@article{ref1,
title="The Traffic Reaction Model: a kinetic compartmental approach to road traffic modeling",
journal="Transportation research part C: emerging technologies",
year="2024",
author="Pereira, M. and Kulcsár, B. and Lipták, Gy. and Kovacs, M. and Szederkényi, G.",
volume="158",
number="",
pages="e104435-e104435",
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.<p /> <p>Language: en</p>",
language="en",
issn="0968-090X",
doi="10.1016/j.trc.2023.104435",
url="http://dx.doi.org/10.1016/j.trc.2023.104435"
}