Data

Three-Stream Model for Arterial Traffic

Bails, Constant
Hofleitner, Aude
Xuan, Yiguang
Bayen, Alexandre M.
2012

In this article, a new analytical traffic flow model is proposed for traffic dynamics at signalized intersections. During each cycle, both the arrival and the departure traffic are approximated by three distinct traffic streams with uniform density. Because of the similar representation of the arrival and the departure traffic, results from a single intersection can easily be extended to a series of intersections. With this model, the number of parameters of the model is tractable, leading to analytical solutions of the problem. It also is proved that the total delay of one-way...

Large-Scale Estimation of Arterial Traffic and Structural Analysis of Traffic Patterns from Probe Vehicles

Hofleitner, Aude
Herring, Ryan
Bayen, Alexandre
Han, Yufei
2012

Estimating and analyzing traffic conditions on large arterial networks is an inherently difficult task. The first goal of this article is to demonstrate how arterial traffic conditions can be estimated using sparsely sampled GPS probe vehicle data provided by a small percentage of vehicles. Traffic signals, stop signs, and other flow inhibitors make estimating arterial traffic conditions significantly more difficult than estimating highway traffic conditions. To address these challenges, a statistical modeling framework is proposed that leverages a large historical database and...

Probability Distributions of Travel Times on Arterial Networks: Traffic Flow and Horizontal Queuing Theory Approach

Hofleitner, Aude
Herring, Ryan
Bayen, Alexandre
2012

In arterial networks, traffic flow dynamics are driven by the presence of traffic signals, for which precise signal timing is difficult to obtain in arbitrary networks or might change over time. A comprehensive model of arterial traffic flow dynamics is necessary to capture its specific features in order to provide accurate traffic estimation approaches. From hydrodynamic theory, arterial traffic dynamics are modeled under specific assumptions standard in transportation engineering. This flow model is used to develop a statistical model of arterial traffic. The statistical approach...

Trade-offs Between Inductive Loops and GPS Probe Vehicles for Travel Time Estimation: Mobile Century Case Study

Mazaré, Pierre-Emmanuel
Tossavainen, Olli‐Pekka
Bayen, Alexandre M.
Work, Daniel B.
2012

This article addresses the trade-offs between (i) velocity data collected from GPS smartphones in probe vehicles, and (ii), velocity data obtained from inductive loop detectors, for the purpose of computing travel times on a stretch of roadway. It is a case study which uses experimental data collected on one day in the San Francisco Bay Area, obtained as part of a 2008 field experiment known as Mobile Century. Estimates of the traffic velocity field are constructed using a velocity model equivalent to the Cell Transmission Model, and a traffic state estimation algorithm known as...

Exponential Stability of Switched Linear Hyperbolic Initial-Boundary Value Problems

Amin, Saurabh
Hante, Falk M.
Bayen, Alexandre M.
2012

We consider the initial-boundary value problem governed by systems of linear hyperbolic partial differential equations in the canonical diagonal form and study conditions for exponential stability when the system discontinuously switches between a finite set of modes. The switching system is fairly general in that the system matrix functions as well as the boundary conditions may switch in time. We show how the stability mechanism developed for classical solutions of hyperbolic initial boundary value problems can be generalized to the case in which weaker solutions become necessary due to...

Reconstruction of Boundary Conditions from Internal Conditions Using Viability Theory

Hofleitner, A.
Claudel, C.
Bayen, A.
2012

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...

On Sequential Data Assimilation for Scalar Macroscopic Traffic Flow Models

Blandin, Sébastien
Couque, Adrien
Bayen, Alexandre
Work, Daniel
2012

We consider the problem of sequential data assimilation for transportation networks using optimal filtering with a scalar macroscopic traffic flow model. Properties of the distribution of the uncertainty on the true state related to the specific nonlinearity and non-differentiability inherent to macroscopic traffic flow models are investigated, derived analytically and analyzed. We show that nonlinear dynamics, by creating discontinuities in the traffic state, affect the performances of classical filters and in particular that the distribution of the uncertainty on the traffic state at...

Probabilistic Formulation of Estimation Problems for a class of Hamilton-Jacobi Equations

Hofleitner, Aude
Claudel, Christian G.
Bayen, Alexandre M.
2012

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...

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

Hofleitner, Aude
Herring, Ryan
Abbeel, Pieter
Bayen, Alexandre M.
2012

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...

Large Scale Estimation in Cyberphysical Systems using Streaming Data: a Case Study with Smartphone Traces

Hunter, Timothy
Das, Tathagata
Zaharia, Matei
Abbeel, Pieter
Bayen, Alexandre M.
2012

Controlling and analyzing cyberphysical and robotics systems is increasingly becoming a Big Data challenge. Pushing this data to, and processing in the cloud is more efficient than on-board processing. However, current cloud-based solutions are not suitable for the latency requirements of these applications. We present a new concept, Discretized Streams or D-Streams, that enables massively scalable computations on streaming data with latencies as short as a second. We experiment with an implementation of D-Streams on top of the Spark computing framework. We demonstrate the usefulness of...