The spatial variability of vehicle densities as determinant of urban network capacity

Mazloumian, Amin; Geroliminis, Nikolas; Helbing, Dirk · 2010 · OpenAlex-citations

DOI: 10.1098/rsta.2010.0099

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Summary

This paper investigates the spatial variability of vehicle densities as a primary determinant of urban network capacity, addressing the limitations of traditional traffic flow theories that rely on single-link fundamental diagrams. While recent research established the existence of a Macroscopic Fundamental Diagram (MFD) linking space-mean flow and density for entire urban networks, significant scattering in congested regimes remains unexplained. The authors argue that this scattering arises from spatial inhomogeneity in congestion distribution, which is influenced by demand, infrastructure, and control settings. The study aims to determine how this spatial variability affects the shape, scatter, and existence of the MFD, and whether network capacity is a deterministic or variable quantity. To address this, the authors employ a macroscopic, fluid-dynamic simulation approach on a 30 × 30 lattice network representing a city center with periodic boundary conditions. The model utilizes a triangular fundamental diagram for individual road sections and incorporates fixed-cycle traffic signals with stochastic offsets to mimic adaptive green waves. Two key methodological innovations are introduced: first, a flow quantization technique that discretizes turning flows into units of single vehicles to generate realistic fluctuations in traffic variables; second, a memoryless routing protocol that directs traffic toward destination areas without requiring complex origin-destination tables or individual route assignments. These methods allow for the simulation of various scenarios, including uniform demand and directed flows, to analyze the relationship between average flow, average density, and density variability. The results demonstrate that urban network capacity is not a deterministic quantity. For low densities, network flow stabilizes at an invariant value, but for intermediate densities, there is high variability in flow for the same average density, ranging from free flow to gridlock. The study identifies the spatial variability of congestion, measured by the standard deviation of density among links, as the key variable explaining this scatter. This variability is strongly correlated with the number of "full links" in the network, which block upstream discharges and reduce overall flow. By treating spatial inhomogeneity as an independent variable, the authors show that the scattering of congested flow measurements can be eliminated, revealing clear functional relationships. The findings are approximated by a simple analytical formula based on the number of full links. The significance of this work lies in its redefinition of urban traffic performance metrics. It establishes that spatial aggregation of traffic variables does not guarantee a well-defined MFD unless spatial heterogeneity is accounted for. The identification of density variability as a critical performance indicator provides a theoretical basis for understanding congestion spreading and network instability. This approach offers a simpler alternative to micro-simulation models by avoiding complex routing assignments while still capturing realistic traffic dynamics, thereby enhancing the understanding of how topological and control-related changes impact urban network capacity.

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• traffic density