Related papers: Comparing comparisons between vehicular traffic st…
The aim of this work is to introduce a two-dimensional macroscopic traffic model for multiple populations of vehicles. Starting from the paper [20], where a two-dimensional model for a single class of vehicles is proposed, we extend the…
In this paper we investigate the sensitivity of the LWR model on network to its parameters and to the network itself. The quantification of sensitivity is obtained by measuring the Wasserstein distance between two LWR solutions…
We study transport distances on metric graphs representing gas networks. Starting from the dynamic formulation of the Wasserstein distance, we review extensions to networks, with and without the possibility of storing mass on the vertices.…
This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…
The paper presents a systematic derivation of macroscopic equations for freeway traffic flow from an Enskog-like kinetic approach. The resulting fluid-dynamic traffic equations for the spatial density, average velocity, and velocity…
This contribution compares several different approaches allowing one to derive macroscopic traffic equation directly from microscopic car-following models. While it is shown that some conventional approaches lead to theoretical problems, it…
Leveraging the Wasserstein distance -- a summation of sample-wise transport distances in data space -- is advantageous in many applications for measuring support differences between two underlying density functions. However, when supports…
The macroscopic fundamental diagram (MFD) is a large scale description of the traffic in a urban area and relates the average car flow to the average car density. This MFD has been observed empirically in several cities but how its…
We develop a discrete Boltzmann-type model that uses dynamics in phase space to describe the behavior of traffic flows. Firstly, we model the traffic flow at mesoscopic scale using dynamics in phase space, which is considered as an…
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…
Starting from the instability diagram of a traffic flow model, we derive conditions for the occurrence of congested traffic states, their appearance, their spreading in space and time, and the related increase in travel times. We discuss…
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…
Traffic safety at intersections is studied quantitatively using methods from Statistical Mechanics on the basis of simple microscopic traffic flow models. In order to determine a relationship between traffic flow and the number of crashes,…
In this paper, a particle method is used to approximate the solutions of a "fluid-like" macroscopic traffic flow model for automated vehicles. It is shown that this method preserves certain differential inequalities that hold for the…
As a typical self-driven many-particle system far from equilibrium, traffic flow exhibits diverse fascinating non-equilibrium phenomena, most of which are closely related to traffic flow stability and specifically the growth/dissipation…
It is understood that congestion in traffic can be interpreted in terms of the instability of the equation of dynamic motion. The evolution of a traffic system from an unstable or metastable state to a globally stable state bears a strong…
We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics…
Due to the complexity of the traffic flow dynamics in urban road networks, most quantitative descriptions of city traffic so far are based on computer simulations. This contribution pursues a macroscopic (fluid-dynamic) simulation approach,…
A microscopic criterion for distinguishing synchronized flow and wide moving jam phases in single vehicle data measured at a single freeway location is presented. Empirical local congested traffic states in single vehicle data measured on…
The rapid urbanization and increasing traffic have serious social, economic, and environmental impact on metropolitan areas worldwide. It is of a great importance to understand the complex interplay of road networks and traffic conditions.…