Aude Hofleitner

Learning the Dynamics of Arterial Traffic From Probe Data Using a Dynamic Bayesian Network

Estimating and predicting traffic conditions in arterial networks using probe data has proven to be a substantial challenge. Sparse probe data represent the vast majority of the data available on arterial roads. This paper proposes a probabilistic modeling framework for estimating and predicting arterial travel-time distributions using sparsely observed probe vehicles. We introduce a model based on hydrodynamic traffic theory to learn the density of vehicles on arterial road segments, illustrating the distribution of delay within a road segment. The characterization of this distribution is essentially to use probe vehicles for traffic estimation: Probe vehicles report their location at random locations, and the travel times between location reports must be properly scaled to match the map discretization. A dynamic Bayesian network represents the spatiotemporal dependence on the network and provides a flexible framework to learn traffic dynamics from historical data and to perform real-time estimation with streaming data. The model is evaluated using data from a fleet of 500 probe vehicles in San Francisco, CA, which send Global Positioning System (GPS) data to our server every minute. The numerical experiments analyze the learning and estimation capabilities on a subnetwork with more than 800 links. The sampling rate of the probe vehicles does not provide detailed information about the location where vehicles encountered delay or the reason for any delay (i.e., signal delay, congestion delay, etc.). The model provides an increase in estimation accuracy of 35% when compared with a baseline approach to process probe-vehicle data.

Estimating arterial traffic conditions using sparse probe data

Estimating and predicting traffic conditions in arterial networks using probe data has proven to be a substantial challenge. In the United States, sparse probe data represents the vast majority of the data available on arterial roads in most major urban environments. This article proposes a probabilistic modeling framework for estimating and predicting arterial travel time distributions using sparsely observed probe vehicles. We evaluate our model using data from a fleet of 500 taxis in San Francisco, CA, which send GPS data to our server every minute. The sampling rate does not provide detailed information about where vehicles encountered delay or the reason for any delay (i.e. signal delay, congestion delay, etc.). Our model provides an increase in estimation accuracy of 35% when compared to a baseline approach for processing probe vehicle data.

Optimal decomposition of travel times measured by probe vehicles using a statistical traffic flow model

Sparse location measurements of probe vehicles are a promising data source for arterial traffic monitoring. One common challenge in processing this source of data is that vehicles are sampled infrequently (on the order of once per minute), which means that many vehicles will travel several links of the network between consecutive measurements. In this article, we propose an optimal decomposition of path travel times of probe vehicles to link travel times for each link traversed. From a model of arterial traffic dynamics, we derive probability distributions of travel times. We prove that these distributions are mixtures of log-concave distributions and derive convex formulations of the travel time allocation problem. We validate our approach using detailed video camera data from the Next Generation Simulation project (NGSIM).

Online Homotopy Algorithm for a Generalization of the LASSO

The LASSO is a widely used shrinkage method for linear regression. We propose an online homotopy algorithm to solve a generalization of the LASSO in which the l1 regularization is applied on a linear transformation of the solution, allowing to input prior information on the structure of the problem and to improve interpretability of the results. The algorithm takes advantage of the sparsity of the solution for computational efficiency and is promising for mining large datasets.

Online least-squares estimation of time varying systems with sparse temporal evolution and application to traffic estimation

Using least-squares with an l1-norm penalty is well-known to encourage sparse solutions. In this article, we propose an algorithm that performs online least-squares estimation of a time varying system with a l1-norm penalty on the variations of the state estimate, leading to state estimates that exhibit few “jumps” over time. The algorithm analytically computes a path to update the state estimate as a new observation becomes available. The algorithm performs computationally efficient and numerically robust state estimation for time varying systems in which the dynamics are slow compared to the sampling rate. We use the algorithm for arterial traffic estimation with streaming probe vehicle data provided by the Mobile Millennium system and show a significant improvement in the estimation capabilities compared to a baseline model of traffic estimation. The estimation framework filters out the inherent noise of traffic dynamics and improves the interpretability and accuracy of the results. Results from an implementation in San Francisco on a network of more than 800 links using a fleet of 500 taxis sending their location every minute illustrate the possibility to use the algorithm to solve important practical estimation problems.

Automatic inference of map attributes from mobile data

The development and update of reliable Geographic Information Systems (GIS) greatly benefits Intelligent Transportation Systems developments including real-time traffic management platforms and assisted driving technologies. The collection and processing of the data required for the development and update of GIS is a long and expensive process which is prone to errors and inaccuracies, making its automation promising. The article introduces a method which leverages the emergence of sparsely sampled probe vehicle data to update and improve existing GIS. We present an unsupervised classification algorithm which discriminates between signalized road segments (as having a signal at the downstream intersection) and non-signalized road segments. This algorithm uses a statistical model of the probability distribution of vehicle location within a link, derived from hydrodynamic traffic flow theory. The decision of whether the link has a traffic signal or not is taken according to model selection criteria. Numerical results performed with sparsely sampled probe data collected by the Mobile Millennium system in the Bay Area of San Francisco, CA underline the importance of the problem addressed by the article to improve the accuracy and update signal information of GIS. They showcase the ability of the method to detect the presence of traffic signals automatically.

Reconstruction of boundary conditions from internal conditions using viability theory

This article presents a method for reconstructing downstream boundary conditions to a HamiltonJacobi partial differential equation for which initial and upstream boundary conditions are prescribed as piecewise affine functions and an internal condition is prescribed as an affine function. Based on viability theory, we reconstruct the downstream boundary condition such that the solution of the Hamilton-Jacobi equation with the prescribed initial and upstream conditions and reconstructed downstream boundary condition satisfies the internal value condition. This work has important applications for estimation in flow networks with unknown capacity reductions. It is applied to urban traffic, to reconstruct signal timings and temporary capacity reductions at intersections, using Lagrangian sensing such as GPS devices onboard vehicles.

Probabilistic formulation of estimation problems for a class of Hamilton-Jacobi equations

This article presents a method for deriving the probability distribution of the solution to a Hamilton-Jacobi partial differential equation for which the value conditions are random. The derivations lead to analytical or semi-analytical expressions of the probability distribution function at any point in the domain in which the solution is defined. The characterization of the distribution of the solution at any point is a first step towards the estimation of the parameters defining the random value conditions. This work has important applications for estimation in flow networks in which value conditions are noisy. In particular, we illustrate our derivations on a road segment with random capacity reductions.