2014/09/30 by Nicholas Polson, Vadim Sokolov
Engineering · Mathematics · #Bayes' theorem #Bayesian inference #Bayesian probability #Flow (mathematics) #Intelligent transportation system #State (computer science) #Tensor decomposition and applications #Traffic Prediction and Management Techniques #Traffic control and management #Traffic count #Traffic flow (computer networking) #Traffic generation model #stat.AP
paper · pdf · doi:10.1214/15-aoas853
published as Annals of Applied Statistics 2015, Vol. 9, No. 4, 1864-1888 · Published at http://dx.doi.org/10.1214/15-AOAS853 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2015/12/01 · arxiv created 2016/01/29 · arxiv updated 2016/02/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.