Non-unimodal and non-concave relationships in the network Macroscopic Fundamental Diagram caused by hierarchical streets

Unimodal, concave relationships between average network productivity and accumulation or density aggregated across spatially compact regions of urban networks-so called network Macroscopic Fundamental Diagrams (MFDs)-have recently been shown to exist on homoge-neous street networks. When present, MFD relationships facilitate the modeling of traffic congestion at a regional level and have led to the development of various regional traffic control strategies. However, real street networks are not homogeneous-they generally have a hierar-chical structure where some streets (e.g., arterials) promote higher mobility than others (e.g., local roads). This paper examines how the presence of hierarchical roadway structures may potentially cause non-unimodal patterns in a network's MFD. These are observed using three types of tools: analytical models of simple network structures, simulations of various idealized roadway networks, and empirical data. The impacts of street hierarchy depend on how vehicles use different roadway types to move within the network; i.e., their routing strategy. The findings suggest that the presence of roadway hierarchies may lead to MFDs that have non-unimodal or non-concave patterns on the free-flow branch when vehicles route themselves according to user equilibrium principles, which is closest to what would be observed in realistic situations. Such patterns are contrary to what is traditionally assumed in most MFD-based modeling frameworks. However, the unimodal and concave MFD should be expected under system optimal routing conditions that maximize network productivity for a given traffic state.

Automated summary

Recent research has shown that there are unimodal, concave relationships between average network productivity and accumulation or density in urban networks. These relationships, known as network Macroscopic Fundamental Diagrams (MFDs), have implications for the modeling of traffic congestion and the development of regional traffic control strategies. However, real street networks are not homogeneous and have hierarchical structures, which may result in non-unimodal patterns in MFDs. This paper examines how the presence of hierarchical roadway structures can affect a network's MFD using analytical models, simulations, and empirical data. The findings suggest that the presence of roadway hierarchies can lead to non-unimodal or non-concave MFD patterns, contrary to traditional assumptions.