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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.29055 |
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| _version_ | 1866911561911631872 |
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| author | Lu, Annie Tan, Hong Kiat Xue, Alexander Koniges, Alice Bertozzi, Andrea L. |
| author_facet | Lu, Annie Tan, Hong Kiat Xue, Alexander Koniges, Alice Bertozzi, Andrea L. |
| contents | The 2023 Lahaina wildfire killed 102 people on a peninsula served by a single two-lane highway, making exit lane capacity the binding constraint on evacuation time. We model the evacuation as a system of hyperbolic scalar conservation laws on a directed graph with game-theoretic junction conditions that maximize total network flux, an evacuation-calibrated piecewise linear-quadratic flux function, and a loss-driven optimization framework that tunes traffic distribution toward priority corridors. Analytical results on a toy network and numerical simulations of the Lahaina road network reveal a phase transition in exit lane capacity. Additional lanes improve throughput linearly until a computable critical threshold, beyond which no route optimization yields further benefit. For Lahaina, reversing one southbound lane captures nearly all achievable improvement, and a fourth lane can be reserved for emergency vehicles with negligible impact on civilian clearance time. These results provide a rigorous mathematical basis for contraflow recommendations in wildland-urban interface evacuations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29055 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Macroscopic Traffic Flow Network Modeling For Wildfire Evacuation: A Game-Theoretic Junction Optimization Approach with Application to Lahaina Fire Lu, Annie Tan, Hong Kiat Xue, Alexander Koniges, Alice Bertozzi, Andrea L. Numerical Analysis Optimization and Control Physics and Society 90B20, 35L65, 90C26, 90C35, 65M08, 91A80 The 2023 Lahaina wildfire killed 102 people on a peninsula served by a single two-lane highway, making exit lane capacity the binding constraint on evacuation time. We model the evacuation as a system of hyperbolic scalar conservation laws on a directed graph with game-theoretic junction conditions that maximize total network flux, an evacuation-calibrated piecewise linear-quadratic flux function, and a loss-driven optimization framework that tunes traffic distribution toward priority corridors. Analytical results on a toy network and numerical simulations of the Lahaina road network reveal a phase transition in exit lane capacity. Additional lanes improve throughput linearly until a computable critical threshold, beyond which no route optimization yields further benefit. For Lahaina, reversing one southbound lane captures nearly all achievable improvement, and a fourth lane can be reserved for emergency vehicles with negligible impact on civilian clearance time. These results provide a rigorous mathematical basis for contraflow recommendations in wildland-urban interface evacuations. |
| title | Macroscopic Traffic Flow Network Modeling For Wildfire Evacuation: A Game-Theoretic Junction Optimization Approach with Application to Lahaina Fire |
| topic | Numerical Analysis Optimization and Control Physics and Society 90B20, 35L65, 90C26, 90C35, 65M08, 91A80 |
| url | https://arxiv.org/abs/2603.29055 |