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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2101.10190 |
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| _version_ | 1866909059166240768 |
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| author | Pereira, M. Kulcsár, B. Lipták, Gy. Kovács, M. Szederkényi, G. |
| author_facet | Pereira, M. Kulcsár, B. Lipták, Gy. Kovács, M. Szederkényi, G. |
| contents | In this work, a family of finite volume discretization schemes for LWR-type first order traffic flow models (with possible on- and off-ramps) is proposed: the Traffic Reaction Model (TRM). These schemes yield systems of ODEs that are formally equivalent to the kinetic systems used to model chemical reaction networks. An in-depth numerical analysis of the TRM is performed. On the one hand, the analytical properties of the scheme (nonnegative, conservative, capacity-preserving, monotone) and its relation to more traditional schemes for traffic flow models (Godunov, CTM) are presented. Finally, the link between the TRM and kinetic systems is exploited to offer a novel compartmental interpretation of traffic models. In particular, kinetic theory is used to derive dynamical properties (namely persistence and Lyapunov stability) of the TRM for a specific road configuration. Two extensions of the proposed model, to networks and changing driving conditions, are also described. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_10190 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Traffic Reaction Model: A kinetic compartmental approach to road traffic modeling Pereira, M. Kulcsár, B. Lipták, Gy. Kovács, M. Szederkényi, G. Numerical Analysis Systems and Control In this work, a family of finite volume discretization schemes for LWR-type first order traffic flow models (with possible on- and off-ramps) is proposed: the Traffic Reaction Model (TRM). These schemes yield systems of ODEs that are formally equivalent to the kinetic systems used to model chemical reaction networks. An in-depth numerical analysis of the TRM is performed. On the one hand, the analytical properties of the scheme (nonnegative, conservative, capacity-preserving, monotone) and its relation to more traditional schemes for traffic flow models (Godunov, CTM) are presented. Finally, the link between the TRM and kinetic systems is exploited to offer a novel compartmental interpretation of traffic models. In particular, kinetic theory is used to derive dynamical properties (namely persistence and Lyapunov stability) of the TRM for a specific road configuration. Two extensions of the proposed model, to networks and changing driving conditions, are also described. |
| title | The Traffic Reaction Model: A kinetic compartmental approach to road traffic modeling |
| topic | Numerical Analysis Systems and Control |
| url | https://arxiv.org/abs/2101.10190 |