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.
Highlights Link between traffic flow dynamics and the kinetics of chemical reaction networks. Use of kinetic theory to show persistence and stability of the dynamics. Numerical analysis and error analysis of the scheme.
The Traffic Reaction Model: A kinetic compartmental approach to road traffic modeling
2023-11-20
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
SELF SUSTAINING TRAFFIC MANAGEMENT SYSTEM AND ITS COMPARTMENTAL MODELING
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