Related papers: Reaction-Diffusion Models describing a Two-Lane Tr…
We calculate the distribution of the distance headways (i.e., the instantaneous gap between successive vehicles) as well as the distribution of instantaneous distance between successive jams in the Nagel-Schreckenberg (NS) model of…
We investigate a cellular automaton (CA) model of traffic on a bi-directional two-lane road. Our model is an extension of the one-lane CA model of {Nagel and Schreckenberg 1992}, modified to account for interactions mediated by passing, and…
Based on the Nagel-Schreckenberg (NS) model with periodic boundary conditions, a modified model considered overtaking strategy (NSOS) has been proposed \cite{su2016occurrence,su2016the}. In this paper, we focus on the theoretical analysis…
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…
The Nagel-Schreckenberg traffic flow model shows a transition from a free flow regime to a jammed regime for increasing car density. The measurement of the dynamical structure factor offers the chance to observe the evolution of jams…
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…
We extend the Aw-Rascle macroscopic model of car traffic into a two-way multi-lane model of pedestrian traffic. Within this model, we propose a technique for the handling of the congestion constraint, i.e. the fact that the pedestrian…
In this work, we derive first order continuum traffic flow models from a microscopic delayed follow-the-leader model. Those are applicable in the context of vehicular traffic flow as well as pedestrian traffic flow. The microscopic model is…
Within the Nagel-Schreckenberg traffic flow model we consider the transition from the free flow regime to the jammed regime. We introduce a method of analyzing the data which is based on the local density distribution. This analyzes allows…
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…
Although traffic simulations with cellular-automata models give meaningful results compared with empirical data, highway traffic requires a more detailed description of the elementary dynamics. Based on recent empirical results we present a…
Based on experimental traffic data obtained from German and US highways, we propose a novel two-dimensional first-order macroscopic traffic flow model. The goal is to reproduce a detailed description of traffic dynamics for the real road…
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…
We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of…
In the Nagel-Schreckenberg model of vehicular traffic on single-lane highways vehicles are modelled as particles which hop forward from one site to another on a one dimensional lattice and the inter-particle interactions mimic the manner in…
We propose a model describing the traffic flow on a road with variable widths in this paper. The model, which is modified the Aw-Rascle model, is not conservative because of the source term. We obtain the elementary waves of the new traffic…
In [7], Berthelin, Degond, Delitala and Rascle introduced a traffic flow model describing the formation and the dynamics of traffic jams. This model consists of a Pressureless Gas Dynamics system under a maximal constraint on the density…
The Nagel-Schreckenberg model is a simple cellular automaton for a realistic description of single-lane traffic on highways. For the case $v_{max}=1$ the properties of the stationary state can be obtained exactly. For the more relevant case…
The present research article is devoted to the study of two fluid-dynamical traffic models and their steady states by first analyzing the kinetic-type Borsche-Kimathi-Klar model and the Navier-Stokes-type Helbing model. To fulfill this…
Transitions between two lanes often have a significant impact on various forms of road traffic. To address this problem, we have developed a two-lane asymmetric simple exclusion process model and two hypothetical traffic control strategies,…