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arXiv · 2101.10190

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

M. Pereira·B. Kulcsár·Gy. Lipták·M. Kovács·G. Szederkényi
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Abstract

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.

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M. Pereira, B. Kulcsár, Gy. Lipták, M. Kovács, G. Szederkényi. 2021-01-25. The Traffic Reaction Model: A kinetic compartmental approach to road traffic modeling. https://doi.org/10.1016/j.trc.2023.104435

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