Stability analysis of a hyperbolic stochastic Galerkin formulation for the Aw-Rascle-Zhang model with relaxation

Abstract

We investigate the propagation of uncertainties in the Aw-Rascle-Zhang model, which belongs to a class of second order traffic flow models described by a system of nonlinear hyperbolic equations. The stochastic quantities are expanded in terms of wavelet-based series expansions. Then, they are projected to obtain a deterministic system for the coefficients in the truncated series. Stochastic Galerkin formulations are presented in conservative form and for smooth solutions also in the corresponding non-conservative form. This allows to obtain stabilization results, when the system is relaxed to a first-order model. Computational tests illustrate the theoretical results.

Data-driven uncertainty quantification in macroscopic traffic flow models

“…Also, data information can be leveraged to improve existing models or design new ones, as proposed by [14,16,17,18,28,40]. Nevertheless, up to our knowledge few works have been devoted to evaluate the inherent uncertainty of both models and data and its impact on model-based predictions [3,21,29]. Yet, this is a fundamental aspect to improve decision and control strategies based on mathematical models.…”

Stochastic Finite Volume Method for Uncertainty Quantification of Transient Flow in Gas Pipeline Networks

“…The application of uncertainty quantification to hyperbolic conservation laws on graphs has found compelling motivation from the need to model and control vehicle traffic [16] and gas pipeline flows [17]. These recent studies relied on tailored polynomial chaos expansions and the stochastic Galerkin method for forward simulation of the stochastic PDEs subject to distributional uncertainty in initial conditions and parameters [18], and primarily examined the problem of stabilization.…”