Related papers: Maxwell Model of Traffic Flows
In this paper, a new model for traffic on roads with multiple lanes is developed, where the vehicles do not adhere to a lane discipline. Assuming identical vehicles, the dynamics is split along two independent directions: the Y-axis…
We present an energy-conserving multiple-relaxation-time finite difference lattice Boltzmann model for compressible flows. This model is based on a 16-discrete-velocity model. The collision step is first calculated in the moment space and…
The Boltzmann equation for inelastic Maxwell models is used to analyze nonlinear transport in a granular binary mixture in the steady simple shear flow. Two different transport processes are studied. First, the rheological properties (shear…
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…
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…
This paper presents a new mathematical model of vehicular traffic, based on the methods of the generalized kinetic theory, in which the space of microscopic states (position and velocity) of the vehicles is genuinely discrete. While in the…
The Boltzmann equation for $d$-dimensional inelastic Maxwell models is considered to analyze transport properties for monodisperse gas-solid suspensions. The influence of the interstitial gas phase on the dynamics of solid particles is…
In the Maxwell interaction model the collision rate is independent of the relative velocity of the colliding pair and, as a consequence, the collisional moments are bilinear combinations of velocity moments of the same or lower order. In…
Boltzmann equation describes the time development of the velocity distribution in the continuum fluid matter. We formulate the equation using the field theory where the {\it velocity-field} plays the central role. The properties of the…
Due to the complexity of the traffic flow dynamics in urban road networks, most quantitative descriptions of city traffic so far are based on computer simulations. This contribution pursues a macroscopic (fluid-dynamic) simulation approach,…
Various empirical and theoretical studies indicate that cumulative network traffic is a Gaussian process. However, depending on whether the intensity at which sessions are initiated is large or small relative to the session duration tail,…
Traffic flow oscillations, including traffic waves, are a common yet incompletely understood feature of congested traffic. Possible mechanisms include traffic flow instabilities, indifference regions or finite human perception thresholds…
The influence of clustering on the collision rate of inertial particles in a smooth random velocity field, mimicking the smaller scales of a turbulent flow, is analyzed. For small values of the the ratio between the relaxation time of the…
Urban traffic systems are characterized by dynamic interactions between congestion and free-flow states, influenced by human activity and road topology. This study employs percolation theory to analyze traffic dynamics in Seoul, focusing on…
In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the…
This paper presents a new approach to the modeling of vehicular traffic flows on road networks based on kinetic equations. While in the literature the problem has been extensively studied by means of macroscopic hydrodynamic models, to date…
We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase…
We study kinetic models for traffic flow characterized by the property of producing backward propagating waves. These waves may be identified with the phenomenon of stop-and-go waves typically observed on highways. In particular, a refined…
In contrast to molecular gases, granular gases are characterized by inelastic collisions and require therefore permanent driving to maintain a constant kinetic energy. The kinetic theory of granular gases describes how the average velocity…
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…