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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.21039 |
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| _version_ | 1866912296528248832 |
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| author | Chang-Lara, Hector Andres Zapeta-Tzul, Sergio David |
| author_facet | Chang-Lara, Hector Andres Zapeta-Tzul, Sergio David |
| contents | We revisit the classic problem of determining optimal routes in a graph for transporting two given distributions defined on its nodes, originally studied by Wardrop and Beckmann in the 1950s. The global congestion profile at any given time defines a dynamic metric on the graph, for which the routes must be geodesics. Our first contribution is the introduction of a dynamic version of the Beckmann problem, for which we derive the corresponding discrete partial differential equations governing the evolution of the system. These equations enable us to estimate the size of the support of the edge flow. Finally, we present some numerical simulations to illustrate the behavior of efficient equilibria in a dynamic setting with non-local interactions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A dynamic model of congestion Chang-Lara, Hector Andres Zapeta-Tzul, Sergio David Optimization and Control We revisit the classic problem of determining optimal routes in a graph for transporting two given distributions defined on its nodes, originally studied by Wardrop and Beckmann in the 1950s. The global congestion profile at any given time defines a dynamic metric on the graph, for which the routes must be geodesics. Our first contribution is the introduction of a dynamic version of the Beckmann problem, for which we derive the corresponding discrete partial differential equations governing the evolution of the system. These equations enable us to estimate the size of the support of the edge flow. Finally, we present some numerical simulations to illustrate the behavior of efficient equilibria in a dynamic setting with non-local interactions. |
| title | A dynamic model of congestion |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2503.21039 |