Related papers: Microscopic and Macroscopic Traffic Flow Models in…
We prove the well-posedness of a system of balance laws inspired by [8], describing macro-scopically the traffic flow on a multi-lane road network. Motivated by real applications, we allow for the the presence of space discontinuities both…
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…
We present a new class of macroscopic models for pedestrian flows. Each individual is assumed to move towards a fixed target, deviating from the best path according to the instantaneous crowd distribution. The resulting equation is a…
Floating car data of car-following behavior in cities were compared to existing microsimulation models, after their parameters had been calibrated to the experimental data. With these parameter values, additional simulations have been…
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 study the application of a recently introduced hierarchical description of traffic flow control by driver-assist vehicles to include lane changing dynamics. Lane-dependent feedback control strategies are implemented at the level of…
Historically, traffic modelling approaches have taken either a particle-like (microscopic) approach, or a gas-like (meso- or macroscopic) approach. Until recently with the introduction of mean-field games to the controls community, there…
Existing macroscopic traffic control methods often struggle to strictly regulate rare, safety-critical extreme events under stochastic disturbances. In this paper, we develop a rare chance-constrained optimal control framework for…
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…
The Logit lane assignment model has been introduced recently in order to describe multi-lane traffic flow from a macroscopic point of view. The model is based on the idea that each available lane has a specific utility for each driver, who…
A macroscopic model is proposed to depict the traffic dynamics involved in urban traffic systems. The link dynamics are described based on the cell-transmission model and bounded by the link capacities, while the flow dynamics are proposed…
Noise-assisted transport phenomena highlight the nontrivial interplay between environmental effects and quantum coherence in achieving maximal efficiency. Due to the complexity of biochemical systems and their environments, effective open…
Experimental studies on vehicular traffic provide data on quantities like density, flux, and mean speed of the vehicles. However, the diagrams relating these variables (the fundamental and speed diagrams) show some peculiarities not yet…
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…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
Macroscopic dynamical descriptions of complex physical systems are crucial for understanding and controlling material behavior. With the growing availability of data and compute, machine learning has become a promising alternative to…
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…
Two different deterministic microscopic traffic flow models, which are in the context of the Kerner's there-phase traffic theory, are introduced. In an acceleration time delay model (ATD-model), different time delays in driver acceleration…
Car-following behavior is fundamental to traffic flow theory, yet traditional models often fail to capture the stochasticity of naturalistic driving. This paper introduces a new car-following modeling category called the empirical…
We provide a model to understand how adverse weather conditions modify traffic flow dynamic. We first prove that the microscopic Free Flow Speed of the vehicles is changed and then provide a rule to model this change. For this, we consider…