A Macroscopic Traffic Flow Model Accounting for Bounded Acceleration

Abstract

This paper details a new macroscopic traffic flow model accounting for the boundedness of traffic acceleration, which is required for physical realism. Our approach relies on the coupling between a scalar conservation law, which refers to the seminal LWR model, and a system of Ordinary Differential Equations describing the trajectories of accelerating vehicles, which we treat as moving constraints. We propose a Wave-Front Tracking Algorithm to construct approximate solutions. We use this algorithm to prove the existence of entropy weak solutions to the associated Cauchy Problem, and provide some numerical simulations illustrating the solution behaviour.

The Aw–Rascle Traffic Model: Enskog-Type Kinetic Derivation and Generalisations

“…For system (20), the Jacobian matrix is given in (21). The unknowns Q = (ρ, q) T are the same as before, but the fluxes are different:…”

“…[30]. Second order models allow one to overcome the issue of the unbounded acceleration of the vehicles, which first order models may suffer from, see [21] for a very recent contribution on this. However, they may fail to reproduce the correct anisotropy of the interactions among the vehicles, namely the fact that vehicles are mainly influenced by the dynamics ahead than by those behind them.…”

A LWR model with constraints at moving interfaces

“…In their framework, (𝑦 𝑖 ) 𝑖 represented the trajectories of autonomous vehicles, and the authors aimed at modeling the regulation impact on a few autonomous vehicles on the traffic flow. In the same framework but with different applications in mind, the model of [22] accounts for the boundedness of traffic acceleration. Note that in each of these models, the trajectories of the moving interfaces (𝑦 𝑖 ) 𝑖 were not given a priori, but rather obtained as solutions to an ODE involving the density of traffic, a mechanism reminiscent of [4,11,24] for instance.…”

“…In several of these works [17,22], the existence issue is tackled using the wave-front tracking procedure which is very sensitive to the details of the model. On the other hand, when numerical schemes are considered, see [8,12], the numerical analysis is usually left out.…”