Related papers: The deterministic-stochastic flow model
When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy…
We present large scale and detailed analysis of the microscopic empirical data of the traffic flow, focusing on the non-linear interactions between the vehicles when the traffic is congested. By implementing a "renormalisation" procedure…
We present a macroscopic traffic flow model that extends existing fluid-like models by an additional term containing the second derivative of the safe velocity. Two qualitatively different shapes of the safe velocity are explored: a…
In this paper we propose a new modeling technique for vehicular traffic flow, designed for capturing at a macroscopic level some effects, due to the microscopic granularity of the flow of cars, which would be lost with a purely continuous…
In this paper we investigate the ability of some recently introduced discrete kinetic models of vehicular traffic to catch, in their large time behavior, typical features of theoretical fundamental diagrams. Specifically, we address the…
A model for traffic flow in street networks or material flows in supply networks is presented, that takes into account the conservation of cars or materials and other significant features of traffic flows such as jam formation, spillovers,…
We investigate a model for driven exclusion processes where internal states are assigned to the particles. The latter account for diverse situations, ranging from spin states in spintronics to parallel lanes in intracellular or vehicular…
The paper analyzes traffic data of the Dutch freeway A9 with respect to certain aspects which are relevant for traffic flow modeling as well as the calibration of model parameters and functions. Apart from the dynamic velocity distribution,…
The purpose of this paper is to study the properties of kinetic models for traffic flow described by a Boltzmann-type approach and based on a continuous space of microscopic velocities. In our models, the particular structure of the…
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…
We consider one-way road deterministic traffic model with $N$ particles. The simplest local control protocol, which reminds physical interaction)\d{ }with three parameters is considered. We study the stable and unstable domains of the phase…
It is shown that the desire for smooth and comfortable driving is directly responsible for the occurrence of complex spatio-temporal structures (``synchronized traffic'') in highway traffic. This desire goes beyond the avoidance of…
We introduce a counting process to model the random occurrence in time of car traffic accidents, taking into account some aspects of the self-excitation typical of this phenomenon. By combining methods from probability and differential…
This study addresses multilane vehicular traffic modelling, focusing on the transition between microscopic (individual vehicle-based) to macroscopic (aggregate flow-based) descriptions. While previous research on multilane traffic has…
When a new vehicle joins a lane, those behind may have to temporarily slow to accommodate them. Changing lane can be forced due to lane drops or junctions, but may also take place spontaneously at discretion of drivers, and recent studies…
A novel constructive mathematical model based on the multifractal formalism in order to accurately characterizing the localized fluctuations present in the course of traffic flows today high-speed computer networks is presented. The…
The balanced vehicular traffic model is a macroscopic model for vehicular traffic flow. We use this model to study the traffic dynamics at highway bottlenecks either caused by the restriction of the number of lanes or by on-ramps or…
This paper deals with the modeling and numerical simulations of multilane vehicular traffic according to the discrete kinetic theory approach. The nonlinear additive interactions and external actions such as tollgates as well traffic signs…
In this paper a spatial homogeneous vehicular traffic flow model based on a stochastic master equation of Boltzmann type in the acceleration variable is solved numerically for a special driver interaction model. The solution is done by a…
We present an empirical phase diagram of the congested traffic flow measured on a highway section with one effective on-ramp. Through the analysis of local density-flow relations and global spatial structure of the congested region, four…