Related papers: A nonlocal Lagrangian traffic flow model and the z…
This paper studies the continuous-time dynamics generated by control-theoretic Lagrangian methods for equality-constrained optimization. In particular, we consider dynamics induced by proportional-integral and feedback linearization…
In this article, we investigate theoretical and numerical properties of the first-order Lighthill-Whitham-Richards (LWR) traffic flow model with time delay. Since standard results from the literature are not directly applicable to the…
Traffic breakdown, as one of the most puzzling traffic flow phenomena, is characterized by sharply decreasing speed, abruptly increasing density and in particular suddenly plummeting capacity. In order to clarify its root mechanisms and…
This study addresses multilane vehicular traffic modelling, focusing on the transition between microscopic (individual vehicle-based) to macroscopic (aggregate flow-based) descriptions. While previous research on multilane traffic has…
We present a traffic model that extends the linear car-following model as well as the min-plus traffic model (a model based on the min-plus algebra). A discrete-time car-dynamics describing the traffic on a 1-lane road without passing is…
Recently different formulations of the first-order Lighthill-Whitham-Richards (LWR) model have been identified in different coordinates and state variables. However, there exists no systematic method to convert higher-order continuum models…
In this work, we propose an alternative stochastic model for the fundamental diagram of traffic flow with minimal number of parameters. Our approach is based on a mesoscopic viewpoint of the traffic system in terms of the dynamics of…
This paper offers an integrative data-driven physics-inspired approach to model and control traffic congestion in a resilient and efficient manner. While existing physics-based approaches commonly assign density and flow traffic states by…
Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…
In this paper we study a local and a non-local regularization of the system of nonlinear elastodynamics with a non-convex energy. We show that solutions of the non-local model converge to those of the local model in a certain regime. The…
The basic properties of traffic flow are analyzed using a simple deterministic one dimensional "car following model" with continuous variables based on a model introduced by Nagel and Herrmann [Physica A 199 254--269 (1993)] including a few…
In these lecture notes, we provide an introduction to the theory of mixing for incompressible flows from a PDE perspective. We discuss both the Lagrangian (ODE) and Eulerian (PDE, continuity equation) viewpoints, and introduce suitable…
This article investigates the use of a model-based neural-network for the traffic reconstruction problem using noisy measurements coming from probe vehicles. The traffic state is assumed to be the density only, modeled by a partial…
We provide a new existence result for weak solutions to the one-dimensional Euler equations with a maximal density constraint, corresponding to a unilateral constraint on the density. Such models arise in the description of congestion…
The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density…
In this note, we introduce some models of pedestrian traffic and prove existence and uniqueness for these models.
Geophysical flows are typically composed of wave and mean motions with a wide range of overlapping temporal scales, making separation between the two types of motion in wave-resolving numerical simulations challenging. Lagrangian filtering…
Traffic congestion has long been an ubiquitous problem that is exacerbating with the rapid growth of megacities. In this proof-of-concept work we study intrinsic motivation, implemented via the empowerment principle, to control autonomous…
Modeling how network-level traffic flow changes in the urban environment is useful for decision-making in transportation, public safety and urban planning. The traffic flow system can be viewed as a dynamic process that transits between…
Traffic on a circular road is described by dynamic programming equations associated to optimal control problems. By solving the equations analytically, we derive the relation between the average car density and the average car flow, known…