Related papers: A Mixed ODE-PDE Model for Vehicular Traffic
Based on experimental traffic data obtained from German and US highways, we propose a novel two-dimensional first-order macroscopic traffic flow model. The goal is to reproduce a detailed description of traffic dynamics for the real road…
We consider the Follow-the-Leader (FtL) model and study which properties of the initial positioning of the vehicles ensure its convergence to the classical Lighthill-Whitham-Richards (LWR) model for traffic flow. Robustness properties of…
We study a message passing model, applicable also to traffic problems. The model is implemented in a discrete lattice, where particles move towards their destination, with fluctuations around the minimal distance path. A repulsive…
We consider the follow-the-leader model for traffic flow. The position of each car $z_i(t)$ satisfies an ordinary differential equation, whose speed depends only on the relative position $z_{i+1}(t)$ of the car ahead. Each car perceives a…
In this paper, a useful reinterpretation of the city as a porous medium justifies the application of well-known models on fluid dynamics to develop a multi-model study of urban air pollution due to traffic flow in a large city. Thus, to…
A macroscopic model-based approach for estimation of the traffic state, specifically of the (total) density and flow of vehicles, is developed for the case of "mixed" traffic, i.e., traffic comprising both ordinary and connected vehicles.…
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…
This paper presents two one-dimensional mathematical models describing automobile traffic flow on straight road segments at a signalized intersection. When the traffic light is permissive, the flow density and velocity are obtained by…
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…
While macroscopic traffic flow models consider traffic as a fluid, microscopic traffic flow models describe the dynamics of individual vehicles. Capturing macroscopic traffic phenomena remains a challenge for microscopic models, especially…
Hybrid traffic modeling and simulation provide an important way to represent and evaluate large-scale traffic networks at different levels of details. The first level, called "microscopic" allows the description of individual vehicles and…
Monitoring and control of traffic networks represent alternative, inexpensive strategies to minimize traffic congestion. As the number of traffic sensors is naturally constrained by budgetary requirements, real-time estimation of traffic…
In this paper we carry out a computational study of a novel microscopic follow-the-leader model for traffic flow on road networks. We assume that each driver has its own origin and destination, and wants to complete its journey in minimal…
This article proposes a numerical scheme for computing the evolution of vehicular traffic on a road network over a finite time horizon. The traffic dynamics on each link is modeled by the Hamilton-Jacobi (HJ) partial differential equation…
Inthispaper,weintroduceanon-localPDE-ODEtrafficmodeldevotedtothedescriptionof a 1-to-1 junction with buffer. We present an existence result in the free flow case as well as a numerical method to approximate weak solutions in the general…
We propose and study a nonlocal conservation law modelling traffic flow in the existence of inter-vehicle communication. It is assumed that the nonlocal information travels at a finite speed and the model involves a space-time nonlocal…
In this paper we present a numerical study of some variations of the Hughes model for pedestrian flow under different types of congestion effects. The general model consists of a coupled non-linear PDE system involving an eikonal equation…
This paper deals with the Aw-Rascle-Zhang model for traffic flow on uni-directional road networks. For the conservation of the mass and the generalized momentum, we construct weak solutions for Riemann problems at the junctions. We…
We show the existence of the Braess paradox for a traffic network with nonlinear dynamics described by the Lighthill-Whitham-Richards model for traffic flow. Furthermore, we show how one can employ control theory to avoid the paradox. The…
We find a further class of exact solutions to the Lighthill Whitham Richards Payne (LWRP) traffic flow equations. As before, using two consecutive Lagrangian transformations, a linearization is achieved. Next, depending on the initial…