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Main Authors: Chiba, Yuki, Saito, Norikazu, Ueda, Yuki, Yoshida, Hiroaki
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2604.05439
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author Chiba, Yuki
Saito, Norikazu
Ueda, Yuki
Yoshida, Hiroaki
author_facet Chiba, Yuki
Saito, Norikazu
Ueda, Yuki
Yoshida, Hiroaki
contents Recent empirical studies have reported that spatiotemporal congestion clusters in urban traffic exhibit scale-free statistics, with cluster size following a power-law distribution. In this study, we address whether macroscopic continuum descriptions of traffic flow are capable of generating such scale-free spatiotemporal congestion patterns. To this end, we analyze the second-order Aw-Rascle-Zhang model on directed networks under junction coupling. The governing equations are solved by a high-order discontinuous Galerkin scheme, and junction fluxes are determined by an optimization-based coupling procedure enforcing conservation and admissibility at intersections. Congestion is defined by thresholding the road-averaged density, and spatiotemporal clusters are extracted as connected components in space and time. Numerical experiments on lattice networks of varying sizes reveal that the cluster size follows a robust power-law distribution. Moreover, when rescaled by the linear system size inherent to the two-dimensional network geometry, the distribution collapses onto an approximately universal curve, indicating finite-size scaling governed by the linear system size. The observed power-law statistics and finite-size scaling are reminiscent of scale-invariant dynamics characteristic of self-organized criticality. These results demonstrate that macroscopic continuum traffic models can reproduce large-scale statistical features observed in real urban congestion dynamics.
format Preprint
id arxiv_https___arxiv_org_abs_2604_05439
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Scale-free congestion clusters in large-scale traffic networks: a continuum modeling study
Chiba, Yuki
Saito, Norikazu
Ueda, Yuki
Yoshida, Hiroaki
Physics and Society
Statistical Mechanics
Mathematical Physics
Fluid Dynamics
35L65, 65M60, 90B20
G.1.8; G.1.6; G.1.10
Recent empirical studies have reported that spatiotemporal congestion clusters in urban traffic exhibit scale-free statistics, with cluster size following a power-law distribution. In this study, we address whether macroscopic continuum descriptions of traffic flow are capable of generating such scale-free spatiotemporal congestion patterns. To this end, we analyze the second-order Aw-Rascle-Zhang model on directed networks under junction coupling. The governing equations are solved by a high-order discontinuous Galerkin scheme, and junction fluxes are determined by an optimization-based coupling procedure enforcing conservation and admissibility at intersections. Congestion is defined by thresholding the road-averaged density, and spatiotemporal clusters are extracted as connected components in space and time. Numerical experiments on lattice networks of varying sizes reveal that the cluster size follows a robust power-law distribution. Moreover, when rescaled by the linear system size inherent to the two-dimensional network geometry, the distribution collapses onto an approximately universal curve, indicating finite-size scaling governed by the linear system size. The observed power-law statistics and finite-size scaling are reminiscent of scale-invariant dynamics characteristic of self-organized criticality. These results demonstrate that macroscopic continuum traffic models can reproduce large-scale statistical features observed in real urban congestion dynamics.
title Scale-free congestion clusters in large-scale traffic networks: a continuum modeling study
topic Physics and Society
Statistical Mechanics
Mathematical Physics
Fluid Dynamics
35L65, 65M60, 90B20
G.1.8; G.1.6; G.1.10
url https://arxiv.org/abs/2604.05439