Quantification of the Hysteresis of Macroscopic Fundamental Diagrams and Its Relationship with the Congestion Heterogeneity and Performance of a Multimodal Network

Abstract

Recent studies have observed hysteresis loops in the macroscopic fundamental diagram (MFD). In particular, for the same network density, higher network flows occur during congestion onset than during congestion offset. To evaluate management strategies using the MFD, investigating the relationship between the size of these loops and network performance is needed. The existing literature has mainly discussed correlating loop width (difference in density) and height (capacity drop) with congestion heterogeneity, but has failed to prove a relationship between the capacity drop and traffic conditions. Moreover, quantification of the MFD loop in complex multimodal networks has not been investigated. The objective of this paper covers these aspects. We simulated the Sioux Falls network with different mode-share ratios (car and bus users) based on a multi-agent simulation, MATSim. We investigated the relationships between MFD loop size and congestion heterogeneity (standard deviation of density) and network performance (average passenger travel time), and found that both were directly correlated with loop width, while weakly correlated with loop height. Moreover, we divided the MFD loop into two parts according to congestion onset and offset periods and found that the heights of the two parts had opposite effects. Accordingly, we show why the relationship between capacity drop and congestion heterogeneity is not found in the literature. We also found that network performance inversely affected the height of part of the loop while the height of its other part increased with an increase in congestion heterogeneity. These results help to evaluate network performance in the presence of MFD hysteresis, leading to elaborated management decisions.