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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.05439 |
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| _version_ | 1866917387801985024 |
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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 |