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  • Influence
Car-following models: fifty years of linear stability analysis – a mathematical perspective
Abstract A general framework for car-following models is developed and its linear stability properties are analysed. The concepts of uniform flow, platoon stability and string stability areExpand
An analysis of Gipps's car-following model of highway traffic
TLDR
A mathematical analysis of Gipps's (1981) car?following model is performed. Expand
Traffic jams: dynamics and control
TLDR
This introductory paper reviews the current state-of-the-art scientific methods used for modelling, analysing and controlling the dynamics of vehicular traffic. Expand
Bifurcations and multiple traffic jams in a car-following model with reaction-time delay
We investigate an optimal velocity car-following model for n cars on a circular singlelane road, where reaction time delay of drivers is taken into account. The stability of the uniform-∞owExpand
Mechanisms for spatio-temporal pattern formation in highway traffic models
  • R. E. Wilson
  • Computer Science, Biology
  • Philosophical Transactions of the Royal Society A…
  • 13 June 2008
TLDR
This paper will survey the essence of the competing explanations of highway traffic pattern formation and introduce a new mechanism, based on dynamical systems theory and bistability, which can help resolve the conflict. Expand
Reconstructing the Traffic State by Fusion of Heterogeneous Data
TLDR
This paper presents an advanced interpolation method for estimating smooth spatiotemporal profiles for local highway traffic variables such as flow, speed and density. Expand
Real-Time Lagrangian Traffic State Estimator for Freeways
TLDR
We propose a new model-based traffic state estimator based on the EKF technique, in which the discretized Lagrangian Lighthill-Whitham and Richards (LWR) model is used as the process equation, and in which observation models for both Eulerian and LagrangIAN sensor data (from loop detectors and vehicle trajectories, respectively) are incorporated. Expand
Global bifurcation investigation of an optimal velocity traffic model with driver reaction time.
We investigate an optimal velocity model which includes the reflex time of drivers. After an analytical study of the stability and local bifurcations of the steady-state solution, we apply numericalExpand
Analysis of a Reaction-Diffusion System Modeling Man-Environment-Man Epidemics
TLDR
In this paper an old model for the temporal and spatial evolution of orofecal transmitted disease is reexamined. Expand
Proactive empty vehicle redistribution for personal rapid transit and taxis
The empty vehicle redistribution (EVR) problem is to decide when and where to move empty vehicles in a Personal Rapid Transit or taxi system. These decisions are made in real time by an EVRExpand
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