Discrete adjoint gradient computation for multiclass traffic flow models on road networks
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918423259250688 |
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| author | Goatin, Paola Klar, Axel Mezquita-Nieto, Carmen |
| author_facet | Goatin, Paola Klar, Axel Mezquita-Nieto, Carmen |
| contents | This paper applies a discrete adjoint gradient computation method for a multi-class traffic flow model on road networks. Vehicle classes are characterized by their specific velocity functions, which depend on the total traffic density, resulting in a coupled hyperbolic system of conservation laws. The system is discretized using a Godunov-type finite volume scheme based on demand and supply functions, extended to handle complex junction coupling conditions -- such as merges and diverges -- and boundary conditions with buffer lengths to account for congestion spillback. The optimization of different travel-related performance metrics, including total travel time and total travel distance, is formulated as a constrained minimization problem and is accomplished through the use of an adjoint gradient approach, allowing for an efficient computation of sensitivities with respect to the chosen time-dependent control variables. Numerical simulations on a sample network demonstrate the efficiency of the proposed framework, particularly as the number of control parameters increases. This approach provides a robust and computationally efficient solution, making it suitable for large-scale traffic network optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00670 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Discrete adjoint gradient computation for multiclass traffic flow models on road networks Goatin, Paola Klar, Axel Mezquita-Nieto, Carmen Analysis of PDEs Optimization and Control This paper applies a discrete adjoint gradient computation method for a multi-class traffic flow model on road networks. Vehicle classes are characterized by their specific velocity functions, which depend on the total traffic density, resulting in a coupled hyperbolic system of conservation laws. The system is discretized using a Godunov-type finite volume scheme based on demand and supply functions, extended to handle complex junction coupling conditions -- such as merges and diverges -- and boundary conditions with buffer lengths to account for congestion spillback. The optimization of different travel-related performance metrics, including total travel time and total travel distance, is formulated as a constrained minimization problem and is accomplished through the use of an adjoint gradient approach, allowing for an efficient computation of sensitivities with respect to the chosen time-dependent control variables. Numerical simulations on a sample network demonstrate the efficiency of the proposed framework, particularly as the number of control parameters increases. This approach provides a robust and computationally efficient solution, making it suitable for large-scale traffic network optimization. |
| title | Discrete adjoint gradient computation for multiclass traffic flow models on road networks |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2604.00670 |