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December 2015 Bayesian analysis of traffic flow on interstate I-55: The LWR model
Nicholas Polson, Vadim Sokolov
Ann. Appl. Stat. 9(4): 1864-1888 (December 2015). DOI: 10.1214/15-AOAS853

Abstract

Transportation departments take actions to manage traffic flow and reduce travel times based on estimated current and projected traffic conditions. Travel time estimates and forecasts require information on traffic density which are combined with a model to project traffic flow such as the Lighthill–Whitham–Richards (LWR) model. We develop a particle filtering and learning algorithm to estimate the current traffic density state and the LWR parameters. These inputs are related to the so-called fundamental diagram, which describes the relationship between traffic flow and density. We build on existing methodology by allowing real-time updating of the posterior uncertainty for the critical density and capacity parameters. Our methodology is applied to traffic flow data from interstate highway I-55 in Chicago. We provide a real-time data analysis of how to learn the drop in capacity as a result of a major traffic accident. Our algorithm allows us to accurately assess the uncertainty of the current traffic state at shock waves, where the uncertainty is a mixture distribution. We show that Bayesian learning can correct the estimation bias that is present in the model with fixed parameters.

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Nicholas Polson. Vadim Sokolov. "Bayesian analysis of traffic flow on interstate I-55: The LWR model." Ann. Appl. Stat. 9 (4) 1864 - 1888, December 2015. https://doi.org/10.1214/15-AOAS853

Information

Received: 1 February 2015; Revised: 1 September 2015; Published: December 2015
First available in Project Euclid: 28 January 2016

zbMATH: 06560812
MathSciNet: MR3456356
Digital Object Identifier: 10.1214/15-AOAS853

Keywords: Bayesian posterioor , intelligent transportation system , LWR model , particle filtering , traffic flow , traffic prediction

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.9 • No. 4 • December 2015
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