Related papers: Network models for nonlocal traffic flow
We study a 1D scalar conservation law whose non-local flux has a single spatial discontinuity. This model is intended to describe traffic flow on a road with rough conditions. We approximate the problem through an upwind-type numerical…
In this note, we propose a case study of freeway traffic flow modeled as a hybrid system. We describe two general classes of networks that model flow along a freeway with merging onramps. The admission rate of traffic flow from each onramp…
We study a generalized Follow-the-Leader model where the driver considers the position of an arbitrary but finite number of vehicles ahead, as well as the position of the vehicle directly behind the driver. It is proved that this model…
A novel constructive mathematical model based on the multifractal formalism in order to accurately characterizing the localized fluctuations present in the course of traffic flows today high-speed computer networks is presented. The…
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…
We define a minimal model of traffic flows in complex networks containing the most relevant features of real routing schemes, i.e. a trade--off strategy between topological-based and traffic-based routing. The resulting collective behavior,…
We study vehicular traffic on a road with multiple lanes and dense, unidirectional traffic following the traditional Lighthill-Whitham-Richards model where the velocity in each lane depends only on the density in the same lane. The model…
While macroscopic models for single or multi-lane traffic flow are well established, these models are not applicable to the dynamics and characteristics of disordered traffic which is characterized by widely different types of vehicles and…
In a recent paper (see [7]), a quasi-nonlocal coupling method was introduced to seamlessly bridge a nonlocal diffusion model with the classical local diffusion counterpart in a one-dimensional space. The proposed coupling framework removes…
We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase…
We study an optimal control problem for traffic regulation via variable speed limit. The traffic flow dynamics is described with the Lighthill-Whitham-Richards (LWR) model with Newell-Daganzo flux function. We aim at minimizing the $L^2$…
In this work, we study a Lighthill-Whitham-Richard (LWR) type traffic flow model with a non-local flux. We identify a threshold condition for shock formation for traffic flow models with Arrhenius look-ahead-behind (i.e., nudging) dynamics…
In this study, we start from a Follow-the-Leaders model for traffic flow that is based on a weighted harmonic mean (in Lagrangian coordinates) of the downstream car density. This results in a nonlocal Lagrangian partial differential…
We prove the well-posedness of weak entropy solutions of a scalar non-local traffic flow model with time delay. Existence is obtained by convergence of finite volume approximate solutions constructed by Lax-Friedrich and Hilliges-Weidlich…
We study a nonlocal traffic flow model with an Arrhenius type look-ahead interaction. We show a sharp critical threshold condition on the initial data which distinguishes the global smooth solutions and finite time wave break-down.
This paper presents a new spatial-temporal nonlocal traffic flow model formulated to overcome the boundedness limitations inherent in classical local formulations. The model introduces an adaptive kernel that captures both spatial and…
We present a fluid-dynamic model for the simulation of urban traffic networks with road sections of different lengths and capacities. The model allows one to efficiently simulate the transitions between free and congested traffic, taking…
Efficient and exact algorithms are important for performing fast and accurate traffic network simulations with macroscopic traffic models. In this paper, we extend the semi-analytical Lax-Hopf algorithm in order to compute link inflows and…
We propose in this article an adaptation of the basic techniques of the deterministic network calculus theory to the road traffic flow theory. Network calculus is a theory based on min-plus algebra. It uses algebraic techniques to compute…
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…