A Topological Threshold for Bidirectional Coordination in One-Dimensional Poisson Proximity Networks
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2026
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| _version_ | 1866901343420022784 |
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| author | Ji, Jian |
| author_facet | Ji, Jian |
| contents | <p>We derive a topological threshold for bidirectional coordination in one-dimensional Poisson proximity networks. For agents distributed with intensity <span>$\lambda$</span> interacting within range <span>$\ell$</span>, the coordination cluster size follows a geometric distribution with mean <span>$E[N] = e^{\lambda\ell}$</span>, derived from the memoryless property of Poisson inter-arrivals.</p> <p><strong>Bidirectional coordination</strong> requires a minimum cluster of three agents (initiator plus one relay in each direction), giving the characteristic threshold <strong><span>$\lambda\ell = ln(3) \approx 1.099$</span></strong> with no parameters fitted to the validation data.</p> <p><strong>Empirical consistency:</strong></p> <ol> <li> <p><strong>Five freeway datasets (N=334,909):</strong> Weighted-mean LWR exponent <span>$\hat{\theta} = 1.095 \pm 0.051$</span>, within <span>$0.08\sigma$</span> of <span>$ln(3)$</span>.</p> </li> <li> <p><strong>Chengdu V2X data (N=19,782,736 OBU records):</strong> <span>$1.60\times$</span> speed-variance reduction at <span>$\lambda\ell = ln(3)$</span>.</p> </li> <li> <p><strong>Rope3D RSU perception data (18 highway scenes, N=48,518 gaps):</strong> <span>$ln(3)$</span> separates free-flow (<span>$CV=0.952$</span>) from congested scenes (<span>$CV=1.238$</span>) with 100% classification accuracy.</p> </li> <li> <p><strong>DAIR-V2X urban intersection (N=959 gaps):</strong> <span>$CV=1.182 > ln(3)$</span>, consistent with congested urban threshold exceedance.</p> </li> </ol> <p><strong>Critical penetration bound:</strong> <span>$p_c = ln(3)/(\rho_0\ell) = 12.2\%$</span> at standard motorway parameters, explaining the 10-15% simulation consensus. Submitted to <em>Physical Review Letters</em> (March 2026). Submission ID: <strong>es2026mar19_577</strong>.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19102077 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | A Topological Threshold for Bidirectional Coordination in One-Dimensional Poisson Proximity Networks Ji, Jian percolation theory ln(3) cooperative coordination traffic flow V2X collective behaviour statistical physics proximity networks phase transition universal constant <p>We derive a topological threshold for bidirectional coordination in one-dimensional Poisson proximity networks. For agents distributed with intensity <span>$\lambda$</span> interacting within range <span>$\ell$</span>, the coordination cluster size follows a geometric distribution with mean <span>$E[N] = e^{\lambda\ell}$</span>, derived from the memoryless property of Poisson inter-arrivals.</p> <p><strong>Bidirectional coordination</strong> requires a minimum cluster of three agents (initiator plus one relay in each direction), giving the characteristic threshold <strong><span>$\lambda\ell = ln(3) \approx 1.099$</span></strong> with no parameters fitted to the validation data.</p> <p><strong>Empirical consistency:</strong></p> <ol> <li> <p><strong>Five freeway datasets (N=334,909):</strong> Weighted-mean LWR exponent <span>$\hat{\theta} = 1.095 \pm 0.051$</span>, within <span>$0.08\sigma$</span> of <span>$ln(3)$</span>.</p> </li> <li> <p><strong>Chengdu V2X data (N=19,782,736 OBU records):</strong> <span>$1.60\times$</span> speed-variance reduction at <span>$\lambda\ell = ln(3)$</span>.</p> </li> <li> <p><strong>Rope3D RSU perception data (18 highway scenes, N=48,518 gaps):</strong> <span>$ln(3)$</span> separates free-flow (<span>$CV=0.952$</span>) from congested scenes (<span>$CV=1.238$</span>) with 100% classification accuracy.</p> </li> <li> <p><strong>DAIR-V2X urban intersection (N=959 gaps):</strong> <span>$CV=1.182 > ln(3)$</span>, consistent with congested urban threshold exceedance.</p> </li> </ol> <p><strong>Critical penetration bound:</strong> <span>$p_c = ln(3)/(\rho_0\ell) = 12.2\%$</span> at standard motorway parameters, explaining the 10-15% simulation consensus. Submitted to <em>Physical Review Letters</em> (March 2026). Submission ID: <strong>es2026mar19_577</strong>.</p> |
| title | A Topological Threshold for Bidirectional Coordination in One-Dimensional Poisson Proximity Networks |
| topic | percolation theory ln(3) cooperative coordination traffic flow V2X collective behaviour statistical physics proximity networks phase transition universal constant |
| url | https://doi.org/10.5281/zenodo.19102077 |