A figure-eight hysteresis pattern in macroscopic fundamental diagrams and its microscopic causes

Abstract

This paper presents macroscopic fundamental diagrams (MFDs) for an urban freeway network in Beijing, China. In the diagrams, a figure-eight hysteresis pattern is observed. To understand the causes, analyses are made ranging from spatiotemporal heterogeneity of vehicles to the flow–occupancy relation for individual locations. Eventually, it is observed at individual locations that free-flow traffic with the same occupancy exhibits different flows in the onset and offset of a rush hour; it is attributed to the counter-clockwise loop in the figure-eight hysteresis pattern at the macroscopic level. Through a simulation scenario based on a cellular automata (CA) model, different lane-changing rates are discussed as the microscopic causes of the flow–occupancy diagram with multiple free-flow branches. In practice, it is inevitable to collect lane-changing data sometimes because of the closeness between detectors and ramps. In the situation, the origin–destination (OD) matrices may influence the shape of MFDs. The paper enriches the knowledge about MFDs and also provides some empirical support for existing theories.