Related papers: Relaxation models for scalar traffic networks and …
In this paper we propose coupling conditions for a kinetic two velocity model for vehicular traffic on networks. These conditions are based on the consideration of the free space on the respective roads. The macroscopic limit of the kinetic…
We consider a kinetic relaxation model and an associated macroscopic scalar nonlinear hyperbolic equation on a network. Coupling conditions for the macroscopic equations are derived from the kinetic coupling conditions via an asymptotic…
In this paper we propose coupling conditions for a kinetic two velocity model for vehicular traffic for junctions with diverging lanes. We consider cases with and without directional preferences and present corresponding kinetic coupling…
A recently introduced scheme for networked conservation laws is analyzed in various experiments. The scheme makes use of a novel relaxation approach that governs the coupling conditions of the network and does not require a solution of the…
We propose a novel scheme to numerically solve scalar conservation laws on networks without the necessity to solve Riemann problems at the junction. The scheme is derived using the relaxation system introduced in [Jin and Xin, Comm. Pure…
In this study we present a non-overlapping Schwarz waveform relaxation (SWR) method applied to a one dimensional model problem representative of the coupling between the ocean and the atmosphere. This problem includes nonlinear interface…
Lane changing dynamics are an important part of traffic microsimulation and are vital for modeling weaving sections and merge bottlenecks. However, there is often much more emphasis placed on car following and gap acceptance models, whereas…
We consider the freeway network control problem where the aim is to optimize the operation of traffic networks modeled by the Cell Transmission Model via ramp metering and partial mainline demand control. Optimal control problems using the…
The simulation of traffic flow on networks requires knowledge on the behavior across traffic intersections. For macroscopic models based on hyperbolic conservation laws there exist nowadays many ad-hoc models describing this behavior. Based…
We derive a nonlinear 2-equation discrete-velocity model for traffic flow from a continuous kinetic model. The model converges to scalar Lighthill-Whitham type equations in the relaxation limit for all ranges of traffic data. Moreover, the…
We propose a macroscopic traffic network flow model suitable for analysis as a dynamical system, and we qualitatively analyze equilibrium flows as well as convergence. Flows at a junction are determined by downstream supply of capacity as…
In this paper we propose a new numerical scheme of relaxation type to approximate the Euler equations of isentropic gas dynamics on the arcs of a network. At the junction mass conservation and a jump transmission condition on the density…
We study the convergence of a class of asymptotic preserving numerical schemes initially proposed by F. Filbet & S. Jin \cite{filb1} and G. Dimarco & L. Pareschi \cite{DimarcoP} in the context of nonlinear and stiff kinetic equations. Here,…
We present in this article an algebraic approach to model and simulate road traffic networks. By defining a set of road traffic systems and adequate concatenating operators in that set, we show that large regular road networks can be easily…
This article deals with macroscopic traffic flow models on a road network. More precisely, we consider coupling conditions at junctions for the Aw-Rascle-Zhang second order model consisting of a hyperbolic system of two conservation laws.…
It has been observed in practical applications and in theoretical analysis that over-parametrization helps to find good minima in neural network training. Similarly, in this article we study widening and deepening neural networks by a…
A numerical scheme of relaxation type is proposed to approximate hyperbolic conservation laws in canal networks. Physical conditions at the junction are given and a novel strategy based on [Briani, Natalini, Ribot, 2025] is introduced to…
We study a scalar harmonic network with pair interactions and a binary collision rule, exchanging the momenta of a randomly-chosen couple of sites. We consider the case of the isolated network where the total energy is conserved. In the…
In this paper, we develop asymptotic theories for a class of latent variable models for large-scale multi-relational networks. In particular, we establish consistency results and asymptotic error bounds for the (penalized) maximum…
We consider networks for isentropic gas and prove existence of weak solutions for a large class of coupling conditions. First, we construct approximate solutions by a vector-valued BGK model with a kinetic coupling function. Introducing…