Optimization of continuous-flow over traffic networks with fundamental diagram constraints
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914129964433408 |
|---|---|
| author | Dong, Anqi Johansson, Karl Henrik Karlsson, Johan |
| author_facet | Dong, Anqi Johansson, Karl Henrik Karlsson, Johan |
| contents | Optimal transport (OT) theory provides a principled framework for modeling mass movement in applications such as mobility, logistics, and economics. Classical formulations, however, generally ignore capacity limits that are intrinsic in applications, in particular in traffic flow problems. We address this limitation by incorporating fundamental diagrams into a dynamic continuous-flow OT model on graphs, thereby including empirical relations between local density and maximal flux. We adopt an Eulerian kinetic action on graphs that preserves displacement interpolation in direct analogy with the continuous theory. Momentum lives on edges and density on nodes, mirroring road-network semantics in which segments carry speed and intersections store mass. The resulting fundamental-diagram-constrained OT problem preserves mass conservation and admits a convex variational discretization, yielding optimal congestion-aware traffic flow over road networks. We establish the existence and uniqueness of the optimal flow with sources and sinks, and develop an efficient convex optimization method. Numerical studies begin with a single-lane line network and scale to a city-level road network. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00500 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimization of continuous-flow over traffic networks with fundamental diagram constraints Dong, Anqi Johansson, Karl Henrik Karlsson, Johan Optimization and Control Systems and Control 49Q22, 90B20, 05C21, 65K10 Optimal transport (OT) theory provides a principled framework for modeling mass movement in applications such as mobility, logistics, and economics. Classical formulations, however, generally ignore capacity limits that are intrinsic in applications, in particular in traffic flow problems. We address this limitation by incorporating fundamental diagrams into a dynamic continuous-flow OT model on graphs, thereby including empirical relations between local density and maximal flux. We adopt an Eulerian kinetic action on graphs that preserves displacement interpolation in direct analogy with the continuous theory. Momentum lives on edges and density on nodes, mirroring road-network semantics in which segments carry speed and intersections store mass. The resulting fundamental-diagram-constrained OT problem preserves mass conservation and admits a convex variational discretization, yielding optimal congestion-aware traffic flow over road networks. We establish the existence and uniqueness of the optimal flow with sources and sinks, and develop an efficient convex optimization method. Numerical studies begin with a single-lane line network and scale to a city-level road network. |
| title | Optimization of continuous-flow over traffic networks with fundamental diagram constraints |
| topic | Optimization and Control Systems and Control 49Q22, 90B20, 05C21, 65K10 |
| url | https://arxiv.org/abs/2511.00500 |