Related papers: A pedestrian flow model with stochastic velocities…
We numerically study jamming transitions in pedestrian flow interacting with an attraction, mostly based on the social force model for pedestrians who can join the attraction. We formulate the joining probability as a function of social…
We show that keeping a constant lower limit on the net-time headway is the key mechanism behind the dynamics of pedestrian streams. There is a large variety in flow and speed as functions of density for empirical data of pedestrian streams,…
The stochastics two-layer quasi-geostrophic flow model is an intermediate system between the single-layer two dimensional barotropic flow model and the continuously stratified three dimensional baroclinic flow model. This model is widely…
Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to…
We present a strategy capable of describing basic features of the dynamics of crowds. The behaviour of the crowd is considered from a twofold perspective. We examine both the large scale behaviour of the crowd, and phenomena happening at…
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…
We consider linear hyperbolic balance law that describe gas flow. Stochastic influences are introduced by series of orthogonal functions. A deterministic stabilization concept, which makes deviations at steady states decay exponentially…
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 consider a stochastic flow driven by a finite dimensional Brownian motion. We show that almost every realization of such a flow exhibits strong statistical properties such as the exponential convergence of an initial measure to the…
This contribution proposes a method to make agents in a microscopic simulation of pedestrian traffic walk approximately along a path of estimated minimal remaining travel time to their destination. Usually models of pedestrian dynamics are…
We consider a kinetic theory approach to model the evacuation of a crowd from bounded domains. The interactions of a person with other pedestrians and the environment, which includes walls, exits, and obstacles, are modeled by using tools…
It is shown how the macroscopic non-equilibrium dynamics of a class of systems whose microscopic stochastic dynamics involves disordered and frustrated but range-free interactions can be well described by closed deterministic flow…
Kinetic models for vehicular traffic are reviewed and considered from the point of view of deriving macroscopic equations. A derivation of the associated macroscopic traffic flow equations leads to different types of equations: in certain…
In mixed traffic scenarios, a certain number of pedestrians might coexist in a small area while interacting with vehicles. In this situation, every pedestrian must simultaneously react to the surrounding pedestrians and vehicles. Analytical…
Random walks and related spatial stochastic models have been used in a range of application areas including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing, and oncology. Classical random walk…
In this work we extend a recent kinetic traffic model to the case of more than one class of vehicles, each of which is characterized by few different microscopic features. We consider a Boltzmann-like framework with only binary…
A multi--cluster model of traffic flow is studied, in which the motion of cars is described by a stochastic master equation. Assuming that the escape rate from a cluster depends only on the cluster size, the dynamics of the model is…
Simulating transition dynamics between metastable states is a fundamental challenge in dynamical systems and stochastic processes with wide real-world applications in understanding protein folding, chemical reactions and neural activities.…
One of the objectives of the pedestrian analysis is to evaluate the effects of proposed policy on the pedestrian facilities before its implementation. The implementation of a policy without pedestrian analysis might lead to a very costly…
We introduce a variant of the asymmetric random average process with continuous state variables where the maximal transport is restricted by a cutoff. For periodic boundary conditions, we show the existence of a phase transition between a…