enables further exploration of how macroscopic factors, such as travel demand and traffic control, and microscopic factors, such as driving behavior, influence MFD hysteresis, uncertainty, and traffic resilience. These findings shed light on developing efficient traffic control and demand management strategies to increase network capacity and resilience, while we count on future connected automated vehicular technologies to conquer the influence of various driving behaviors.