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This paper proposes a new stochastic model of traffic dynamics in Lagrangian coordinates. The source of uncertainty is heterogeneity in driving behavior, captured using driver-specific speed-spacing relations, i.e., parametric uncertainty.…
The formation and development of oscillations is an important traffic flow phenomenon. Recent studies found that along a vehicle platoon described in the Lagrangian specification, traffic oscillations grow in a concave way. Since stationary…
The standard approach to densely reconstruct the motion in a volume of fluid is to inject high-contrast tracer particles and record their motion with multiple high-speed cameras. Almost all existing work processes the acquired multi-view…
We propose a statistical learning-based traffic speed estimation method that uses sparse vehicle trajectory information. Using a convolutional encoder-decoder based architecture, we show that a well trained neural network can learn…
This paper introduces two variational formulations for a model of robust optimal transport, that is, the problem of designing optimal transport networks that are resilient to potential damages, balancing construction costs against the…
In this paper we present a numerical study on control and observation of traffic flow using Lagrangian measurements and actuators. We investigate the effect of some basic control and observation schemes using probe and actuated vehicles…
Trajectory reconstruction is the process of inferring the path of a moving object between successive observations. In this paper, we propose a smoothing spline -- which we name the V-spline -- that incorporates position and velocity…
We propose a new velocity reconstruction method based on the displacement estimation by recently developed methods. The velocity is first reconstructed by transfer functions in Lagrangian space and then mapped into Eulerian space. High…
Lagrangian formulation of kinematic wave provides a more accurate representation than the most commonly used Eulerian formulation. Furthermore, Lagrangian representation offers a flexibility to study certain traffic phenomena (e.g. capacity…
The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion in complex flows. Their trajectories exhibit highly non-trivial statistical behavior, motivating the development of surrogate models…
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes…
Traffic flow forecasting is of great significance for improving the efficiency of transportation systems and preventing emergencies. Due to the highly non-linearity and intricate evolutionary patterns of short-term and long-term traffic…
This work presents new methods and algorithms for tracking the shape and trajectory of moving reflecting obstacles with broken rays, or rays reflecting at an obstacle. While in tomography the focus of the reconstruction method is to recover…
We present a stochastic method for reconstructing missing spatial and velocity data along the trajectories of small objects passively advected by turbulent flows with a wide range of temporal or spatial scales, such as small balloons in the…
Pedestrian trajectory prediction is a key technology in many applications such as video surveillance, social robot navigation, and autonomous driving, and significant progress has been made in this research topic. However, there remain two…
The rapid development of connected vehicle technology and the emergence of ride-hailing services have enabled the collection of a tremendous amount of probe vehicle trajectory data. Due to the large scale, the trajectory data have become a…
The shock response spectrum (SRS) is widely used to characterize the response of single-degree-of-freedom (SDOF) systems to transient accelerations. Because the mapping from acceleration time history to SRS is nonlinear and many-to-one,…
Vehicle movement is frequently captured in the form of GPS trajectories, i.e., sequences of timestamped GPS locations. Such data is widely used for various tasks such as travel-time estimation, trajectory recovery, and trajectory…
Addressing safe and efficient interaction between connected and automated vehicles (CAVs) and human-driven vehicles in a mixed-traffic environment has attracted considerable attention. In this paper, we develop a framework for stochastic…
Predicting particle transport in complex flows is traditionally achieved by solving the Navier-Stokes equations. While various numerical and experimental methods exist, they typically require deep physical insights and incur high…