Related papers: A nonlinear discrete-velocity relaxation model for…
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…
In order to develop a toy model for car's traffic in cities, in this paper we analyze, by means of numerical simulations, the transition among fluid regimes and a congested jammed phase of the flow of "kinetically constrained" hard spheres…
Lane changing is one of the most common maneuvers on motorways. Although, macroscopic traffic models are well known for their suitability to describe fast moving crowded traffic, most of these models are generally developed in one…
Traffic jam in an optimal velocity model with the backward reference function is analyzed. An analytic scaling solution is presented near the critical point of the phase separation. The validity of the solution has been confirmed from the…
In this paper, we introduce a discrete time-finite state model for pedestrian flow on a graph in the spirit of the Hughes dynamic continuum model. The pedestrians, represented by a density function, move on the graph choosing a route to…
We consider an integro-differential equation model for traffic flow which is an extension of the Burgers equation model. To discuss the model, we first examine general settings for integrable integro-differential equations and find that…
We suggest a new model for the dynamics of a suspension bridge through a system of nonlinear nonlocal hyperbolic differential equations. The equations are of second and fourth order in space and describe the behavior of the main components…
We study condensation in one-dimensional transport models with a kinetic constraint. The kinetic constraint results in clustering of immobile vehicles; these clusters can grow to macroscopic condensates, indicating the onset of dynamic…
In this paper, we present a numerical scheme for the diffuse-interface model in [Abels, Garcke, Gr\"un, M3AS 22(3), 2012] for two-phase flow of immiscible, incompressible fluids. As that model is in particular consistent with…
As a dynamical complex system, traffic is characterized by a transition from free flow to congestions, which is mostly studied in highways. However, despite its importance in developing congestion mitigation strategies, the understanding of…
We develop an unconditionally energy-stable tensor-product space-time discretization framework for the solution of a linear kinetic transport equation in one space dimension. The kinetic equation is a simplified model of radiative transfer…
In this work, we introduce a novel first-order nonlocal partial differential equation with saturated diffusion to describe the macroscopic behavior of traffic dynamics. We show how the proposed model is better in comparison with existing…
This paper examines the optimal velocity follow-the-leader dynamics, a microscopic traffic model, and explores different aspects of the dynamical model, with particular emphasis on collision analysis. More precisely, we present a rigorous…
We study numerically the behavior of the Biham-Middleton-Levine traffic model in three dimensions. Our extensive numerical simulations show that the phase diagram for this model in three dimensions is markedly different from that in one and…
We study traffic flow on roads with a localized periodic inhomogeneity such as traffic signals, using a stochastic car-following model. We find that in cases of congestion, traffic flow can be optimized by controlling the inhomogeneity's…
Statistical mechanics of a small system of cars on a single-lane road is developed. The system is not characterized by a Hamiltonian but by a conditional probability of a velocity of a car for the given velocity and distance of the car…
This paper develops output feedback boundary control to mitigate traffic congestion of a unidirectional two-lane freeway segment. The macroscopic traffic dynamics are described by the Aw-Rascle-Zhang (ARZ) model respectively for both the…
We discuss numerical strategies to deal with PDE systems describing traffic flows, taking into account a density threshold, which restricts the vehicles density in the situation of congestion. These models are obtained through asymptotic…
We consider a nonlinear damped hyperbolic reaction-diffusion system in a bounded interval of the real line with homogeneous Neumann boundary conditions and we study the metastable dynamics of the solutions. Using an "energy approach"…
A discrete model of traffic on a multilane road is considered. The traffic is presented as particles movement with a deterministic component and a stochastic one. Formulas for the traffic characteristics have been found. The model can…