Related papers: Kinetic derivation of a Hamilton-Jacobi traffic fl…
Equation-free methods make possible an analysis of the evolution of a few coarse-grained or macroscopic quantities for a detailed and realistic model with a large number of fine-grained or microscopic variables, even though no equations are…
From single vehicle data a number of new empirical results about the temporal evolution, correlation, and density-dependence of macroscopic traffic quantities have been determined. These have relevant implications for traffic modeling and…
Microscopic traffic flow models can be distinguished in lane-based or lane-free depending on the degree of lane-discipline. This distinction holds true only if motorcycles are neglected in lane-based traffic. In cities, as opposed to…
Despite the importance of urban traffic flows, there are only a few theoretical approaches to determine fundamental relationships between macroscopic traffic variables such as the traffic density, the utilization, the average velocity, and…
The rarely used Hamilton-Jacobi equation has been utilized as an elegant way to find the trajectories of mechanical systems and to derive symplectic maps. Further, the exact solution in kick approximation of Hamilton's equations of motion…
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…
The gas-kinetic foundation of fluid-dynamic traffic equations suggested in previous papers [Physica A 219, 375 and 391 (1995)] is further refined by applying the theory of dense gases and granular materials to the Boltzmann-like traffic…
We present simulations of congested traffic in circular and open systems with a non-local, gas-kinetic-based traffic model and a novel car-following model. The model parameters are all intuitive and can be easily calibrated. Micro- and…
In this work we present a two-dimensional kinetic traffic model which takes into account speed changes both when vehicles interact along the road lanes and when they change lane. Assuming that lane changes are less frequent than…
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…
A new vehicular traffic flow model based on a stochastic jump process in vehicle acceleration and braking is introduced. It is based on a master equation for the single car probability density in space, velocity and acceleration with an…
Critical analyses of well-known methods of derivation of kinetic and hydrodynamic equations is presented. Another method of derivation of kinetic and hydrodynamic equations from classic mechanics is described. It is shown that equations of…
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…
Vehicular traffic is a classical example of a multi-agent system in which autonomous drivers operate in a shared environment. The article provides an overview of the state-of-the-art in microscopic traffic modeling and the implications for…
Traffic on a circular road is described by dynamic programming equations associated to optimal control problems. By solving the equations analytically, we derive the relation between the average car density and the average car flow, known…
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…
In this paper, a particle method is used to approximate the solutions of a "fluid-like" macroscopic traffic flow model for automated vehicles. It is shown that this method preserves certain differential inequalities that hold for the…
Nowadays, traffic management has become a challenge for urban areas, which are covering larger geographic spaces and facing the generation of different kinds of traffic data. This article presents a robust traffic estimation framework for…
In recent years statistical physicists have developed {\it discrete} "particle-hopping" models of vehicular traffic, usually formulated in terms of {\it cellular automata}, which are similar to the microscopic models of interacting charged…
Macroscopic traffic simulations are based on coupled non-linear partial differential equations, the solutions of which are either shock-like or inhomogeneous with steep gradients, at least in the interesting density regime. We discuss…