Related papers: Nonlocal approaches for multilane traffic models
Statistical traffic data analysis is a hot topic in traffic management and control. In this field, current research progresses focus on analyzing traffic flows of individual links or local regions in a transportation network. Less attention…
The question of deriving general force/flux relationships that apply out of the linear response regime is a central topic of theories for nonequilibrium statistical mechanics. This work applies an information theory perspective to compute…
Nonlinear time series models with exogenous regressors are essential in econometrics, queuing theory, and machine learning, though their statistical analysis remains incomplete. Key results, such as the law of large numbers and the…
This contribution summarizes and explains various principles from physics which are used for the simulation of traffic flows in large street networks, the modeling of destination, transport mode, and route choice, or the simulation of urban…
Modeling and simulating movement of vehicles in established transportation infrastructures, especially in large urban road networks is an important task. It helps with understanding and handling traffic problems, optimizing traffic…
In the present paper a review and numerical comparison of a special class of multi-phase traffic theories based on microscopic, kinetic and macroscopic traffic models is given. Macroscopic traffic equations with multi-valued fundamental…
Biological machines like molecular motors and enzymes operate in dynamic cycles representable as stochastic flows on networks. Current stochastic dynamics describes such flows on fixed networks. Here, we develop a scalable approach to…
The goal of the paper is a rigorous derivation of a macroscopic traffic flow model with a bifurcation or a local perturbation from a microscopic one. The microscopic model is a simple follow-the-leader with random parameters. The random…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
We present an optimization-based coupling method for local and nonlocal continuum models. Our approach couches the coupling of the models into a control problem where the states are the solutions of the nonlocal and local equations, the…
Accurately forecasting traffic flows is critically important to many real applications including public safety and intelligent transportation systems. The challenges of this problem include both the dynamic mobility patterns of the people…
Urban streets patterns form planar networks whose empirical properties cannot be accounted for by simple models such as regular grids or Voronoi tesselations. Striking statistical regularities across different cities have been recently…
We introduce a new class of nonlocal nonlinear conservation laws in one space dimension that allow for nonlocal interactions over a finite horizon. The proposed model, which we refer to as the nonlocal pair interaction model, inherits at…
Real-time traffic prediction from high-fidelity spatiotemporal traffic sensor datasets is an important problem for intelligent transportation systems and sustainability. However, it is challenging due to the complex topological dependencies…
We are concerned with multidimensional stochastic balance laws. We identify a class of nonlinear balance laws for which uniform spatial $BV$ bounds for vanishing viscosity approximations can be achieved. Moreover, we establish temporal…
This paper deals with the modeling and mathematical analysis of vehicular traffic phenomena according to a kinetic theory approach, where the microscopic state of vehicles is described by: (i) position, (ii) velocity, as a continuous…
The lateral position of vehicles within their lane is a decisive factor for the range of vision of vehicle sensors. This, in turn, is crucial for a vehicle's ability to perceive its environment and gain a high situational awareness by…
This paper presents a mixed traffic control policy designed to optimize traffic efficiency across diverse road topologies, addressing issues of congestion prevalent in urban environments. A model-free reinforcement learning (RL) approach is…
In this article we consider a large family of nonlinear nonlocal equations involving gradient nonlinearity and provide a unified approach, based on the Ishii-Lions type technique, to establish Liouville properties of the solutions. We also…
Nonlocal models provide accurate representations of physical phenomena ranging from fracture mechanics to complex subsurface flows, where traditional partial differential equations fail to capture effects caused by long-range forces at the…