Related papers: Representation of a vehicular traffic model using …
This article deals with the observation problem in traffic flow theory. The model used is the semilinear viscous Burgers equation. Instead of using the traditional fixed sensors to estimate the state of the traffic at given points, the…
Simple physical models based on fluid mechanics have long been used to understand the flow of vehicular traffic on freeways; analytically tractable models of flow on an urban grid, however, have not been as extensively explored. In an ideal…
A fundamental challenge in car-following modeling lies in accurately representing the multi-scale complexity of driving behaviors, particularly the intra-driver heterogeneity where a single driver's actions fluctuate dynamically under…
In this paper we study a model for traffic flow on networks based on a hyperbolic system of conservation laws with discontinuous flux. Each equation describes the density evolution of vehicles having a common path along the network. In this…
Floating car data of car-following behavior in cities were compared to existing microsimulation models, after their parameters had been calibrated to the experimental data. With these parameter values, additional simulations have been…
Smart cities are revolutionizing the transportation infrastructure by the integration of technology. However, ensuring that various transportation system components are operating as expected and in a safe manner is a great challenge. In…
The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…
Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport. These features arise across a wide range of domains, including physical, engineered,…
We investigate the automatic differentiation of hybrid models, viz. models that may contain delays, logical tests and discontinuities or loops. We consider differentiation with respect to parameters, initial conditions or the time. We…
In recent years statistical physicists have developed {\it discrete} "particle-hopping" models of vehicular traffic, usually formulated in terms of {\it cellular automata}, which are similar to the microscopic models of interacting charged…
We formally verify a hybrid control law designed to perform a station keeping maneuver for a planar vehicle. Such maneuver requires that the vehicle reaches a neighborhood of its station in finite time and remains in it while waiting for…
In this paper we propose a Godunov-based discretization of a hyperbolic system of conservation laws with discontinuous flux, modeling vehicular flow on a network. Each equation describes the density evolution of vehicles having a common…
We introduce a formalism to deal with the microscopic modeling of vehicular traffic on a road network. Traffic on each road is uni-directional, and the dynamics of each vehicle is described by a Follow-the-Leader model. From a mathematical…
The rapid development of autonomous vehicles (AVs) holds vast potential for transportation systems through improved safety, efficiency, and access to mobility. However, the progression of these impacts, as AVs are adopted, is not well…
Diffusion models have made substantial progress in facilitating image generation and editing. As the technology matures, we see its potential in the context of driving simulations to enhance the simulated experience. In this paper, we…
Already today, driver assistance systems help to make daily traffic more comfortable and safer. However, there are still situations that are quite rare but are hard to handle at the same time. In order to cope with these situations and to…
Starting from a non-local version of the Prigogine-Herman traffic model, we derive a natural hierarchy of kinetic discrete velocity models for traffic flow consisting of systems of quasi-linear hyperbolic equations with relaxation terms.…
Safety-critical traffic scenarios are integral to the development and validation of autonomous driving systems. These scenarios provide crucial insights into vehicle responses under high-risk conditions rarely encountered in real-world…
A two-lane extension of a recently proposed cellular automaton model for traffic flow is discussed. The analysis focuses on the reproduction of the lane usage inversion and the density dependence of the number of lane changes. It is shown…