The Traffic Reaction Model: A kinetic compartmental approach to road traffic modeling

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...

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Bibliographic Details
Published in:arXiv.org 2024-01
Main Authors: Pereira, M, Kulcsár, B, Gy Lipták, Kovács, M, Szederkényi, G
Format: Article
Language:English
Subjects:
Conservation laws
Control systems design
Discretization
Empirical analysis
Graphical representations
Nonlinear differential equations
Nonlinear equations
Partial differential equations
Polynomials
Ramps
Stability analysis
Traffic flow
Traffic models
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2101.10190