Related papers: A Mixed ODE-PDE Model for Vehicular Traffic

This paper deals with the construction of a discontinuous Galerkin scheme for the solution of Lighthill-Whitham-Richards traffic flows on networks. The focus of the paper is the construction of two new numerical fluxes at junctions, which…

This paper proposes a imitation learning model for autonomous driving on highway traffic by mimicking human drivers' driving behaviours. The study utilizes the HighD traffic dataset, which is complex, high-dimensional, and diverse in…

The scientific field of traffic engineering encompasses a rich set of mathematical techniques, as well as researchers with entirely different backgrounds. This paper provides an overview of what is currently the state-of-the-art with…

Facing the congestion challenges of mixed road networks comprising expressways and arterial road networks, traditional control solutions fall short. To effectively alleviate traffic congestion in mixed road networks, it is crucial to clear…

We present simulations of congested traffic in circular and open systems with a non-local, gas-kinetic-based traffic model and a novel car-following model. The model parameters are all intuitive and can be easily calibrated. Micro- and…

We introduce a novel differentiable hybrid traffic simulator, which simulates traffic using a hybrid model of both macroscopic and microscopic models and can be directly integrated into a neural network for traffic control and flow…

This paper presents a simple technique of multifractal traffic modeling. It proposes a method of fitting model to a given traffic trace. A comparison of simulation results obtained for an exemplary trace, multifractal model and Markov…

Motivated by the need for accurate traffic flow prediction in transportation management, we propose a functional data method to analyze traffic flow patterns and predict future traffic flow. In this study we approach the problem by sampling…

In this work, a family of finite volume discretization schemes for LWR-type first order traffic flow models (with possible on- and off-ramps) is proposed: the Traffic Reaction Model (TRM). These schemes yield systems of ODEs that are…

We study phase transitions of a system of particles on the one-dimensional integer lattice moving with constant acceleration, with a collision law respecting slower particles. This simple deterministic ``particle-hopping'' traffic flow…

In this paper, we introduce and study one-dimensional models for the behavior of pedestrians in a narrow street or corridor. We begin at the microscopic level by formulating a stochastic cellular automata model with explicit rules for…

We review our analytical and numerical results obtained on the microscopic Follow-The-Leader (FTL) many particle approximation of one-dimensional conservation laws. More precisely, we introduce deterministic particle schemes for the Hughes…

Fundamental diagrams of vehicular traffic flow are generally multi-valued in the congested flow regime. We show that such set-valued fundamental diagrams can be constructed systematically from simple second order macroscopic traffic models,…

Dense human flow has been a concern for the safety of public events for a long time. Macroscopic pedestrian models, which are mainly based on fluid dynamics, are often used to simulate huge crowds due to their low computational costs.…

Despite the importance of urban traffic flows, there are only a few theoretical approaches to determine fundamental relationships between macroscopic traffic variables such as the traffic density, the utilization, the average velocity, and…

In this paper we propose two models describing the dynamics of heavy and light vehicles on a road network, taking into account the interactions between the two classes. The models are tailored for two-lane highways where heavy vehicles…

In this paper, we aim at developing new methods to join machine learning techniques and macroscopic differential models for vehicular traffic estimation and forecast. It is well known that data-driven and model-driven approaches have…

This paper presents a mesoscopic traffic flow model that explicitly describes the spatio-temporal evolution of the probability distributions of vehicle trajectories. The dynamics are represented by a sequence of factor graphs, which enable…

We study kinetic models for traffic flow characterized by the property of producing backward propagating waves. These waves may be identified with the phenomenon of stop-and-go waves typically observed on highways. In particular, a refined…

In traffic flow, self-organized wave propagation, which characterizes congestion, has been reproduced in macroscopic and microscopic models. Hydrodynamic models, a subset of macroscopic models, can be derived from microscopic-level…