Relationship Between Macroscopic Fundamental Diagram Hysteresis and Network-Wide Traffic Conditions

Abstract

Abstract The macroscopic fundamental diagram (MFD) is a graph relating an average network flow to the average density and is used to evaluate traffic-control strategies. However, a large urban network may have multiple flows for any given density; such a condition is termed an MFD hysteresis loop. The relationships between this loop and network conditions must be studied when evaluating the effects of traffic-control strategies on network performance, especially for multi-modal networks that have received little attention to date. Here, we investigated relationships between loop width and height, the spatial density distribution, and network performance, via multi-agent simulation of various traffic conditions for cars and buses. We partitioned the MFD loop into two parts (the congestion-building and dissipation periods) and found that the correlations between the density distribution and network performance, and the heights, of the two parts were stronger than the correlations obtained when the overall loop height was used, because the two heights exhibited opposite effects on traffic conditions. We conclude that network performance inversely affects flow reduction when the network is loading, whereas the heterogeneous density distribution increases flow reduction during network unloading (as congestion dissipates). The criteria for loop partitioning that we develop reveal several relationships not yet addressed in the literature, and aid in the evaluation of network performance when MFD hysteresis is in play, facilitating appropriate traffic-control decisions.