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

TL;DR

This paper introduces the Traffic Reaction Model (TRM), a finite volume discretization scheme for traffic flow that links kinetic systems with chemical reaction networks, providing new insights into traffic dynamics and stability.

Contribution

The paper presents a novel finite volume scheme for traffic modeling that connects kinetic theory with chemical reaction networks, including stability analysis and extensions to networks.

Findings

TRM is nonnegative, conservative, and capacity-preserving.

The scheme relates to traditional traffic models like Godunov and CTM.

Kinetic theory provides stability insights for TRM.

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.