Related papers: Dynamic analysis in Greenberg's traffic model

We present a model of traffic flow, with rules that describe the behaviour of automated vehicles in an open system. We show first of all that the fundamental diagram of this system collapses to a point, where states of free and jammed…

There is a great diversity of formal models to understand the dynamics of transport and vehicular flow on a road. Many of these models are inspired by the dynamics of flows governed by partial differential equations. However, it is possible…

Single-file dynamics has been studied intensively, both experimentally and theoretically. It shows interesting collective effects, such as stop-and-go waves, which are validation cornerstones for any agent-based modeling approach of traffic…

Day-to-day traffic dynamics are widely used to model flow evolution due to travelers' learning and adjustment behavior, yet empirical analysis of these models often relies on descriptive calibration with limited inferential content. This…

In this paper we consider a kinetic description of follow-the-leader traffic models, which we use to study the effect of vehicle-wise driver-assist control strategies at various scales, from that of the local traffic up to that of the…

In this paper, we propose a kinetic model of traffic flow with uncertain binary interactions, which explains the scattering of the fundamental diagram in terms of the macroscopic variability of aggregate quantities, such as the mean speed…

The simulation of traffic flow on networks requires knowledge on the behavior across traffic intersections. For macroscopic models based on hyperbolic conservation laws there exist nowadays many ad-hoc models describing this behavior. Based…

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…

We analyze the pattern formation in systems of active particles with chiral forces in the context of pedestrian dynamics. To describe the interparticle interactions, we use the standard social force model and supplement it with a new type…

Our goal is to use overhead imagery to understand patterns in traffic flow, for instance answering questions such as how fast could you traverse Times Square at 3am on a Sunday. A traditional approach for solving this problem would be to…

In this paper, we investigate a nonlocal traffic flow model based on a scalar conservation law, where a stochastic velocity function is assumed. In addition to the modeling, theoretical properties of the stochastic nonlocal model are…

This paper presents a rigorous analytical model of traffic dynamics on a circular track, demonstrating the emergence of standing oscillations resulting from microscopic driver behaviour, delay responses, and proximity pressure. Without…

This paper proposes a graph-based approach to representing spatio-temporal trajectory data that allows an effective visualization and characterization of city-wide traffic dynamics. With the advance of sensor, mobile, and Internet of Things…

A generalized optimal velocity model is analyzed, where the optimal velocity function depends not only on the headway of each car but also the headway of the immediately preceding one. The stability condition of the model is derived by…

This paper presents two one-dimensional mathematical models describing automobile traffic flow on straight road segments at a signalized intersection. When the traffic light is permissive, the flow density and velocity are obtained by…

The propagation of traffic congestion along roads is a commonplace nonlinear phenomenon. When many roads are connected in a network, congestion can spill from one road to others as drivers queue to enter a congested road, creating further…

A model equation has been proposed to describe bimodal features in vehicular traffic flows. The dynamics of the bimodal distribution reveals the existence of a fixed point that is connected to itself by a homoclinic trajectory. The…

Experimental results for congested pedestrian traffic are presented. For data analysis we apply a method providing measurements on an individual scale. The resulting velocity-density relation shows a coexistence of moving and stopping…

Starting from interaction rules based on two levels of stochasticity we study the influence of the microscopic dynamics on the macroscopic properties of vehicular flow. In particular, we study the qualitative structure of the resulting…

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…