Data-driven uncertainty quantification in macroscopic traffic flow models

Abstract

We propose a Bayesian approach for parameter uncertainty quantification in macroscopic traffic flow models from cross-sectional data. A bias term is introduced and modeled as a Gaussian process to account for the traffic flow models limitations. We validate the results comparing the error metrics of both first and second order models, showing that second order models globally perform better in reconstructing traffic quantities of interest.

A Linearizing Transformation-Based Evaluation Approach of the Fundamental Diagram

“…The WLSM is a more suitable fitting method because of the reduced sample selection bias ( 14 ). In Figure 4 b , the FDs FD_a and FD_d obtained by the LSM and the WLSM of the Underwood model are presented.…”

“…Since it is important to accurately describe the functional relationship among traffic flow parameters, many FD models have been proposed, such as single-regime models (e.g., by Greenshields et al [ 4 ], Underwood [ 5 ], Gazis et al [ 6 ], Drake et al [ 7 ], Franklin [ 8 ], and Newell [ 9 ]), multi-regime models (e.g., by Daganzo [ 10 ] and Smulders [ 11 ]), and stochastic models considering the heterogeneity of drivers (e.g., Jabari et al [ 12 ], Bai et al [ 13 ], and Würth et al [ 14 ]). Recently, Bramich et al ( 15 ) also proposed a general framework for modeling any observed flow–density–speed relationship.…”

The initial boundary value problem for second order traffic flow models with vacuum: Existence of entropy weak solutions

“…In traffic flow applications (see e.g. [39]), it is natural to consider the Initial Boundary Value Problem (IBVP) for (1.1) on a bounded interval ]x in , x out [ ⊂ R, namely…”

Validation of Calibration Strategies for Macroscopic Traffic Flow Models on Synthetic Data

“…However, data noise and congested traffic situations make the parameter identification process difficult to deal with (see e.g. [3]). In this paper, we consider the following alternative approaches.…”