Citation

Pereira M, Kulcsár B, Lipták G, Kovacs M, Szederkényi G. Transp. Res. C Emerg. Technol. 2024; 158: e104435.

Copyright

(Copyright © 2024, Elsevier Publishing)

DOI

10.1016/j.trc.2023.104435

PMID

unavailable

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.

Language: en

Keywords

Chemical reaction network; Flow modeling; Persistence; Stability; Traffic flow modeling and control