Traffic Theory

A Class of Perturbed Cell-Transmission Models to Account for Traffic Variability

Blandin, Sébastien
Work, Daniel
Goatin, Paola
Piccoli, Benedetto
Bayen, Alexandre M.
2010

We introduce a general class of traffic models derived as perturbations of cell-transmission type models. These models use different dynamics in free-flow and in congestion phases. They can be viewed as extensions to cell transmission type models by considering the velocity to be a function not only of the density but also of a second state variable describing perturbations. We present the models in their discretized form under a new formulation similar to the classical supply demand formulation used by the seminal Cell-Transmission Model. We then show their equivalence to hydrodynamic...

A Traffic Model for Velocity Data Assimilation

Work, Daniel B.
Blandin, Sébastien
Tossavainen, Olli‐Pekka
Piccoli, Benedetto
Bayen, Alexandre M.
2010

This article is motivated by the practical problem of highway traffic estimation using velocity measurements from GPS enabled mobile devices such as cell phones. In order to simplify the estimation procedure, a velocity model for highway traffic is constructed, which results in a dynamical system in which the observation operator is linear. This article presents a new scalar hyperbolic partial differential equation (PDE) model for traffic velocity evolution on highways, based on the seminal Lighthill-Whitham-Richards (LWR) PDE for density. Equivalence of the solution of the new velocity...

Incorporation of Lagrangian Measurements in Freeway Traffic State Estimation

Herrera, Juan C.
Bayen, Alexandre M.
2010

Cell-phones equipped with a global positioning system (GPS) provide new opportunities for location-based services and traffic estimation. When traveling on-board vehicles, these phones can be used to accurately provide position and velocity of the vehicle as probe traffic sensors. This article presents a new technique to incorporate mobile probe measurements into highway traffic flow models, and compares it to a Kalman filtering approach. These two techniques are both used to reconstruct traffic density. The first technique modifies the Lighthill–Whitham–Richards partial differential...

Mobile Millenium Stockholm

Allström, Andreas
Archer, Jeffery
Bayen, Alexandre M.
Blandin, Sébastien
2011

The need for accurate real time traffic information is growing in almost all big cities around the world. One of these cities is Stockholm, recently named as the fifth most congested city in Western Europe. The Mobile Millennium Stockholm project was initiated by the Swedish Transport Administration in order to address the need for a useful and timely traffic information system. The purpose of the project is to assimilate the knowledge gained from the Mobile Millennium project at University of California, Berkeley and develop new methods for data fusion, one of the most challenging...

A Dual Decomposition Method for Sector Capacity Constrained Traffic Flow Optimization

Sun, Dengfeng
Clinet, Alexis
Bayen, Alexandre M.
2011

An aggregate air traffic flow model based on a multicommodity network is used for traffic flow management in the National Airspace System. The problem of minimizing the total travel time of flights in the National Airspace System of the United States, subject to sector capacity constraints, is formulated as an Integer Program. The resulting solution achieves optimal delay control. The Integer Program implemented for the scenarios investigated has billions of variables and constraints. It is relaxed to a Linear Program for computational efficiency. A dual decomposition method is...

A General Phase Transition Model for Vehicular Traffic

Blandin, S.
Work, D.
Goatin, P.
Piccoli, B.
Bayen, A.
2011

This paper provides a mathematical model of the phenomenon of phase transitions in traffic flow. The model consists of a scalar conservation law coupled with a 2 × 2 system of conservation laws. The coupling is achieved via a free boundary, where the phase transition takes place. For this model, the Riemann problem is stated and globally solved. The Cauchy problem is proved to admit a solution defined globally in time without any assumption about the smallness of the initial data or the number of phase boundaries. Qualitative properties of real traffic flow are shown to agree with...

A Tractable Class of Algorithms for Reliable Routing in Stochastic Networks

Samaranayake, S.
Blandin, S.
Bayen, A.
2012

The goal of this article is to provide the theoretical basis for enabling tractable solutions to the “arriving on time” problem and enabling its use in real-time mobile phone applications. Optimal routing in transportation networks with highly varying traffic conditions is a challenging problem due to the stochastic nature of travel-times on links of the network. The definition of optimality criteria and the design of solution methods must account for the random nature of the travel-time on each link. Most common routing algorithms consider the expected value of link travel-time as a...

Mobile Millennium: GPS Mobile Phones as Traffic Probes, California Networked Traveler - Safe Trip 21 Phase II

Bayen, Alexander M.
2011

Recent advances in mobile devices and internet technology have led the California Department of Transportation (Caltrans) to investigate a data collection solution that offers improved data reliability and availability at a significantly lower cost. It has been postulated that information from GPS cell phones could provide position and speed data -- referred to as probe data -- for highways and arterials in near real time over much of the transportation network. The Mobile Millennium project was established to determine if the collection and use of probe data for traveler information...

An Adaptive Routing System for Location-Aware Mobile Devices on the Road Network

Borokhov, Paul
Blandin, Sébastien
Samaranayake, Samitha
Goldschmidt, Olivier
Bayen, Alexandre M.
2011

As congestion problems become a greater concern and negatively impact society, solutions which alleviate them are needed to improve the performance of the transportation system. Routing systems which take into account the travel-time experienced by the driver have been largely unexplored in the domain of adaptive routing. In this article, we present a system which enables users of smartphones to obtain directions generated using an algorithm which provides an optimal routing policy for reliable on-time arrival; that is, directions which seek to maximize the probability of arriving to the...

Optimal Decomposition of Travel Times Measured by Probe Vehicles Using a Statistical Traffic Flow Model

Hofleitner, A.
Bayen, A.
2011

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...