Macroscopic Fundamental Diagram for Network Traffic Flow: From Uncongested State to Congested State

Urban traffic congestion poses a significant global challenge, prompting a shift from unsustainable infrastructure expansion towards optimizing existing networks through intelligent management. This requires robust modeling tools that transcend the limitations of single-link models, which are computationally expensive and fail to capture network-wide phenomena like gridlock. This survey provides a comprehensive review of the Macroscopic Fundamental Diagram (MFD), a pivotal advancement that offers an aggregate description of network traffic flow. We focus specifically on the MFD's characteristics and behavior during the critical transition from uncongested to congested states. The MFD defines a network’s performance through a relationship between vehicle density and flow, forming a curve with a free-flow branch, a critical capacity point, and a congested branch. The manuscript delves into the MFD's theoretical foundations, empirical observations, and modeling approaches. A key insight is that the state transition is complex, exhibiting hysteresis and phase-transition-like behavior, heavily influenced by network heterogeneity and demand patterns. We also address persistent challenges in empirical MFD estimation, including data limitations, while noting how advancements in big data are improving accuracy. Finally, we explore the MFD's practical applications as a foundational tool for developing perimeter control strategies that regulate traffic flow to maintain network efficiency and prevent systemic congestion. This review underscores the MFD's role as a critical paradigm in modern traffic management.