Related papers: Numerical Simulation of Macroscopic Traffic Equati…
Autonomous vehicles (AVs) have the potential to significantly revolutionize society by providing a secure and efficient mode of transportation. Recent years have witnessed notable advancements in autonomous driving perception and…
We propose a microscopic decision model for route choice based on discrete choice theory. The correlation of overlapping routes is included in the random portions of the utility explicitly. For computational efficiency, we restrict the…
In this paper we propose a new modeling technique for vehicular traffic flow, designed for capturing at a macroscopic level some effects, due to the microscopic granularity of the flow of cars, which would be lost with a purely continuous…
Traffic simulation is a great tool to demonstrate complex traffic structures which can be extremely useful for the planning, development, and management of road traffic networks. Current traffic simulators offer limited features when it…
Nowadays the city-wide traffic contains hundreds of thousands of vehicles with different scenarios of their behavior. If a microscopic approach is used it leads to solving tremendous systems of ordinary differential equations whose…
We introduce a new micro-macro decomposition of collisional kinetic equations in the specific case of the diffusion limit, which naturally incorporates the incoming boundary conditions. The idea is to write the distribution function $f$ in…
Kinetic equations model the position-velocity distribution of particles subject to transport and collision effects. Under a diffusive scaling, these combined effects converge to a diffusion equation for the position density in the limit of…
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,…
The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the…
We provide a both qualitative and quantitative comparison among different approaches aimed to solve the problem of non-linear diffusive acceleration of particles at shocks. In particular, we show that state-of-the-art models (numerical,…
We show how the nonlinear interaction effects `volume filling' and `adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with…
In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…
The equation of motion of a general class of macroscopic traffic flow models is linearized around a steady uniform flow. A closed-form solution of a boundary-initial value problem is obtained, and it is used to describe several phenomena.…
We present a method to derive macroscopic fluid-dynamic models from microscopic car-following models via a coarse-graining procedure. The method is first demonstrated for the optimal velocity model. The derived macroscopic model consists of…
The mathematical modeling and the stability analysis of multi-lane traffic in the macroscopic scale is considered. We propose a new first order model derived from microscopic dynamics with lane changing, leading to a coupled system of…
We present different techniques to numerically solve the equations of motion for the widely studied Discrete Nonlinear Schroedinger equation (DNLS). Being a Hamiltonian system, the DNLS requires symplectic routines for an efficient…
Urban intersections are prone to delays and inefficiencies due to static precedence rules and occlusions limiting the view on prioritized traffic. Existing approaches to improve traffic flow, widely known as automatic intersection…
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…
This paper introduces a new approach to hybrid traffic modeling, along with its implementation in software. The software allows modelers to assign traffic models to individual links in a network. Each model implements a series of methods,…
Differential equations with constant and variable coefficients over octonions are investigated. It is found that different types of differential equations over octonions can be resolved. For this purpose non-commutative line integration is…