Related papers: Constructing set-valued fundamental diagrams from …

Networks are a powerful tool to model the structure and dynamics of complex systems across scales. Direct connections between system components are often represented as edges, while paths and walks capture indirect interactions. This…

Standard approach to dynamical random matrix models relies on the description of trajectories of eigenvalues. Using the analogy from optics, based on the duality between the Fermat principle(trajectories) and the Huygens principle…

We consider two scalar conservation laws with non-local flux functions, describing traffic flow on roads with rough conditions. In the first model, the velocity of the car depends on an averaged downstream density, while in the second model…

Diagonal or chevron patterns are known to spontaneously emerge at the intersection of two perpendicular flows of self-propelled particles, e.g. pedestrians. The instability responsible for this pattern formation has been studied in previous…

"Phantom jams," traffic blockages that arise without apparent cause, have long frustrated transportation scientists. Herein, we draw a novel homology between phantom jams and a related class of self-sustained transonic waves, namely…

A two--dimensional cellular automaton is introduced to model the flow and jamming of vehicular traffic in cities. Each site of the automaton represents a crossing where a finite number of cars can wait approaching the crossing from each of…

We propose a stochastic cellular-automaton model for two-lane traffic flow based on the misanthrope process in one dimension. The misanthrope process is a stochastic process allowing for an exact steady-state solution; hence we have an…

We study spatially non-homogeneous kinetic models for vehicular traffic flow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by…

We show that a noncommutative dynamical system of the type that occurs in quantum theory can often be associated with a dynamical principle; that is, an infinitesimal structure that completely determines the dynamics. The nature of these…

This contribution investigates an original stochastic approach for the emergence of stop-and-go waves in traffic flow, a collective phenomenon with significant safety and environmental implications. Using a stable nonlinear car-following…

The macroscopic fundamental diagram (MFD) is a powerful and popular tool that describes a network scale traffic operational state and serve as the plant model of perimeter control. As both the supply and the demand suffer from random…

We propose a simple and effective method to derive the Fundamental Diagram (FD) from platoon vehicle trajectories. Average traffic state variables are computed using Edie's generalized definitions within time-dependent trapezoidal…

The path-preference traffic flow cellular automaton is suggested to model the dynamics of transcription. The main difference from the simple traffic flow model is that it contains another preferential paths at some sites. In this paper, we…

We discuss a phenomenological approach to the description of unstable vehicle motion on multilane highways that explains in a simple way the observed sequence of the phase transitions "free flow -> synchronized motion -> jam" as well as the…

Based on simulations with the ``intelligent driver model'', a microscopic traffic model, we explain the recently discovered transition from free over ``synchronized'' traffic to stop-and-go patterns [B. S. Kerner, Phys. Rev. Lett. 81, 3797…

Hybrid traffic modeling and simulation provide an important way to represent and evaluate large-scale traffic networks at different levels of details. The first level, called "microscopic" allows the description of individual vehicles and…

This paper shows how particle hopping models fit into the context of traffic flow theory. Connections between fluid-dynamical traffic flow models, which derive from the Navier-Stokes-equations, and particle hopping models are shown. In some…

We consider traffic flows described by conservation laws. We study a 2:1 junction (with two incoming roads and one outgoing road) or a 1:2 junction (with one incoming road and two outgoing roads). At the mesoscopic level, the priority law…

We prove existence and uniqueness of solutions to a transport equation modelling vehicular traffic in which the velocity field depends non-locally on the downstream traffic density via a discontinuous anisotropic kernel. The result is…

Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…