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

TL;DR

This paper introduces a Bayesian particle filtering approach to real-time traffic density estimation and parameter learning for the LWR model, enabling accurate, uncertainty-aware traffic flow analysis on I-55 during incidents.

Contribution

It develops a novel real-time Bayesian learning algorithm for updating traffic model parameters and density estimates, improving upon fixed-parameter methods.

Findings

Accurately estimates current traffic density during shock waves.

Quantifies uncertainty in traffic state estimates.

Detects capacity drops due to accidents in real-time.

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.