The Annals of Applied Statistics

Bayesian analysis of traffic flow on interstate I-55: The LWR model

Nicholas Polson and Vadim Sokolov

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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.

Article information

Source
Ann. Appl. Stat. Volume 9, Number 4 (2015), 1864-1888.

Dates
Received: February 2015
Revised: September 2015
First available in Project Euclid: 28 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1453993096

Digital Object Identifier
doi:10.1214/15-AOAS853

Mathematical Reviews number (MathSciNet)
MR3456356

Zentralblatt MATH identifier
06560812

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

Citation

Polson, Nicholas; Sokolov, Vadim. Bayesian analysis of traffic flow on interstate I-55: The LWR model. Ann. Appl. Stat. 9 (2015), no. 4, 1864--1888. doi:10.1214/15-AOAS853. https://projecteuclid.org/euclid.aoas/1453993096


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